Given that
\(x \frac{\mathrm{~d}^{2} y}{\mathrm{~d} x^{2}}+(2 x+2) \frac{\mathrm{d} y}{\mathrm{~d} x}+(2-3 x) y=10 \mathrm{e}^{2 x}\)
and that \(v=x y\), show that
\(\frac{\mathrm{d}^{2} v}{\mathrm{~d} x^{2}}+2 \frac{\mathrm{~d} v}{\mathrm{~d} x}-3 v=10 \mathrm{e}^{2 x}\)

Find the general solution for \(y\) in terms of \(x\).