bashar27

i can not find out the prbl of solve...

Asked: bashar27 55 Product: Maple 18

August 06 2021

2 0

solve({-mu*a[1]+2*c[2]*a[1]*a[2]^2-a[1]*k^2*c[1]+2*c[2]*a[1]*a[0]^2+5*c[4]*a[0]^4*a[1]+5*c[4]*a[1]*a[2]^4+3*c[3]*a[1]*a[2]^2+3*c[3]*a[0]^2*a[1]+a[1]*c[1]+30*c[4]*a[0]^2*a[1]*a[2]^2-20*c[4]*a[1]*a[2]*a[0]^3-4*c[2]*a[1]*a[0]*a[2]-8*c[2]*a[1]^3*A*B+24*c[1]*a[1]*A*B-6*c[3]*a[0]*a[1]*a[2]-20*c[4]*a[0]*a[1]*a[2]^3+48*c[2]*a[1]*a[0]^2*A*B+176*c[2]*a[1]*a[2]^2*A*B-224*c[2]*a[1]*A*B*a[0]*a[2] = 0, -16*c[2]*a[1]^3-6*mu*a[1]+156*c[2]*a[1]*a[2]^2-6*a[1]*k^2*c[1]-20*c[2]*a[1]*a[0]^2+30*c[4]*a[0]^4*a[1]-20*c[4]*a[1]^3*a[2]^2+30*c[4]*a[1]*a[2]^4-6*c[3]*a[1]*a[2]^2+18*c[3]*a[0]^2*a[1]+20*c[4]*a[0]^2*a[1]^3+c[4]*a[1]^5+2*a[1]^3*c[3]-10*a[1]*c[1]-60*c[4]*a[0]^2*a[1]*a[2]^2-24*c[2]*a[1]^3*A*B+8*c[1]*a[1]*A*B+16*c[2]*a[1]*a[0]^2*A*B+336*c[2]*a[1]*a[2]^2*A*B+352*c[2]*a[1]*A*B*a[0]*a[2] = 0, -32*c[2]*a[2]*a[0]^2*A*B-8*c[2]*a[1]^2*a[0]*A*B+64*c[2]*a[2]^2*a[0]*A*B+8*c[2]*a[1]^2*a[2]*A*B-5*c[4]*a[0]^4*a[2]+10*c[4]*a[0]^3*a[2]^2-10*c[4]*a[0]^2*a[2]^3+5*c[4]*a[0]*a[2]^4-a[0]*k^2*c[1]+a[2]*k^2*c[1]-3*c[3]*a[0]^2*a[2]+3*c[3]*a[0]*a[2]^2-32*c[2]*a[2]^3*A*B-16*c[1]*a[2]*A*B+c[4]*a[0]^5-c[4]*a[2]^5+c[3]*a[0]^3-c[3]*a[2]^3-a[0]*mu+a[2]*mu = 0, 4*c[2]*a[1]^3-4*mu*a[1]-64*c[2]*a[1]*a[2]^2-4*a[1]*k^2*c[1]-8*c[2]*a[1]*a[0]^2+20*c[4]*a[0]^4*a[1]+10*c[4]*a[1]^3*a[2]^2-20*c[4]*a[1]*a[2]^4+12*c[3]*a[0]^2*a[1]+10*c[4]*a[0]^2*a[1]^3+a[1]^3*c[3]-4*a[1]*c[1]+40*c[4]*a[1]*a[2]*a[0]^3-72*c[2]*a[1]*a[0]*a[2]-8*c[1]*a[1]*A*B+12*c[3]*a[0]*a[1]*a[2]+20*c[4]*a[0]*a[1]^3*a[2]-40*c[4]*a[0]*a[1]*a[2]^3-16*c[2]*a[1]*a[0]^2*A*B-16*c[2]*a[1]*a[2]^2*A*B-32*c[2]*a[1]*A*B*a[0]*a[2] = 0, 4*c[2]*a[1]^3-4*mu*a[1]-64*c[2]*a[1]*a[2]^2-4*a[1]*k^2*c[1]-8*c[2]*a[1]*a[0]^2+20*c[4]*a[0]^4*a[1]+10*c[4]*a[1]^3*a[2]^2-20*c[4]*a[1]*a[2]^4+12*c[3]*a[0]^2*a[1]+10*c[4]*a[0]^2*a[1]^3+a[1]^3*c[3]-4*a[1]*c[1]-40*c[4]*a[1]*a[2]*a[0]^3+72*c[2]*a[1]*a[0]*a[2]+64*c[2]*a[1]^3*A*B+40*c[1]*a[1]*A*B-12*c[3]*a[0]*a[1]*a[2]-20*c[4]*a[0]*a[1]^3*a[2]+40*c[4]*a[0]*a[1]*a[2]^3+80*c[2]*a[1]*a[0]^2*A*B-624*c[2]*a[1]*a[2]^2*A*B+160*c[2]*a[1]*A*B*a[0]*a[2] = 0, 3*c[3]*a[0]*a[2]^2+6*c[2]*a[1]^2*a[0]-32*c[2]*a[2]^2*a[0]-5*a[0]*k^2*c[1]+10*c[4]*a[0]^3*a[2]^2-6*c[2]*a[1]^2*a[2]-15*c[4]*a[0]^4*a[2]-15*c[4]*a[0]*a[2]^4+10*c[4]*a[0]^2*a[2]^3+3*a[2]*k^2*c[1]-9*c[3]*a[0]^2*a[2]+16*c[2]*a[2]*a[0]^2-5*a[0]*mu+3*a[2]*mu-30*c[4]*a[0]^2*a[1]^2*a[2]+30*c[4]*a[0]*a[1]^2*a[2]^2+288*c[2]*a[2]^3*A*B+16*c[1]*a[2]*A*B+32*c[2]*a[2]*a[0]^2*A*B+104*c[2]*a[1]^2*a[0]*A*B-320*c[2]*a[2]^2*a[0]*A*B-216*c[2]*a[1]^2*a[2]*A*B+5*c[4]*a[0]^5+5*c[4]*a[2]^5+5*c[3]*a[0]^3+c[3]*a[2]^3-3*c[3]*a[1]^2*a[2]-10*c[4]*a[1]^2*a[2]^3+3*c[3]*a[0]*a[1]^2+10*c[4]*a[0]^3*a[1]^2+16*c[2]*a[2]^3+8*c[1]*a[2] = 