ODE's: IVP Existence/Uniqueness

[middleramen]

Homework Statement

Find a nontrivial solution of the IVP

dy/dx = tx^p (p is any number); y(0) = 0

Does this violate the uniqueness part of the Existence/Uniqueness Theorem? Explain

Homework Equations

The Attempt at a Solution

I've found two solutions: one for p = 1 and one for all other cases.

It seems that having two solutions would violate the uniqueness part of the theorem. Both dy/dx and it's partial derivative of y are continuous, so the Theorem can apply, but not sure other than that.

Any help would be appreciated.
Thanks

 

[HallsofIvy]

No, having different solutions for different values of t does NOT violate the theorem. With different values of p we have different differential equations. But how does 't' come into this equation? Are you sure the left isn't "dx/dt"?

 

[haruspex]

Bad post - removed.