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Question: general solution of six order differential equation?

Question:general solution of six order differential equation?

torabi 85 Maple 2016
dsolve
November 27 2016
0

hi every body...

general solution of six order differential equation for example following equation

diff(w(x), x, x, x, x, x, x)+A*(diff(w(x), x, x, x, x))+B*(diff(w(x), x, x))+(-chi*omega^2+C)*w(x) = 0

is 

w := C1*sinh(upsilon*x)+C2*cosh(upsilon*x)+C3*sin(kappa*x)+C4*cos(kappa*x)+C5*sin(varsigma*x)+C6*cos(varsigma*x)

??

OR

w := C1*(cosh(upsilon*x)-sinh(upsilon*x))+C2*(cosh(upsilon*x)+sinh(upsilon*x))+C3*(cosh(kappa*x)-sinh(kappa*x))+C4*(cosh(kappa*x)+sinh(kappa*x))+C5*(cosh(varsigma*x)-sinh(varsigma*x))+C6*(cosh(varsigma*x)+sinh(varsigma*x))

or another form? is correct both of them or no??

please see maple attaced file.

please help me

thanks...

3.mw
 

restart; dsys3 := diff(w(x), x, x, x, x, x, x)+A*(diff(w(x), x, x, x, x))+B*(diff(w(x), x, x))+(-chi*omega^2+C)*w(x) = 0

diff(diff(diff(diff(diff(diff(w(x), x), x), x), x), x), x)+A*(diff(diff(diff(diff(w(x), x), x), x), x))+B*(diff(diff(w(x), x), x))+(-chi*omega^2+C)*w(x) = 0

 (1)

dsol5 := dsolve(dsys3):

H := subs(36*B*A+108*chi*omega^2-108*C-8*A^3+12*sqrt(-12*A^3*chi*omega^2+81*chi^2*omega^4+54*A*B*chi*omega^2+12*A^3*C-3*A^2*B^2-162*C*chi*omega^2-54*A*B*C+12*B^3+81*C^2) = E, (4*I)*A^2*sqrt(3)-I*sqrt(3)*E^(2/3)-(12*I)*B*sqrt(3)-4*A^2-4*A*E^(1/3)-E^(2/3)+12*B = F, (4*I)*A^2*sqrt(3)-I*sqrt(3)*E^(2/3)-(12*I)*B*sqrt(3)+4*A^2+4*A*E^(1/3)+E^(2/3)-12*B = G, 4*A^2-2*A*E^(1/3)+E^(2/3)-12*B = S, rhs(dsol5))

 

_C1*exp(-(1/6)*3^(1/2)*(E^(1/3)*F)^(1/2)*x/E^(1/3))+_C2*exp((1/6)*3^(1/2)*(E^(1/3)*F)^(1/2)*x/E^(1/3))+_C3*exp(-(1/6)*(-3*E^(1/3)*G)^(1/2)*x/E^(1/3))+_C4*exp((1/6)*(-3*E^(1/3)*G)^(1/2)*x/E^(1/3))+_C5*exp(-(1/6)*6^(1/2)*(E^(1/3)*S)^(1/2)*x/E^(1/3))+_C6*exp((1/6)*6^(1/2)*(E^(1/3)*S)^(1/2)*x/E^(1/3))

 (2)

convert(H, trig)

_C1*(cosh((1/6)*3^(1/2)*(E^(1/3)*F)^(1/2)*x/E^(1/3))-sinh((1/6)*3^(1/2)*(E^(1/3)*F)^(1/2)*x/E^(1/3)))+_C2*(cosh((1/6)*3^(1/2)*(E^(1/3)*F)^(1/2)*x/E^(1/3))+sinh((1/6)*3^(1/2)*(E^(1/3)*F)^(1/2)*x/E^(1/3)))+_C3*(cosh((1/6)*(-3*E^(1/3)*G)^(1/2)*x/E^(1/3))-sinh((1/6)*(-3*E^(1/3)*G)^(1/2)*x/E^(1/3)))+_C4*(cosh((1/6)*(-3*E^(1/3)*G)^(1/2)*x/E^(1/3))+sinh((1/6)*(-3*E^(1/3)*G)^(1/2)*x/E^(1/3)))+_C5*(cosh((1/6)*6^(1/2)*(E^(1/3)*S)^(1/2)*x/E^(1/3))-sinh((1/6)*6^(1/2)*(E^(1/3)*S)^(1/2)*x/E^(1/3)))+_C6*(cosh((1/6)*6^(1/2)*(E^(1/3)*S)^(1/2)*x/E^(1/3))+sinh((1/6)*6^(1/2)*(E^(1/3)*S)^(1/2)*x/E^(1/3)))

 (3)

NULL

``


 

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