Find the power series equation

Question

Find the power series solution to

x^2 y"-y=0 at x_{0 =1}

Answer 1

We first translate the axes , by putting x −1 = u.

Then the equation becomes ( u +1)² d²y/du² − y = 0

As usual we put y= ∑a_nuⁿ from n=0 to n=∞.

Then you proceed as usual.

Do not forget to change your answer at the end so is given in terms of x.