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Question: ODESteps seems little confused on this ode.

Question:ODESteps seems little confused on this ode.

nm 10189 Maple 2024
ode differential-equations odesteps
June 20 2024
0

How did Student:-ODEs:-ODESteps([ode,ic]); managed to get this zero solution to this ode? I can't follow the logic it did.

Any ideas what it is doing in the 4th step there?
 

13496

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interface(version);

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

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ode := diff(y(x), x) = y(x)*(2*y(x) - x)/(x*(-2*x + 3*y(x)));
ic:=y(1)=-1;
dsolve([ode,ic]);

diff(y(x), x) = y(x)*(2*y(x)-x)/(x*(-2*x+3*y(x)))

y(1) = -1

y(x) = (1/6)*(I*((-27*x^2+x^3+3*3^(1/2)*(-2*x^5+27*x^4)^(1/2))^(2/3)-x^2)*3^(1/2)-((-27*x^2+x^3+3*3^(1/2)*(-2*x^5+27*x^4)^(1/2))^(1/3)-x)^2)/(-27*x^2+x^3+3*3^(1/2)*(-2*x^5+27*x^4)^(1/2))^(1/3)

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#now try ODEsteps
Student:-ODEs:-ODESteps([ode,ic]);
 

"[[,,"Let's solve"],[,,[(ⅆ)/(ⅆx) y(x)=(y(x) (2 y(x)-x))/(x (-2 x+3 y(x))),y(1)=-1]],["•",,"Highest derivative means the order of the ODE is" 1],[,,(ⅆ)/(ⅆx) y(x)],["•",,"Solve for the highest derivative"],[,,(ⅆ)/(ⅆx) y(x)=(y(x) (2 y(x)-x))/(x (-2 x+3 y(x)))],["•",,"Use initial condition" y(1)=-1],[,,0],["•",,"Solve for" 0],[,,0=0],["•",,"Substitute" 0=0 "into general solution and simplify"],[,,0],["•",,"Solution to the IVP"],[,,0]]"

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odetest(y(x)=0,[ode,ic])

[0, -1]

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