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Question: why Maple sometimes solves an ode using method different than what odeadvisor gives?

Question:why Maple sometimes solves an ode using method different than what odeadvisor gives?

nm 9718 Maple 2024
ode dsolve differential-equations odeadvisor
August 13 2024
3

I noticed sometimes Maple dsolve solves an ode using a method different than what odeadvisor says it is.

In this example ode, advisor said it is separable. But when solving it, dsolve actually solved it as dAlembert.

Why is that? Should not these be the same?

I also noticed Maple does not verify the solution of the ode when asked to solve it as separable, which is what the advisor says. But it does verify the solution using dAlembert.

So in this example, should not advisor have said this ode is dAlembert and not separable then?

> 

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 1786 and is the same as the version installed in this computer, created 2024, August 10, 8:50 hours Pacific Time.`

> 

ode:=y(x) = x + 3*ln(diff(y(x), x));
DEtools:-odeadvisor(ode);

y(x) = x+3*ln(diff(y(x), x))

[_separable]

> 

infolevel[dsolve]:=5:
sol_1:=dsolve(ode);

Methods for first order ODEs:

-> Solving 1st order ODE of high degree, 1st attempt

trying 1st order WeierstrassP solution for high degree ODE

trying 1st order WeierstrassPPrime solution for high degree ODE

trying 1st order JacobiSN solution for high degree ODE

trying 1st order ODE linearizable_by_differentiation

trying differential order: 1; missing variables

trying d'Alembert

<- d'Alembert successful

y(x) = x, y(x) = x+3*ln(exp(-(1/3)*x)*c__1/(-1+exp(-(1/3)*x)*c__1))

> 

map(X->odetest(X,ode),[sol_1]);

[0, 0]

> 

sol_2:=dsolve(ode,[separable]);

Classification methods on request

Methods to be used are: [separable]

----------------------------

* Tackling ODE using method: separable

--- Trying classification methods ---

trying separable

<- separable successful

y(x) = -3*ln(exp(-(1/3)*x)-(1/3)*c__1)

> 

#notice, solution does not verify.
odetest(sol_2,ode);

-3*ln(3*exp(-(1/3)*x)-c__1)-x-3*ln(exp(-(1/3)*x)/(3*exp(-(1/3)*x)-c__1))

 

 

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