0, -6*c[3]*a[0]*a[2]^2-22*c[2]*a[1]^2*a[0]+64*c[2]*a[2]^2*a[0]-10*a[0]*k^2*c[1]-20*c[4]*a[0]^3*a[2]^2-66*c[2]*a[1]^2*a[2]+10*c[4]*a[0]^4*a[2]+10*c[4]*a[0]*a[2]^4-20*c[4]*a[0]^2*a[2]^3-2*a[2]*k^2*c[1]+6*c[3]*a[0]^2*a[2]-16*c[2]*a[2]*a[0]^2-10*a[0]*mu-2*a[2]*mu+30*c[4]*a[0]^2*a[1]^2*a[2]-30*c[4]*a[0]*a[1]^2*a[2]^2+96*c[2]*a[2]^3*A*B+48*c[1]*a[2]*A*B+5*c[4]*a[1]^4*a[2]+5*c[4]*a[0]*a[1]^4+96*c[2]*a[2]*a[0]^2*A*B-40*c[2]*a[1]^2*a[0]*A*B+192*c[2]*a[2]^2*a[0]*A*B-40*c[2]*a[1]^2*a[2]*A*B+10*c[4]*a[0]^5+10*c[4]*a[2]^5+10*c[3]*a[0]^3-2*c[3]*a[2]^3+3*c[3]*a[1]^2*a[2]-30*c[4]*a[1]^2*a[2]^3+9*c[3]*a[0]*a[1]^2+30*c[4]*a[0]^3*a[1]^2+80*c[2]*a[2]^3-8*c[1]*a[2] = 0, -6*c[3]*a[0]*a[2]^2-22*c[2]*a[1]^2*a[0]+64*c[2]*a[2]^2*a[0]-10*a[0]*k^2*c[1]-20*c[4]*a[0]^3*a[2]^2+66*c[2]*a[1]^2*a[2]-10*c[4]*a[0]^4*a[2]+10*c[4]*a[0]*a[2]^4+20*c[4]*a[0]^2*a[2]^3+2*a[2]*k^2*c[1]-6*c[3]*a[0]^2*a[2]+16*c[2]*a[2]*a[0]^2-10*a[0]*mu+2*a[2]*mu-30*c[4]*a[0]^2*a[1]^2*a[2]-30*c[4]*a[0]*a[1]^2*a[2]^2-352*c[2]*a[2]^3*A*B+80*c[1]*a[2]*A*B-5*c[4]*a[1]^4*a[2]+5*c[4]*a[0]*a[1]^4+160*c[2]*a[2]*a[0]^2*A*B+72*c[2]*a[1]^2*a[0]*A*B-192*c[2]*a[2]^2*a[0]*A*B+312*c[2]*a[1]^2*a[2]*A*B+10*c[4]*a[0]^5-10*c[4]*a[2]^5+10*c[3]*a[0]^3+2*c[3]*a[2]^3-3*c[3]*a[1]^2*a[2]+30*c[4]*a[1]^2*a[2]^3+9*c[3]*a[0]*a[1]^2+30*c[4]*a[0]^3*a[1]^2-80*c[2]*a[2]^3+8*c[1]*a[2] = 0, a[0]^5*c[4]+5*a[0]^4*a[2]*c[4]+10*a[0]^3*a[2]^2*c[4]+10*a[0]^2*a[2]^3*c[4]+5*a[0]*a[2]^4*c[4]+a[2]^5*c[4]-k^2*a[0]*c[1]-k^2*a[2]*c[1]+a[0]^3*c[3]+3*a[0]^2*a[2]*c[3]+3*a[0]*a[2]^2*c[3]+a[2]^3*c[3]-mu*a[0]-mu*a[2] = 0, 5*a[0]^4*a[1]*c[4]+20*a[0]^3*a[1]*a[2]*c[4]+30*a[0]^2*a[1]*a[2]^2*c[4]+20*a[0]*a[1]*a[2]^3*c[4]+5*a[1]*a[2]^4*c[4]-k^2*a[1]*c[1]+2*a[0]^2*a[1]*c[2]+3*a[0]^2*a[1]*c[3]+4*a[0]*a[1]*a[2]*c[2]+6*a[0]*a[1]*a[2]*c[3]+2*a[1]*a[2]^2*c[2]+3*a[1]*a[2]^2*c[3]-mu*a[1]+a[1]*c[1] = 0, 5*a[0]^5*c[4]+15*a[0]^4*a[2]*c[4]+10*a[0]^3*a[1]^2*c[4]+10*a[0]^3*a[2]^2*c[4]+30*a[0]^2*a[1]^2*a[2]*c[4]-10*a[0]^2*a[2]^3*c[4]+30*a[0]*a[1]^2*a[2]^2*c[4]-15*a[0]*a[2]^4*c[4]+10*a[1]^2*a[2]^3*c[4]-5*a[2]^5*c[4]-5*k^2*a[0]*c[1]-3*k^2*a[2]*c[1]+5*a[0]^3*c[3]-16*a[0]^2*a[2]*c[2]+9*a[0]^2*a[2]*c[3]+6*a[0]*a[1]^2*c[2]+3*a[0]*a[1]^2*c[3]-32*a[0]*a[2]^2*c[2]+3*a[0]*a[2]^2*c[3]+6*a[1]^2*a[2]*c[2]+3*a[1]^2*a[2]*c[3]-16*a[2]^3*c[2]-a[2]^3*c[3]-5*mu*a[0]-3*mu*a[2]-8*a[2]*c[1] = 0}, {B, mu, a[0], a[1], a[2]})

