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 \(a+b\).