For a Cauchy Euler Dif EQ, its auxiliary equation for this Dif EQ:

$\displaystyle at^2y'' + bty' + cy = g(t)$ is:

$\displaystyle am^2 + (b-a)m + c = 0$.

Use this auxiliary equation to solve the Cauchy-Euler equation below:

$\displaystyle t^2y'' - 5ty' + 8y = 0$ subject to $\displaystyle y(2) = 32$ and $\displaystyle y'(2) = 0$