I have a 2nd order homogeneous non-const. coefficients linear DE, and don't remember how we used to solve it or even if we did at all, looked through the book, but it only covers a case of Cauchy-Euler.(adsbygoogle = window.adsbygoogle || []).push({});

The original question actually goes like this:

verify that y(x) = sin (x^{2}) is in the kernel of L,

L = D^{2}- x^{-1}D + 4x^{2}, where D is a differetiation operator.

so what I have so far is this:

Ly = 0

when I distribute I get this DE and get stuck with it:

y'' - x^{-1}y' + 4x^{2}y = 0

Thanks for any help.

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# Homework Help: Second order homog. DE non-const coeff.

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