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Question: Same equation but different parameter?

Question:Same equation but different parameter?

salim-barzani 1785 Maple 2021
ode parameters homework differential-equations odetest
July 24 2024
0

Hi

i use other code for equation too when i use allvalues(Root(...)) it is more near but question is this why not satisfy the ode equation this is my equation this parameter are find for this ODe why not satisfy otherwise my equestions must be wrong!

> 

restart
> 

with(PDEtools)
> 

undeclare(prime)

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

 (1)
> 

with(DEtools)
> 

``
> 

with(LinearAlgebra)
> 

with(sumtools)
> 

eq0 := 2*beta*g[1]^3*r[0]^3+2*p^2*sigma*g[1]*r[0]^3 = 0
> 

eq1 := 6*beta*g[1]^3*r[0]^2*r[1]+3*p^2*sigma*g[1]*r[0]^2*r[1]+6*beta*f[0]*g[1]^2*r[0]^2 = 0
> 

eq2 := 6*beta*g[1]^3*r[0]^2*r[2]+6*beta*g[1]^3*r[0]*r[1]^2+2*p^2*sigma*g[1]*r[0]^2*r[2]+p^2*sigma*g[1]*r[0]*r[1]^2+12*beta*f[0]*g[1]^2*r[0]*r[1]+6*beta*f[1]*g[1]^2*r[0]^2+6*beta*f[0]^2*g[1]*r[0]-k^2*sigma*g[1]*r[0]-2*w*g[1]*r[0] = 0
> 

eq3 := 12*beta*g[1]^3*r[0]*r[1]*r[2]+2*beta*g[1]^3*r[1]^3+2*p^2*sigma*g[1]*r[0]*r[1]*r[2]+12*beta*f[0]*g[1]^2*r[0]*r[2]+6*beta*f[0]*g[1]^2*r[1]^2+12*beta*f[1]*g[1]^2*r[0]*r[1]+p^2*sigma*f[1]*r[0]*r[1]+6*beta*f[0]^2*g[1]*r[1]+12*beta*f[0]*f[1]*g[1]*r[0]-k^2*sigma*g[1]*r[1]+2*beta*f[0]^3-k^2*sigma*f[0]-2*w*g[1]*r[1]-2*w*f[0] = 0
> 

eq4 := 6*beta*g[1]^3*r[0]*r[2]^2+6*beta*g[1]^3*r[1]^2*r[2]+2*p^2*sigma*g[1]*r[0]*r[2]^2+p^2*sigma*g[1]*r[1]^2*r[2]+12*beta*f[0]*g[1]^2*r[1]*r[2]+12*beta*f[1]*g[1]^2*r[0]*r[2]+6*beta*f[1]*g[1]^2*r[1]^2+2*p^2*sigma*f[1]*r[0]*r[2]+p^2*sigma*f[1]*r[1]^2+6*beta*f[0]^2*g[1]*r[2]+12*beta*f[0]*f[1]*g[1]*r[1]+6*beta*f[1]^2*g[1]*r[0]-k^2*sigma*g[1]*r[2]+6*beta*f[0]^2*f[1]-k^2*sigma*f[1]-2*w*g[1]*r[2]-2*w*f[1] = 0
> 

eq5 := 6*beta*g[1]^3*r[1]*r[2]^2+3*p^2*sigma*g[1]*r[1]*r[2]^2+6*beta*f[0]*g[1]^2*r[2]^2+12*beta*f[1]*g[1]^2*r[1]*r[2]+3*p^2*sigma*f[1]*r[1]*r[2]+12*beta*f[0]*f[1]*g[1]*r[2]+6*beta*f[1]^2*g[1]*r[1]+6*beta*f[0]*f[1]^2 = 0
> 

eq6 := 2*beta*g[1]^3*r[2]^3+2*p^2*sigma*g[1]*r[2]^3+6*beta*f[1]*g[1]^2*r[2]^2+2*p^2*sigma*f[1]*r[2]^2+6*beta*f[1]^2*g[1]*r[2]+2*beta*f[1]^3 = 0
> 

NULL
> 

NULL
> 

COEFFS := solve({eq0, eq1, eq2, eq3, eq4, eq5, eq6}, {p, f[0], f[1], g[1]}, explicit)
> 

NULL
> 

ode := 2*beta*U(xi)^3+(-k^2*sigma-2*w)*U(xi)+(diff(diff(U(xi), xi), xi))*p^2*sigma = 0

