Ordinary Differential Equations 1

Calculus Level 5

Solve the following differential equation:(x24x+4)y+(4x8)y+2y=0({x}^{2}-4x+4)y''+(4x-8)y'+2y=0 where y(0)=1/2y(0)=1/2 y(0)=1/4.y'(0)=1/4.

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

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