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Use the substitution $x=e_{t}$ to transform the given Cauchy-Euler equation to a differential equation with constant coefficients. (Use $yp$ for $dtdy $ and $ypp$ for $dt_{2}d_{2}y $.) $x_{2}y_{′′}+9xy_{′}+7y=x_{2}$ Solve the original equation by solving the new equation using the procedures in Sections 4.3-4.5. $y(x)=C_{1}x_{−1}+C_{2}x_{−7}+27x_{2} $

The given differential equation is

This is a Cauchy–Euler equation of second order.

Thus to solve e...

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