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Question: dsolve solution does not satisfy IC when using dAlembert method

Question:dsolve solution does not satisfy IC when using dAlembert method

nm 10411 Maple 2024
ode dsolve differential-equations
July 02 2024
1

Maple gives type of this first order ode as _homogeneous, `class C`, but it is also dAlembert ode.

When asking it to solve as  dAlembert using the method option, it solves it.

But it returns singular solution which is wrong as it does not satisfy the IC. Singular solution should also satisfy IC like particular solutions do.

Is this a bug or Am I overlooking something?

Should not the solution returned satisfy the IC even though method used is not listed from odeadvisor?
 

29028

> 

interface(version);

`Standard Worksheet Interface, Maple 2024.0, Windows 10, March 01 2024 Build ID 1794891`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1764 and is the same as the version installed in this computer, created 2024, June 28, 12:19 hours Pacific Time.`

> 

restart;

29028

> 

ode:=diff(y(x), x) = (3*x - y(x) + 1)/(3*y(x) - x + 5);
ic:=y(0)=0;

diff(y(x), x) = (3*x-y(x)+1)/(3*y(x)-x+5)

y(0) = 0

> 

sol:=dsolve([ode,ic],[dAlembert]); #this solution is singular solution.

y(x) = x-1

> 

odetest(sol,[ode,ic]); #notice, solution do not satisfy IC

[0, 1]

> 

sol2:=dsolve([ode,ic]):
odetest(sol2,[ode,ic]); #this is OK since used default method, not dAlembert

[0, 0]

> 

DEtools:-odeadvisor(ode)

[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

> 

 


 

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