Error, (in collect) cannot collect a^Phi...

Asked: bashar27 55 Product: Maple

March 24 2021

2 0

restart;
T := diff(Phi(xi), xi);
d
---- Phi(xi)
dxi
restart;
T := (p*a^(-Phi(xi))+q+r*a^Phi(xi))/ln(a);
(-Phi(xi)) Phi(xi)
p a + q + r a
------------------------------
ln(a)
u[0] := C[0]+C[1]*a^Phi(xi)+C[2]*a^(2*Phi(xi));
Phi(xi) (2 Phi(xi))
C[0] + C[1] a + C[2] a
u[1] := diff(u[0], xi);
Phi(xi) / d \
C[1] a |---- Phi(xi)| ln(a)
\ dxi /

(2 Phi(xi)) / d \
+ 2 C[2] a |---- Phi(xi)| ln(a)
\ dxi /
d[1] := C[1]*a^Phi(xi)*T*ln(a)+2*C[2]*a^(2*Phi(xi))*T*ln(a);
Phi(xi) / (-Phi(xi)) Phi(xi)\
C[1] a \p a + q + r a /

(2 Phi(xi)) / (-Phi(xi)) Phi(xi)\
+ 2 C[2] a \p a + q + r a /
u[2] := diff(d[1], xi);
Phi(xi) / d \ / (-Phi(xi))
C[1] a |---- Phi(xi)| ln(a) \p a + q
\ dxi /

Phi(xi)\ Phi(xi) /
+ r a / + C[1] a |
\
(-Phi(xi)) / d \
-p a |---- Phi(xi)| ln(a)
\ dxi /

Phi(xi) / d \ \ (2 Phi(xi)) / d
+ r a |---- Phi(xi)| ln(a)| + 4 C[2] a |----
\ dxi / / \ dxi

\ / (-Phi(xi)) Phi(xi)\
Phi(xi)| ln(a) \p a + q + r a / + 2 C[2]
/

(2 Phi(xi)) / (-Phi(xi)) / d \
a |-p a |---- Phi(xi)| ln(a)
\ \ dxi /

Phi(xi) / d \ \
+ r a |---- Phi(xi)| ln(a)|
\ dxi / /
d[2] := C[1]*a^Phi(xi)*T*ln(a)*(p*a^(-Phi(xi))+q+r*a^Phi(xi))+C[1]*a^Phi(xi)*(-p*a^(-Phi(xi))*T*ln(a)+r*a^Phi(xi)*T*ln(a))+4*C[2]*a^(2*Phi(xi))*T*ln(a)*(p*a^(-Phi(xi))+q+r*a^Phi(xi))+2*C[2]*a^(2*Phi(xi))*(-p*a^(-Phi(xi))*T*ln(a)+r*a^Phi(xi)*T*ln(a));
2
Phi(xi) / (-Phi(xi)) Phi(xi)\ Phi(xi) /
C[1] a \p a + q + r a / + C[1] a \
(-Phi(xi)) / (-Phi(xi)) Phi(xi)\
-p a \p a + q + r a /

Phi(xi) / (-Phi(xi)) Phi(xi)\\
+ r a \p a + q + r a //

2
(2 Phi(xi)) / (-Phi(xi)) Phi(xi)\
+ 4 C[2] a \p a + q + r a / + 2 C[

(2 Phi(xi)) /
2] a \
(-Phi(xi)) / (-Phi(xi)) Phi(xi)\
-p a \p a + q + r a /

Phi(xi) / (-Phi(xi)) Phi(xi)\\
+ r a \p a + q + r a //
expand((2*k*k)*w*beta*d[2]-(2*alpha*k*k)*d[1]-2*w*u[0]+k*u[0]*u[0]);
2 Phi(xi)
-2 alpha k C[1] p + 2 k C[0] C[1] a

