Consider the following initial$-$value problem to be solved using a power series.

$(x-1)y^{\text{'}\text{'}}-x{y}^{\text{'}}+y=0,y(0)=-2,y^{\text{'}}(0)=7$

Using the substitution $y={\displaystyle \underset{n=0}{\overset{}{}}}{c}_n{x}^n,$ find an expression $c_{k+2}$ in terms of $c_k$ for $k=1,2,3$dots.

$c_{k+2}=$

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Solve the given initial value problem. $($Format your answer as an elementary function.$)$

$y=$

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