I am trying to solve y''+(3-1/x^2)y=0. Is it possible to solve by separation? Or will this require a series solution?

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- Oct 21st 2011, 12:17 PMtoobusySecond order ODE with non-constant coefficients
I am trying to solve y''+(3-1/x^2)y=0. Is it possible to solve by separation? Or will this require a series solution?

- Oct 21st 2011, 01:28 PMHallsofIvyRe: Second order ODE with non-constant coefficients
If by "separation" you mean writing it as $\displaystyle \frac{d^2y}{dx^2}= (\frac{1}{x^2}- 3)y$ and then to

$\displaystyle \frac{d^2y}{y}= (\frac{1}{x^2}- 3)dx^2$, then, no, you cannot "separate" a**second order**derivative like you can a first order derivative. The "differentials" dy and dx are defined in Calculus, but such things as "$\displaystyle d^2y$" and "$\displaystyle dx^2$" are NOT defined. - Oct 21st 2011, 05:52 PMAckbeetRe: Second order ODE with non-constant coefficients
- Oct 21st 2011, 07:39 PMtoobusyRe: Second order ODE with non-constant coefficients
Thanks! I just figured it out!