2 3
/ Phi(xi)\ / Phi(xi)\
+ 2 k C[0] C[2] \a / + 2 k C[1] \a / C[2]

2 Phi(xi)
- 2 w C[0] + k C[0] - 2 w C[1] a

2 2
/ Phi(xi)\ 2 / Phi(xi)\
- 2 w C[2] \a / + k C[1] \a /

4
2 / Phi(xi)\ 2 Phi(xi)
+ k C[2] \a / + 4 k w beta C[1] a p r

2
2 / Phi(xi)\
+ 6 k w beta C[1] \a / q r

2 Phi(xi)
+ 12 k w beta C[2] a p q

2
2 / Phi(xi)\
+ 16 k w beta C[2] \a / p r

3
2 / Phi(xi)\ 2 2
+ 20 k w beta C[2] \a / q r + 4 k w beta C[2] p

2
2 Phi(xi) 2 / Phi(xi)\
- 2 alpha k C[1] a q - 2 alpha k C[1] \a / r

2
2 Phi(xi) 2 / Phi(xi)\
- 4 alpha k C[2] a p - 4 alpha k C[2] \a / q

3
2 / Phi(xi)\ 2
- 4 alpha k C[2] \a / r + 2 k w beta C[1] p q

2 Phi(xi) 2
+ 2 k w beta C[1] a q

3
2 / Phi(xi)\ 2
+ 4 k w beta C[1] \a / r

2
2 / Phi(xi)\ 2
+ 8 k w beta C[2] \a / q

4
2 / Phi(xi)\ 2
+ 12 k w beta C[2] \a / r
value(%);
2 Phi(xi)
-2 alpha k C[1] p + 2 k C[0] C[1] a

2 3
/ Phi(xi)\ / Phi(xi)\
+ 2 k C[0] C[2] \a / + 2 k C[1] \a / C[2]

2 Phi(xi)
- 2 w C[0] + k C[0] - 2 w C[1] a

2 2
/ Phi(xi)\ 2 / Phi(xi)\
- 2 w C[2] \a / + k C[1] \a /

4
2 / Phi(xi)\ 2 Phi(xi)
+ k C[2] \a / + 4 k w beta C[1] a p r

2
2 / Phi(xi)\
+ 6 k w beta C[1] \a / q r

2 Phi(xi)
+ 12 k w beta C[2] a p q

2
2 / Phi(xi)\
+ 16 k w beta C[2] \a / p r

3
2 / Phi(xi)\ 2 2
+ 20 k w beta C[2] \a / q r + 4 k w beta C[2] p

2
2 Phi(xi) 2 / Phi(xi)\
- 2 alpha k C[1] a q - 2 alpha k C[1] \a / r

2
2 Phi(xi) 2 / Phi(xi)\
- 4 alpha k C[2] a p - 4 alpha k C[2] \a / q

3
2 / Phi(xi)\ 2
- 4 alpha k C[2] \a / r + 2 k w beta C[1] p q

2 Phi(xi) 2
+ 2 k w beta C[1] a q

3
2 / Phi(xi)\ 2
+ 4 k w beta C[1] \a / r

2
2 / Phi(xi)\ 2
+ 8 k w beta C[2] \a / q

4
2 / Phi(xi)\ 2
+ 12 k w beta C[2] \a / r
simplify(%);
2 Phi(xi)
-2 alpha k C[1] p + 2 k C[0] C[1] a

(2 Phi(xi)) (3 Phi(xi))
+ 2 k C[0] C[2] a + 2 k C[1] a C[2]

(2 Phi(xi)) 2 (2 Phi(xi))
- 2 w C[2] a + k C[1] a

2 (4 Phi(xi)) 2 (2 Phi(xi))
+ k C[2] a - 2 alpha k C[1] a r

2 (2 Phi(xi))
- 4 alpha k C[2] a q

2 (3 Phi(xi)) 2
- 4 alpha k C[2] a r - 2 w C[0] + k C[0]

Phi(xi) 2 (2 Phi(xi))
- 2 w C[1] a + 6 k w beta C[1] a q r

2 (2 Phi(xi))
+ 16 k w beta C[2] a p r

2 (3 Phi(xi))
+ 20 k w beta C[2] a q r

2 Phi(xi)
+ 4 k w beta C[1] a p r

2 Phi(xi) 2 2
+ 12 k w beta C[2] a p q + 4 k w beta C[2] p

2 Phi(xi) 2 Phi(xi)
- 2 alpha k C[1] a q - 4 alpha k C[2] a p

2 (3 Phi(xi)) 2
+ 4 k w beta C[1] a r

2 (2 Phi(xi)) 2
+ 8 k w beta C[2] a q

2 (4 Phi(xi)) 2 2
+ 12 k w beta C[2] a r + 2 k w beta C[1] p q

2 Phi(xi) 2
+ 2 k w beta C[1] a q
collect(%, a^Phi(xi));
Error, (in collect) cannot collect a^Phi(xi)

fix the problem to solve polynomial...

