# Question:Why Maple gives solution to Euler ode which has no solution?

## Question:Why Maple gives solution to Euler ode which has no solution?

Maple 2024

This second order (Euler type) ode has no solution for the given two initial conditions. but Maple gives solution with one unresolved constant of integration.

```ode:=x^2*diff(y(x),x\$2)-2*y(x)=0;
ic:=y(0)=4,D(y)(0)=-1;

sol_no_IC:=dsolve(ode)
```

The IC's are given at x=0 as a trick to see what Maple will do. We see that at x=0 there is division by zero. So no solution exist for these IC's. But see what happens

```sol_with_IC:=dsolve([ode,ic])
```

It seems Maple simply threw away the part of the solution it could not handle due to the x=0 and just returned the rest.

```odetest(sol_with_IC,[ode,ic])
```

The correct answer should have been the NULL solution (i.e. no solution).

What Am I missing here? Why does Maple do this? Should Maple have returned such a solution?

Maple 2024 on windows 10.

update:

Reported to Maplesoft support.

update:

Here is another example ode. This is first order ode. Maple gives a solution that does not satisfy the initial condition also. I wish I can understand how Maple comes up with these solutions since when I solve these by hand I see it is not possible to satisfy the IC, hence no solution exist.

 > interface(version);

 > Physics:-Version();

 > restart;

 > ode:=diff(y(x),x)+y(x)/x=x^2; ic:=y(0)=a;

 > dsolve(ode)

 > sol:=dsolve([ode,ic])

 > odetest(sol,[ode,ic])

 > Student:-ODEs:-ODESteps([ode,ic])

Error, (in Student:-ODEs:-applyICO1) numeric exception: division by zero