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Question: what does it mean when odetest return the ode itself back instead of zero for a correct solution?

Question:what does it mean when odetest return the ode itself back instead of zero for a correct solution?

nm 11003 Maple 2022
ode differential-equations odetest
November 14 2022
2

This ode from textbook, and the solution is given in back of book and I verified it is correct.

odetest gives zero also when asked to verify the solution.

but when asked to verify both the solution and the initial conditions, instead of returning [0,0] as expected, it returns [the_ode,0]

Here is an example
 

> 

interface(version);

`Standard Worksheet Interface, Maple 2022.2, Windows 10, October 23 2022 Build ID 1657361`

> 

restart
> 

ode:=diff(y(x), x) = 2*(2*y(x) - x)/(x + y(x));
ic:=y(0) = 2;
booksol:=(x-y(x))^2/( y(x)-2*x)^3 = 1/2;

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

y(0) = 2

(x-y(x))^2/(y(x)-2*x)^3 = 1/2

> 

#this returns zero, so maple agree the book solution is correct
odetest(booksol,ode)

0

> 

#when adding ic, when does it not give [0,0] ?
odetest(booksol,[ode,ic])

[diff(y(x), x)-2*(2*y(x)-x)/(x+y(x)), 0]

> 

 


How shoulld one interpret the above answer?

Download question_on_odetest_nov_14_2022.mw
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