Asked: bashar27 55 Product: Maple 18

April 22 2020

0 2

restart;
solve({l*(2*l^2*lambda^4*sigma*w*a[2]+l^2*lambda^2*mu*w*b[1]+6*l*lambda^2*m*sigma*a[0]^2-6*l*lambda^2*m*b[1]^2+6*l*m*mu^2*a[0]^2-l*lambda^2*rho*sigma*a[0]-l*mu^2*rho*a[0]+4*lambda^2*sigma*w*a[0]+4*mu^2*w*a[0]) = 0, l*(2*l^2*lambda^3*sigma*w*a[1]+6*l^2*lambda^2*mu*w*b[2]+2*l^2*lambda*mu^2*w*a[1]+12*l*lambda^2*m*sigma*a[0]*a[1]-12*l*lambda^2*m*b[1]*b[2]-l*lambda^2*rho*sigma*a[1]+12*l*m*mu^2*a[0]*a[1]-l*mu^2*rho*a[1]+4*lambda^2*sigma*w*a[1]+4*mu^2*w*a[1]) = 0, l*(5*l^2*lambda^3*sigma*w*b[2]-3*l^2*lambda^2*mu*sigma*w*a[1]-7*l^2*lambda*mu^2*w*b[2]-3*l^2*mu^3*w*a[1]+12*l*lambda^2*m*sigma*a[0]*b[2]+12*l*lambda^2*m*sigma*a[1]*b[1]-l*lambda^2*rho*sigma*b[2]+24*l*lambda*m*mu*b[1]*b[2]+12*l*m*mu^2*a[0]*b[2]+12*l*m*mu^2*a[1]*b[1]-l*mu^2*rho*b[2]+4*lambda^2*sigma*w*b[2]+4*mu^2*w*b[2]) = 0, l*(8*l^2*lambda^3*sigma*w*a[2]+6*l^2*lambda*mu^2*w*a[2]+12*l*lambda^2*m*sigma*a[0]*a[2]+6*l*lambda^2*m*sigma*a[1]^2+l^2*lambda*mu*w*b[1]-6*l*lambda^2*m*b[2]^2-l*lambda^2*rho*sigma*a[2]+12*l*m*mu^2*a[0]*a[2]+6*l*m*mu^2*a[1]^2-6*l*lambda*m*b[1]^2-l*mu^2*rho*a[2]+4*lambda^2*sigma*w*a[2]+4*mu^2*w*a[2]) = 0, -l*(4*l^2*lambda^3*mu*sigma*w*a[2]-l^2*lambda^3*sigma*w*b[1]+l^2*lambda*mu^2*w*b[1]-12*l*lambda^2*m*sigma*a[0]*b[1]+l*lambda^2*rho*sigma*b[1]-12*l*lambda*m*mu*b[1]^2-12*l*m*mu^2*a[0]*b[1]+l*mu^2*rho*b[1]-4*lambda^2*sigma*w*b[1]-4*mu^2*w*b[1]) = 0, 6*l^2*(l*lambda^2*sigma*w*a[2]+lambda^2*m*sigma*a[2]^2+l*mu^2*w*a[2]+m*mu^2*a[2]^2-lambda*m*b[2]^2) = 0, 2*l^2*(l*lambda^2*sigma*w*a[1]+6*lambda^2*m*sigma*a[1]*a[2]+3*l*lambda*mu*w*b[2]+l*mu^2*w*a[1]+6*m*mu^2*a[1]*a[2]-6*lambda*m*b[1]*b[2]) = 0, -2*l^2*(5*l*lambda^2*mu*sigma*w*a[2]-l*lambda^2*sigma*w*b[1]+5*l*mu^3*w*a[2]-6*lambda^2*m*sigma*a[1]*b[2]-6*lambda^2*m*sigma*a[2]*b[1]-l*mu^2*w*b[1]-6*lambda*m*mu*b[2]^2-6*m*mu^2*a[1]*b[2]-6*m*mu^2*a[2]*b[1]) = 0, 6*l^2*b[2]*(l*w+2*m*a[2]) = 0}, {a[0], a[1], a[2], b[1], b[2]});
Warning, solutions may have been lost
{a[0] = 0, a[1] = 0, a[2] = 0, b[1] = 0, b[2] = 0},

/ l rho - 4 w \
{ a[0] = -----------, a[1] = 0, a[2] = 0, b[1] = 0, b[2] = 0 }
\ 6 l m /

combining contour 2d and 3d plot for fol...

Asked: bashar27 55 Product: Maple 18

November 19 2019

3 0

;

= 2*1/10);
1
-
5
= -1;
-1

= 10;
10
= -25;
-25

C= 1;
1

= (1/12*sqrt6/sqrtbeta*lambda*mu);
1 (1/2) (1/2)
--- I 6 2
24
= alpha/((10*sqrt-lambda*mu)*beta);
1 (1/2)
- - 5
4
A0]= (1/2*alpha/((10*sqrt-lambda*mu)*(1/12*beta*sqrt6/sqrtbeta*lambda*mu)));
1 (1/2) (1/2) (1/2)
-- I 5 6 2
4
A1]= -(1/10*alpha/((1/12*beta*mu*sqrt6/sqrtbeta*lambda*mu));
1 (1/2) (1/2)
-- I 6 2
2
A[2] := -(12*((112)*sqrt(6)/sqrt(beta*lambda*mu)))*lambda^2*alpha/(10*sqrt(-lambda*mu));
1 (1/2) (1/2) (1/2)
--- I 6 2 5
20
H := ln(sqrt(lambda/(-mu))*tanh(sqrt(-lambda*mu)*(xi+C)));
/1/2) /1 (1/2 \\
ln|- 5 tanh|- 5 ( 1)||
\5 \5 //
xi := k*x-t*w;
1 (1/2) (1/2) 1 (1/2)
--- I 6 2 x + t
      2       4
u[0] := A[0]+A[1]*exp(-H)+A[2]*exp(-H)*exp(-H);
1 (1/2) (1/2) (1/2)
-- I 5 6 2
4

