Second order ODE

1. Nov 10, 2008

kasse

Can someone explain to me why the solution of $$\frac{d^{2}\Phi (\phi)}{d\phi^{2}} = -m_{l}^{2}$$ is $$\Phi = e^{im_{l}\phi}$$?

2. Nov 10, 2008

Dick

It's not. A solution of
$$\frac{d^{2}\Phi (\phi)}{d\phi^{2}} = -m_{l}^{2}\Phi(\phi)$$ is $$\Phi = e^{im_{l}\phi}$$.
Just substitute Phi into the ODE.

3. Nov 11, 2008

kasse

If I'm given the ODE, is inspection the only way to find the solution?

4. Nov 11, 2008

HallsofIvy

If you have not learned to solve differential equations, yes!

If you have then you would know how to use the solutions to the characteristic equation, then you could use that method.