# Thread: Linear Diff. Equ. of Second Order

1. ## Linear Diff. Equ. of Second Order

Please help me to Solve these Diff. Equ.s by transforming an independent variable:

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

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

(3) $(x-3)\frac{d^2y}{dx^2}-(4x-9)\frac{dy}{dx}+3(x-2)y=0$

(4) $(1-x^2)\frac{d^2y}{dx^2}+3x\frac{dy}{dx}+y=0$

(5) $\frac{d^2y}{dx^2}+4x\frac{dy}{dx}+4x^2y=0$

(6) $x\frac{d^2y}{dx^2}-(2x-1)\frac{dy}{dx}+(x-1)y=0$

(7) $\frac{d^2y}{dx^2}+x\frac{dy}{dx}-y=f(x)$

(8) $(x\sin x+\cos x)\frac{d^2y}{dx^2}-x\cos x\frac{dy}{dx}+ y\cos x$

3. Method of transforming the independent variables, I took $z=\int e^{-\int Pdx} \; dx$
But I didn't gt it properly.. and $Q_1 \ne constant$
I also supposed $Q_1=constant$, but in this case I also didint get it.