1 (1/2) (1/2) (1/2)
- I 6 2 5
2
- -------------------------------------------------------
(1/2) / 1 (1/2) (1/2) 1 (1/2) \\
tanh|- 5 |--- I 6 2 x + - t 5 + 1||
\5 \ 24 4 //

1 (1/2) (1/2) (1/2)
- I 6 2 5
4
- --------------------------------------------------------
2
  (1/2) / 1 (1/2) (1/2) 1 (1/2) \\
tanh|- 5 |--- I 6 2 x + - t 5 + 1||
    \ 24 4 //

plot3d(Im(u[0]), x = -10 .. 10, t = -10 .. 10);

solve set satisfy problem...

Asked: bashar27 55 Product: Maple 18

October 06 2019

2 1

restart;
P := -lambda*exp(-Phi(xi))-mu*exp(Phi(xi));
-lambda exp(-Phi(xi)) - mu exp(Phi(xi))
u[0] := A[0]+A[1]*exp(-Phi(xi))+A[2]*exp(-Phi(xi))*exp(-Phi(xi));
2
A[0] + A[1] exp(-Phi(xi)) + A[2] (exp(-Phi(xi)))
u[1] := diff(u[0], xi);
/ d \
-A[1] |---- Phi(xi)| exp(-Phi(xi))
\ dxi /

2 / d \
- 2 A[2] (exp(-Phi(xi))) |---- Phi(xi)|
\ dxi /
d[1] := -A[1]*P*exp(-Phi(xi))-2*A[2]*(exp(-Phi(xi)))^2*P;
-A[1] (-lambda exp(-Phi(xi)) - mu exp(Phi(xi))) exp(-Phi(xi)) - 2

2
A[2] (exp(-Phi(xi))) (-lambda exp(-Phi(xi)) - mu exp(Phi(xi)))
u[2] := diff(d[1], xi);
/ / d \
-A[1] |lambda |---- Phi(xi)| exp(-Phi(xi))
\ \ dxi /

2
xi)) + 4 A[2] (exp(-Phi(xi))) (-lambda exp(-Phi(xi))

/ d \ 2
- mu exp(Phi(xi))) |---- Phi(xi)| - 2 A[2] (exp(-Phi(xi)))
\ dxi /

/ / d \
|lambda |---- Phi(xi)| exp(-Phi(xi))
\ \ dxi /

/ d \ \
- mu |---- Phi(xi)| exp(Phi(xi))|
\ dxi / /

d[2] := -A[1]*(lambda*P*exp(-Phi(xi))-mu*P*exp(Phi(xi)))*exp(-Phi(xi))+A[1]*(-lambda*exp(-Phi(xi))-mu*exp(Phi(xi)))*P*exp(-Phi(xi))+4*A[2]*(exp(-Phi(xi)))^2*(-lambda*exp(-Phi(xi))-mu*exp(Phi(xi)))*P-2*A[2]*(exp(-Phi(xi)))^2*(lambda*P*exp(-Phi(xi))-mu*P*exp(Phi(xi)));
-A[1] (lambda (-lambda exp(-Phi(xi)) - mu exp(Phi(xi))) exp(-Phi(

xi))

- mu (-lambda exp(-Phi(xi)) - mu exp(Phi(xi))) exp(Phi(xi)))

exp(-Phi(xi))

2
+ A[1] (-lambda exp(-Phi(xi)) - mu exp(Phi(xi))) exp(-Phi(xi)) + 4

2
A[2] (exp(-Phi(xi)))

2
(-lambda exp(-Phi(xi)) - mu exp(Phi(xi))) - 2 A[2]

2
(exp(-Phi(xi))) (lambda (-lambda exp(-Phi(xi))

- mu exp(Phi(xi))) exp(-Phi(xi))

- mu (-lambda exp(-Phi(xi)) - mu exp(Phi(xi))) exp(Phi(xi)))

collect(expand((2*k*k)*w*beta*d[2]-(2*alpha*k*k)*d[1]-2*w*u[0]+k*u[0]*u[0]), exp(Phi(xi)));
2 2 2 2
4 k w beta A[2] mu - 2 alpha k A[1] mu + k A[0] - 2 w A[0] +

1 / 2 2
------------ \4 beta k lambda mu w A[1] - 4 alpha k mu A[2]
exp(Phi(xi))

\ 1 / 2
+ 2 k A[0] A[1] - 2 w A[1]/ + --------------- \16 beta k
2
(exp(Phi(xi)))

2
lambda mu w A[2] - 2 alpha k lambda A[1] + 2 k A[0] A[2]

2 \ 1 / 2 2
+ k A[1] - 2 w A[2]/ + --------------- \4 beta k lambda w A
3
(exp(Phi(xi)))

