Ordinary Differential Equations 1

Calculus Level 5

Solve the following differential equation: $({x}^{2}-4x+4)y''+(4x-8)y'+2y=0$ where $y(0)=1/2$ $y'(0)=1/4.$

Ifthe sum of the first 10 terms of the power series expansion for $y(x)$ is $\frac{a}{b}$ calculate $a+b$ .