Please help me to Solve these Diff. Equ.s by transforming an independent variable: (Where I'm wrong?)

$\displaystyle \frac{d^2y}{dx^2}+\frac{2}{x}\frac{dy}{dx}-n^2y=0$

Take $\displaystyle z=\int e^{-\int Pdx}\;dx$ to make $\displaystyle P_1=0$

Here $\displaystyle P=\frac{2}{x}$

$\displaystyle \therefore z=\int e^{-\int \frac{2}{x}\,dx}\;dx$

$\displaystyle \therefore z=\int e^{-2\log x}\, dx$

$\displaystyle \therefore z= \int e^{\log x^{-2}}\, dx$

$\displaystyle \therefore z=\int x^{-2} \, dx$

$\displaystyle \therefore z=\frac{-1}{x}$

Now,

$\displaystyle \frac{dz}{dx}=x^{-2}$

so,

$\displaystyle Q_1=\frac{Q}{{\left( \frac{dz}{dx}\right)}^2}$

$\displaystyle \therefore Q_1=\frac{-n^2}{{\left( x^{-2} \right)}^2}$

$\displaystyle \therefore Q_1=\frac{-n^2}{z^4}$

So, the reduced equation is now,

$\displaystyle \frac{d^2y}{dz^2}+Q_1y=0$

$\displaystyle \frac {d^2y}{dz^2}-\frac{n^2}{z^4}y=0$

Ok, now I do not work out... pl help..