Y 1x2y - 1x3y 0 a show that x 0 is an irregular singular

Question

y" + (1/x²)y' - (1/x³)y = 0

a) Show that x = 0 is an irregular singular point

b) Use the fact that y₁ = x is a solution to find a second independent solution y₂ by the method discussed earlier in the book.

c) Show that the second solution y₂ that we found in part (b) cannot be expressed as a Frobenius series.