Monday, May 9, 2011

Substitution for $t^2 y^{\prime \prime}+t y^{\prime}+ y =0$

$t^2 y^{\prime \prime}+t y^{\prime}+ y =0$
Make the substitution $u=\ln t$
Then compute $\frac{dy}{dt}=\frac{dy}{du}\frac{du}{dt}$ and
compute $\frac{d^2y}{dt^2}=\frac{d^2y}{d^2u}(\frac{du}{dt})^2+\frac{dy}{du}\frac{d^2u}{dt^2}$

I'll get the page reference soon. Just wanted to get this up because I said I would.

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