2*beta*U(xi)^3+(-k^2*sigma-2*w)*U(xi)+(diff(diff(U(xi), xi), xi))*p^2*sigma = 0

 (2)
> 

P := f[0]+sum(f[i]*R(xi)^i, i = 1 .. 1)+sum(g[i]*((diff(R(xi), xi))/R(xi))^i, i = 1 .. 1)

f[0]+f[1]*R(xi)+g[1]*(diff(R(xi), xi))/R(xi)

 (3)
> 

case1 := {p = -sqrt(2)*sqrt(sigma*(4*r[0]*r[2]-r[1]^2)*(k^2*sigma+2*w))/(sigma*(4*r[0]*r[2]-r[1]^2)), f[0] = -(k^2*sigma+2*w)*r[1]/sqrt(-2*beta*(4*r[0]*r[2]-r[1]^2)*(k^2*sigma+2*w)), f[1] = -(2*(k^2*sigma+2*w))*r[2]/sqrt(-2*beta*(4*r[0]*r[2]-r[1]^2)*(k^2*sigma+2*w)), g[1] = -sqrt(-2*beta*(4*r[0]*r[2]-r[1]^2)*(k^2*sigma+2*w))/(beta*(4*r[0]*r[2]-r[1]^2))}

{p = -2^(1/2)*(sigma*(4*r[0]*r[2]-r[1]^2)*(k^2*sigma+2*w))^(1/2)/(sigma*(4*r[0]*r[2]-r[1]^2)), f[0] = -(k^2*sigma+2*w)*r[1]/(-2*beta*(4*r[0]*r[2]-r[1]^2)*(k^2*sigma+2*w))^(1/2), f[1] = -2*(k^2*sigma+2*w)*r[2]/(-2*beta*(4*r[0]*r[2]-r[1]^2)*(k^2*sigma+2*w))^(1/2), g[1] = -(-2*beta*(4*r[0]*r[2]-r[1]^2)*(k^2*sigma+2*w))^(1/2)/(beta*(4*r[0]*r[2]-r[1]^2))}

 (4)
> 

NULL

``

 (5)
> 

K := diff(R(xi), xi) = r[0]+r[1]*R(xi)+r[2]*R(xi)^2

diff(R(xi), xi) = r[0]+r[1]*R(xi)+r[2]*R(xi)^2

 (6)
> 

S1 := subs(K, P)

f[0]+f[1]*R(xi)+g[1]*(r[0]+r[1]*R(xi)+r[2]*R(xi)^2)/R(xi)

 (7)

NULL

> 

C1 := subs(case1, S1)

-(k^2*sigma+2*w)*r[1]/(-2*beta*(4*r[0]*r[2]-r[1]^2)*(k^2*sigma+2*w))^(1/2)-2*(k^2*sigma+2*w)*r[2]*R(xi)/(-2*beta*(4*r[0]*r[2]-r[1]^2)*(k^2*sigma+2*w))^(1/2)-(-2*beta*(4*r[0]*r[2]-r[1]^2)*(k^2*sigma+2*w))^(1/2)*(r[0]+r[1]*R(xi)+r[2]*R(xi)^2)/(beta*(4*r[0]*r[2]-r[1]^2)*R(xi))

 (8)
> 

f := U(xi) = C1

U(xi) = -(k^2*sigma+2*w)*r[1]/(-2*beta*(4*r[0]*r[2]-r[1]^2)*(k^2*sigma+2*w))^(1/2)-2*(k^2*sigma+2*w)*r[2]*R(xi)/(-2*beta*(4*r[0]*r[2]-r[1]^2)*(k^2*sigma+2*w))^(1/2)-(-2*beta*(4*r[0]*r[2]-r[1]^2)*(k^2*sigma+2*w))^(1/2)*(r[0]+r[1]*R(xi)+r[2]*R(xi)^2)/(beta*(4*r[0]*r[2]-r[1]^2)*R(xi))

 (9)

NULL

> 

SO := subs(case1, ode)

2*beta*U(xi)^3+(-k^2*sigma-2*w)*U(xi)+2*(diff(diff(U(xi), xi), xi))*(k^2*sigma+2*w)/(4*r[0]*r[2]-r[1]^2) = 0

 (10)

NULL

> 

odetest(f, SO)


same_equation_different_parameter.mw
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