Show that, with a suitable value of the constant $\displaystyle \alpha$, the substitution $\displaystyle y=x^{\alpha}w$ reduces the differential equation

$\displaystyle 2x^{2}\frac{d^{2}y}{dx^2}+(3x^2+8x)\frac{dy}{dx}+( x^2+6x+4)=f(x)$

to

$\displaystyle 2\frac{d^{2}w}{dx^2}+3\frac{dw}{dx}+w=f(x)$

Preparing for an exam,so all help is greatly appreciated

Edit

Ooops.Forgot the y

The expression is

$\displaystyle 2x^{2}\frac{d^{2}y}{dx^2}+(3x^2+8x)\frac{dy}{dx}+( x^2+6x+4)y=f(x)$