2 \
[1] - 4 alpha k lambda A[2] + 2 k A[1] A[2]/

2 2 2
12 beta k lambda w A[2] + k A[2]
+ -----------------------------------
4
(exp(Phi(xi)))

restart;
solve({12*beta*k^2*lambda^2*w*A[2]+k*A[2]^2, 4*beta*k^2*lambda^2*w*A[1]-4*alpha*k^2*lambda*A[2]+2*k*A[1]*A[2], 4*beta*k^2*mu^2*w*A[2]-2*alpha*k^2*mu*A[1]+k*A[0]^2-2*w*A[0], 4*beta*k^2*lambda*mu*w*A[1]-4*alpha*k^2*mu*A[2]+2*k*A[0]*A[1]-2*w*A[1], 16*beta*k^2*lambda*mu*w*A[2]-2*alpha*k^2*lambda*A[1]+2*k*A[0]*A[2]+k*A[1]^2-2*w*A[2]}, {k, w, A[0], A[1], A[2]});
{k = 0, w = 0, A[0] = A[0], A[1] = A[1], A[2] = A[2]},

{k = k, w = w, A[0] = 0, A[1] = 0, A[2] = 0},

/
/ 2 w \ |
{ k = k, w = w, A[0] = ---, A[1] = 0, A[2] = 0 }, <
\ k / |
\

/ 2 \
k = RootOf\24 beta lambda mu _Z - 1/,

/ 2 \
RootOf\100 lambda mu _Z + 1/ alpha
w = -----------------------------------,
beta

/ 2 \
RootOf\100 lambda mu _Z + 1/ alpha
A[0] = ----------------------------------------,
/ 2 \
2 beta RootOf\24 beta lambda mu _Z - 1/

alpha
A[1] = --------------------------------------------, A[2] = -12
/ 2 \
10 beta mu RootOf\24 beta lambda mu _Z - 1/

/ 2 \ 2 /
RootOf\24 beta lambda mu _Z - 1/ lambda RootOf\100 lambda mu

\ /
2 \ | | / 2 \
_Z + 1/ alpha >, < k = RootOf\24 beta lambda mu _Z + 1/,
| |
/ \

/ 2 \
RootOf\100 lambda mu _Z + 1/ alpha
w = -----------------------------------,
beta

/ 2 \
3 RootOf\100 lambda mu _Z + 1/ alpha
A[0] = ----------------------------------------,
/ 2 \
2 beta RootOf\24 beta lambda mu _Z + 1/

alpha
A[1] = - --------------------------------------------, A[2] = -
/ 2 \
10 beta mu RootOf\24 beta lambda mu _Z + 1/

/ 2 \ 2 /
12 RootOf\24 beta lambda mu _Z + 1/ lambda RootOf\100 lambda

\
2 \ |
mu _Z + 1/ alpha >
|
/
set 1;
Error, missing operation
Typesetting:-mambiguous(Typesetting:-mambiguous(set 1,

Typesetting:-merror("missing operation")))
{k = RootOf(24*_Z^2*beta*lambda*mu-1), w = RootOf(100*_Z^2*lambda*mu+1)*alpha/beta, A[0] = (1/2)*RootOf(100*_Z^2*lambda*mu+1)*alpha/(beta*RootOf(24*_Z^2*beta*lambda*mu-1)), A[1] = (1/10)*alpha/(beta*mu*RootOf(24*_Z^2*beta*lambda*mu-1)), A[2] = -12*RootOf(24*_Z^2*beta*lambda*mu-1)*lambda^2*RootOf(100*_Z^2*lambda*mu+1)*alpha};
/
| / 2 \
< k = RootOf\24 beta lambda mu _Z - 1/,
|
\

/ 2 \
RootOf\100 lambda mu _Z + 1/ alpha
w = -----------------------------------,
beta

/ 2 \
RootOf\100 lambda mu _Z + 1/ alpha
A[0] = ----------------------------------------,
/ 2 \
2 beta RootOf\24 beta lambda mu _Z - 1/

alpha
A[1] = --------------------------------------------, A[2] = -12
/ 2 \
10 beta mu RootOf\24 beta lambda mu _Z - 1/

/ 2 \ 2 /
RootOf\24 beta lambda mu _Z - 1/ lambda RootOf\100 lambda mu

\
2 \ |
_Z + 1/ alpha >
|
/
restart;
restart;
solve({24*Z^2*beta*lambda*mu-1}, {Z});
/ (1/2) \
| 6 |
< Z = ------------------------ >,
| (1/2)|
\ 12 (beta lambda mu) /

