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Math Help - x^2 φ'' (x)+xφ' (x)-λφ(x)=0

  1. #1
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    x^2 φ'' (x)+xφ' (x)-λφ(x)=0

    x^2 \varphi'' (x)+x\varphi' (x)-\lambda\varphi(x)=0

    How is this DE solved?

    This is a separation from PDE. I don't know what to do at this point.
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by dwsmith View Post
    x^2 \varphi'' (x)+x\varphi' (x)-\lambda\varphi(x)=0

    How is this DE solved?

    This is a separation from PDE. I don't know what to do at this point.
    It's a Cauchy-Euler equation. You assume that the solution is of the form \varphi(x)=x^r. Thus, the characteristic equation for the ODE in question is r^2-\lambda=0.

    I'm sure you can finish this off.
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