Given \(y=\mathrm e^{-2x}x^2\),
\(y\) is a solution of the equation \(\mathrm e^{2x}\left(4y+4\dfrac{\mathrm{d}y}{\mathrm{d}x}+\dfrac{\mathrm{d}^2y}{\mathrm{d}x^2}\right)=k\), where \(k\) is a constant. Show that \(k=2\).[6]
find the range of values of \(x\) for which \(y\) increases as \(x\) increases.[3]