Chapter 12.11, Problem 11P

Solve the following differential equations by the method of Frobenius (generalized power series). Remember that the point of doing these problems is to learn about the method (which we will use later), not just to find a solution. You may recognize some series [as we did in ( 11.6)] or you can check your series by expanding a computer answer.

$36x^2{y}^{\prime \prime }+\left(5-9x^2\right)y=0$