/ (1/2) \
| 6 |
< Z = - ------------------------ >
| (1/2)|
\ 12 (beta lambda mu) /
solve({100*Z^2*lambda*mu+1}, {Z});
/ 1 \ / 1 \
|Z = - --------------------| , |Z = --------------------|
< (1/2) > < (1/2) >
| 10 (-lambda mu) | | 10 (-lambda mu) |
\ / \ /
restart;
k := (1/12)*sqrt(6)/sqrt(beta*lambda*mu);
(1/2)
6
------------------------
(1/2)
12 (beta lambda mu)
w := -alpha/((10*sqrt(-lambda*mu))*beta);
alpha
- -------------------------
(1/2)
10 (-lambda mu) beta
A[0] := 1/2*(-alpha/((10*sqrt(-lambda*mu))*((1/12)*beta*sqrt(6)/sqrt(beta*lambda*mu))));
(1/2) (1/2)
alpha 6 (beta lambda mu)
- ----------------------------------
(1/2)
10 (-lambda mu) beta
A[1] := (1/10)*alpha/((1/12)*beta*mu*sqrt(6)/sqrt(beta*lambda*mu));
(1/2) (1/2)
alpha 6 (beta lambda mu)
----------------------------------
5 beta mu
A[2] := (12*(1/12))*sqrt(6)*lambda^2*alpha/(sqrt(beta*lambda*mu)*(10*sqrt(-lambda*mu)));
(1/2) 2
6 lambda alpha
------------------------------------------
(1/2) (1/2)
10 (beta lambda mu) (-lambda mu)
lambda := 3;
3
mu := 2;
2
H := -ln(sqrt(lambda/mu)*tan(sqrt(lambda*mu)*(xi+C)));
/1 (1/2) / (1/2) \\
-ln|- 6 tan\6 (xi + C)/|
\2 /
u[0] := A[0]+A[1]*exp(-H)+A[2]*exp(-H)*exp(-H);
(1/2) (1/2) / (1/2) \
alpha (-6) 3 alpha 6 tan\6 (xi + C)/
--------------- + -----------------------------------
(1/2) (1/2)
10 beta 10 beta

2
(1/2) / (1/2) \
9 alpha (-6) tan\6 (xi + C)/
- ---------------------------------------
(1/2)
40 beta
f := diff(u[0], xi);
/ 2\
| / (1/2) \ | /
9 alpha \1 + tan\6 (xi + C)/ / 1 |
----------------------------------- - ------------ \9 alpha
(1/2) (1/2)
5 beta 20 beta

/ 2\
(1/2) / (1/2) \ | / (1/2) \ |
(-6) tan\6 (xi + C)/ \1 + tan\6 (xi + C)/ /

\
(1/2)|
6 /
S := diff(f, xi);
/ 2\
/ (1/2) \ | / (1/2) \ | (1/2)
18 alpha tan\6 (xi + C)/ \1 + tan\6 (xi + C)/ / 6
----------------------------------------------------------------
(1/2)
5 beta

2
/ 2\
(1/2) | / (1/2) \ |
27 alpha (-6) \1 + tan\6 (xi + C)/ /
- ----------------------------------------------- -
(1/2)
10 beta

/ 2 /
1 | (1/2) / (1/2) \ |
----------- \27 alpha (-6) tan\6 (xi + C)/ \1
(1/2)
5 beta

2\\
/ (1/2) \ ||
+ tan\6 (xi + C)/ //

eq := (2*k*k)*w*beta*S-(2*alpha*k*k)*f-2*w*u[0]+k*u[0]*u[0];
/ /
| |
| |
1 | (1/2) |
--------- |alpha (-6) |
4320 beta | |
\ \

/ 2\
/ (1/2) \ | / (1/2) \ | (1/2)
18 alpha tan\6 (xi + C)/ \1 + tan\6 (xi + C)/ / 6
----------------------------------------------------------------
(1/2)
5 beta

2
/ 2\
(1/2) | / (1/2) \ |
27 alpha (-6) \1 + tan\6 (xi + C)/ /
- ----------------------------------------------- -
(1/2)
10 beta

/ 2 /
1 | (1/2) / (1/2) \ |
----------- \27 alpha (-6) tan\6 (xi + C)/ \1
(1/2)
5 beta

\\
|| / /
2\\|| | |
/ (1/2) \ |||| 1 | |
+ tan\6 (xi + C)/ //|| - ------- |alpha |
|| 72 beta | |
// \ \

/ 2\
| / (1/2) \ | /
9 alpha \1 + tan\6 (xi + C)/ / 1 |
----------------------------------- - ------------ \9 alpha
(1/2) (1/2)
5 beta 20 beta

/ 2\
(1/2) / (1/2) \ | / (1/2) \ |
(-6) tan\6 (xi + C)/ \1 + tan\6 (xi + C)/ /

\\ / /
\|| | | (1/2)
(1/2)||| 1 | (1/2) |alpha (-6)
6 /|| - ------- |alpha (-6) |---------------
|| 30 beta | | (1/2)
// \ \ 10 beta

(1/2) / (1/2) \
3 alpha 6 tan\6 (xi + C)/
+ -----------------------------------
(1/2)
10 beta

2\\ /
(1/2) / (1/2) \ || |
9 alpha (-6) tan\6 (xi + C)/ || 1 |
- ---------------------------------------|| + ------------ |
(1/2) || (1/2) |
40 beta // 12 beta \

/
| (1/2) (1/2) / (1/2) \
|alpha (-6) 3 alpha 6 tan\6 (xi + C)/
|--------------- + -----------------------------------
| (1/2) (1/2)
\ 10 beta 10 beta

2\ \
(1/2) / (1/2) \ | |
9 alpha (-6) tan\6 (xi + C)/ | |
- ---------------------------------------|^2|
(1/2) | |
40 beta / /
value(%);
/ /
| |
| |
1 | (1/2) |
--------- |alpha (-6) |
4320 beta | |
\ \