One way to proceed would be to use Euler's formula:
By the principle of superposition, we then find:
Please help for finding 2 Linearly Independent solutions of
x^{2}y'' + xy' + 4y = 0
my method:
factoring first
let y=x^{A }so y' = Ax^{(A-1)} and y'' = A(A-1)x^{(A-2) }So A(A-1) + A + 4 =0
which is A^{2} + 4 = 0
A = +/- 2i
then I don't know how to find 2 LI solutions, please help..