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Question: another challenging odetest verification

Question:another challenging odetest verification

nm 9934 Maple 2024
ode assuming dsolve simplification differential-equations odetest
September 02 2024
2

Here is another ode solution by Maple, I am not able to get zero from odetest. 

If someone could come up with a trick or method to verify this, that will be great. I tried all sort of assumptions and not able to get zero. Even coulditbe() could not give zero. 

It is a Chini ode and also homogeneous, `class G`.

Solving using either method, odetest do not returns zero.  There are no initial conditions. I am sure the solutions are correct, but odetest need some help or may be this requires different method to verify not using odetest?

Worksheet below.

 

> 

interface(version);

`Standard Worksheet Interface, Maple 2024.1, Windows 10, June 25 2024 Build ID 1835466`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1796 and is the same as the version installed in this computer, created 2024, August 29, 14:22 hours Pacific Time.`

> 

libname;

"C:\Users\Owner\maple\toolbox\2024\Physics Updates\lib", "C:\Program Files\Maple 2024\lib"

> 

restart;
> 

ode:=diff(y(x),x) = a*x^(n/(1-n))+b*y(x)^n;
DEtools:-odeadvisor(ode,y(x));

diff(y(x), x) = a*x^(n/(1-n))+b*y(x)^n

[[_homogeneous, `class G`], _Chini]

> 

maple_sol:=dsolve(ode,y(x),[Chini],useInt,implicit); #explicit makes it take very long time
 

Intat(1/(_a^n/(b^(-n-1)*(a*x^(-n/(-1+n)))^(-2*n+1)*(-x^(-n/(-1+n)-1)*a*n*b/(-1+n))^n*n^(-n))-_a+1), _a = -y(x)/((-1+n)*x*a*x^(-n/(-1+n))))-(Int(-1/((-1+n)*x), x))+c__1 = 0

> 

residual:=odetest(maple_sol,ode); #how to show this is zero?

n^n*(-y(x)*x^(1/(-1+n))/(a*(-1+n)))^n*(a*x^(-n/(-1+n)))^(2*n)*(-a*b*n*x^(-2*n/(-1+n)+1/(-1+n))/(-1+n))^(-n)*b^(n+1)-b*y(x)^n

> 

coulditbe(residual=0) assuming real;

FAIL

> 

#now solving as homog. (which gives simpler looking solution
> 

maple_sol:=dsolve(ode,y(x),[homogeneous]);

Int(x^(n/(-1+n))/((b*x*(-1+n)*_a^n+_a)*x^(n/(-1+n))+a*x*(-1+n)), _a = _b .. y(x))-c__1 = 0

> 

residual:=odetest(maple_sol,ode); #how to show this is zero?

-b*y(x)^n*n/(-1+n)-x^(-1-1/(-1+n))*a*n/(-1+n)+b*y(x)^n/(-1+n)+x^(-1-1/(-1+n))*a/(-1+n)-y(x)/(x*(-1+n))

> 

coulditbe(residual=0) assuming real;

FAIL

> 

 


 

Download challenge_odetest_sept_1_2024.mw

 
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