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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 $a+b$.

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