It is given that \(y=x^{2} w\) and
\[x^{2} \frac{\mathrm{~d}^{2} w}{\mathrm{~d} x^{2}}+4 x(x+1) \frac{\mathrm{d} w}{\mathrm{~d} x}+\left(5 x^{2}+8 x+2\right) w=5 x^{2}+4 x+2\]
(a) Show that
\[\frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}+4 \frac{\mathrm{~d} y}{\mathrm{~d} x}+5 y=5 x^{2}+4 x+2\]
(b) Find the general solution for \(w\) in terms of \(x\).