Chapter 12.1, Problem 8P

Solve the following differential equations by series and also by an elementary method and verify that your solutions agree. Note that the goal of these problems is not to get the answer (that’s easy by computer or by hand) but to become familiar with the method of series solutions which we will be using later. Check your results by computer.

$\left(x^2+2x\right)y^{\prime \prime }-2(x+1)y^{\prime }+2y=0$