Use a power series method to find the solution of
x^2 y'' + 2xy' + 4y = 0
that is valid in any interval not including the singular point.
y=0 is a trivial solution which exists for any linear
Homogeneous equation. So it is correct but absolutely not enough to complete the problem. Since the equation is linear and has non-trivial general solutions you have to find it.
Pay attention that x=0 is a singular point; Frobenius method is expected.
The Frobenius method is used to solve a differential equation. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.