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Question: When i do substitute in equation two parameter contain each other and again apear in my equation how put all my case in equation? without apearing again

Question:When i do substitute in equation two parameter contain each other and again apear in my equation how put all my case in equation? without apearing again

salim-barzani 1775 Maple 2021
ode substitution differential-equations odetest
September 30 2024
1

how fixed this for ode test

> 

restart
> 

with(PDEtools)
> 

with(Physics)
> 

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

 (1)
> 

``
> 

pde := -I*(diff(U(xi), xi))*gamma*k*mu+I*gamma*(diff(U(xi), xi))*sigma*w+(diff(diff(U(xi), xi), xi))*gamma*k*w+U(xi)*gamma*mu*sigma+(2*I)*(diff(U(xi), xi))*k*sigma+2*alpha*U(xi)^3+(diff(diff(U(xi), xi), xi))*k^2-I*(diff(U(xi), xi))*w-U(xi)*sigma^2-U(xi)*mu

-I*gamma*(diff(U(xi), xi))*k*mu+I*gamma*(diff(U(xi), xi))*sigma*w+gamma*(diff(diff(U(xi), xi), xi))*k*w+gamma*U(xi)*mu*sigma+(2*I)*(diff(U(xi), xi))*k*sigma+2*alpha*U(xi)^3+(diff(diff(U(xi), xi), xi))*k^2-I*(diff(U(xi), xi))*w-U(xi)*sigma^2-U(xi)*mu

 (2)
> 

case1 := [mu = -(4*gamma*k*w+4*k^2-sigma^2)/(gamma*sigma-1), A[0] = 0, A[1] = -RootOf(_Z^2*alpha+gamma*k*w+k^2), B[1] = RootOf(_Z^2*alpha+gamma*k*w+k^2), w = (gamma*k*mu-2*k*sigma)/(gamma*sigma-1)]

[mu = -(4*gamma*k*w+4*k^2-sigma^2)/(gamma*sigma-1), A[0] = 0, A[1] = -RootOf(_Z^2*alpha+gamma*k*w+k^2), B[1] = RootOf(_Z^2*alpha+gamma*k*w+k^2), w = (gamma*k*mu-2*k*sigma)/(gamma*sigma-1)]

 (3)
> 

G1 := U(xi) = 2*RootOf(_Z^2*alpha+gamma*k*w+k^2)/sinh(2*xi)

U(xi) = 2*RootOf(_Z^2*alpha+gamma*k*w+k^2)/sinh(2*xi)

 (4)
> 

pde1 := subs(case1, pde)

I*gamma*(diff(U(xi), xi))*k*(4*gamma*k*w+4*k^2-sigma^2)/(gamma*sigma-1)+I*gamma*(diff(U(xi), xi))*sigma*(gamma*k*mu-2*k*sigma)/(gamma*sigma-1)+gamma*(diff(diff(U(xi), xi), xi))*k*(gamma*k*mu-2*k*sigma)/(gamma*sigma-1)-gamma*U(xi)*(4*gamma*k*w+4*k^2-sigma^2)*sigma/(gamma*sigma-1)+(2*I)*(diff(U(xi), xi))*k*sigma+2*alpha*U(xi)^3+(diff(diff(U(xi), xi), xi))*k^2-I*(diff(U(xi), xi))*(gamma*k*mu-2*k*sigma)/(gamma*sigma-1)-U(xi)*sigma^2+U(xi)*(4*gamma*k*w+4*k^2-sigma^2)/(gamma*sigma-1)

 (5)
> 

pde2 := subs(case1, pde1)

I*gamma*(diff(U(xi), xi))*k*(4*gamma*(gamma*k*mu-2*k*sigma)*k/(gamma*sigma-1)+4*k^2-sigma^2)/(gamma*sigma-1)+I*gamma*(diff(U(xi), xi))*sigma*(-gamma*k*(4*gamma*k*w+4*k^2-sigma^2)/(gamma*sigma-1)-2*k*sigma)/(gamma*sigma-1)+gamma*(diff(diff(U(xi), xi), xi))*k*(-gamma*k*(4*gamma*k*w+4*k^2-sigma^2)/(gamma*sigma-1)-2*k*sigma)/(gamma*sigma-1)-gamma*U(xi)*(4*gamma*(gamma*k*mu-2*k*sigma)*k/(gamma*sigma-1)+4*k^2-sigma^2)*sigma/(gamma*sigma-1)+(2*I)*(diff(U(xi), xi))*k*sigma+2*alpha*U(xi)^3+(diff(diff(U(xi), xi), xi))*k^2-I*(diff(U(xi), xi))*(-gamma*k*(4*gamma*k*w+4*k^2-sigma^2)/(gamma*sigma-1)-2*k*sigma)/(gamma*sigma-1)-U(xi)*sigma^2+U(xi)*(4*gamma*(gamma*k*mu-2*k*sigma)*k/(gamma*sigma-1)+4*k^2-sigma^2)/(gamma*sigma-1)

 (6)
> 

odetest(G1, pde2)
 

NULL

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