I haven't taking Differential Equations for over 2 or 3 years and it escapes my memory how to determine when would an IVP (Initial Value Problem) would have
- no solutions
- more than one solution
- precisely one solution
Can someone refresh my memory? For example, we have the problem
$tx'=2x$ with $t \epsilon [-1,1]$ and $x(t_0)=x_0$
After working out the problem I have the following solution:
$x_0=C t_0^2$ where C is arbitrary.
When does this have no solution? And etc.