sigma1:=10^(-5):sigma2:=10^(5):sigma3:=3.7*10^(6):alpha:=5*10^(-7):beta1:=0.5*10^(-4):beta2:=0.5*10^(-4):beta3:=0.5*10^(-4):ky:=1:kz:=10^4:mu1:=10:mu2:=11:mu3:=0.86:mu4:=0.2:mu5:=1:v1:=0.5:v2:=1:alphaa:=0.6:alphas:=0.24:alphad:=0.16:A:=0.5:mus:=0.17:k:=0.2:#parameters 
dsys:={diff(x1(t),t)=sigma1*y(t)-beta1*x1(t)*y(t)/(ky+x1(t)+x2(t))-v1*x1(t)-mu1*x1(t)+(2*alphad+alphaa)*k*A*S(t),diff(x2(t),t)=v1*x1(t)-beta2*x2(t)*y(t)/(ky+x1(t)+x2(t))+alpha*v2*x1(t)*z(t)-mu2*x2(t),diff(y(t),t)=sigma2*(beta1*x1(t)*y(t)/(ky+x1(t)+x2(t))+beta2*x2(t)*y(t)/(ky+x1(t)+x2(t)))-mu4*y(t)-mu5*y(t)^2,diff(z(t),t)=sigma3+y(t)*beta3/(kz+y(t))-mu3*z(t)-v2*z(t)*x2(t),diff(S(t),t)=(k*(alphas-alphad)-mus)*S(t) }; #SYS ODE

rhs; with(DEtools);# to find the equilibrium points
fx1 = sigma1*y-beta1*x1*y-v1*x1-mu1*x1+(2*alphad+alphaa)*k*A*s; fx2 = alpha*v2*x1*z-beta2*x2*y-mu2*x2+v1*x1; fy = sigma2*(beta1*x1*y+beta2*x2*y)-mu4*y-mu5*y^2; fz = sigma3+y*(kz+y)-mu3*z-v2*z*x2; fs = (k*(alphas-alphad)-mus)*s;

eqs := solve({fs, fx1, fx2, fy, fz}, {s, x1, x2, y, z})

L := map(subs, [eqs], [x1, x2, y, z, s])

J := unapply(VectorCalculus:-Jacobian([fx1, fx2, fy, fz, fs], [x1, x2, y, z, s]), x1, x2, y, z, s); J(x1, x2, y, z, s)

hi

I have a linear system with varibles trying to plot 3d the solutions x, y, z

here is my code: linear_var.mw

please any comment might help.

*******************************

restart;

Omega:=10:N:=0.5:M:=sqrt(N(N+1)):

a11:=0.5*(1+2*N)+M*cos(phi):
a12:=-0.5*((1+theta)^3+(1-theta)^3):a13:=-0.5*(N+M*cos(phi))*((1+theta)^3-(1-theta)^3): a21:=M*sin(phi): a22:=(-(1+2*N)+0.5*M*cos(phi))*((1+theta)^3+(1-theta)^3): a23:=-(Omega+0.5*((1+theta)^3-(1-theta)^3)*M*sin(phi)): a31:=0.25*((1+theta)^3-(1-theta)^3): a32:=Omega: a33:=-0.5-(N+0.25)*((1+theta)^3+(1-theta)^3): b1:=-0.5*a31: b2:=0: b3:=0.25+((1+theta)^3+(1-theta)^3)/8:

slove([a11*x+a12*y+a13*z=b1,a21*x+a22*y+a23*z=b2,a31*x+a32*y+a33*z=b3[,[x,y,z]);
Error, unable to match delimiters
Typesetting:-mambiguous(Typesetting:-mambiguous(slovelparlsqba11

  sdotx + a12sdoty + a13sdotzequalsb1commaa21sdotx + a22sdoty + 

  a23sdotzequalsb2commaa31sdotx + a32sdoty + a33sdotzequalsb3lsqb

  comma(xyz)rparsemi, 

  Typesetting:-merror("unable to match delimiters")))

plot3d(x, theta = .1 .. 5, phi = 0 .. 2*Pi, axes = boxed);
plot3d(y, theta = .1 .. 5, phi = 0 .. 2*Pi, axes = boxed); plot3d(z, theta = .1 .. 5, phi = 0 .. 2*Pi, axes = boxed);

I tryning to to plot 3d and then contour plot of the function N vs alpha

This is my try please any comments might help

N_vs_alpha.mw

Hhow can i solve R it says here root of

Calculate.mws

H all expert

first this Expression 

ni := diff(Q(x, t), t)+a*Q*(x, t)*(diff(Q(x, t), x))+b*(diff(Q(x, t), t$3))+d*(diff(Q(x, t), t$5)) = 0

then I want to solve  diff(Q(x, t), t$5) 

diff(Q(x, t), t$5) = solve(ni, diff(Q(x, t), t$5))#eq2

p (x, t) :=H1(t)*Q(x*H2(t), H3(t)) #assumption 

k := diff(p(x, t), t)+a*p(x, t)*(diff(p(x, t), x))+diff(p(x, t), t$3)+d*(diff(p(x, t), t$5))+c*p(x, t) #eq3

r := subs(diff(Q(x, t), t$5), k) #subs eq2 in eq3

i recived error

SUBS1.mw