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Homework Help: Second order ODE

  1. Nov 10, 2008 #1
    Can someone explain to me why the solution of [tex]\frac{d^{2}\Phi (\phi)}{d\phi^{2}} = -m_{l}^{2}[/tex] is [tex]\Phi = e^{im_{l}\phi}[/tex]?
     
  2. jcsd
  3. Nov 10, 2008 #2

    Dick

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    Science Advisor
    Homework Helper

    It's not. A solution of
    [tex]
    \frac{d^{2}\Phi (\phi)}{d\phi^{2}} = -m_{l}^{2}\Phi(\phi)
    [/tex] is [tex]
    \Phi = e^{im_{l}\phi}
    [/tex].
    Just substitute Phi into the ODE.
     
  4. Nov 11, 2008 #3
    If I'm given the ODE, is inspection the only way to find the solution?
     
  5. Nov 11, 2008 #4

    HallsofIvy

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    Science Advisor

    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.
     
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