# Thread: Linear Diff. Equ. of Second Order

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

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

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

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

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

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

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

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

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

2. Please limit your post to 1 question, if you have multiple problems post them in separate threads.

Also show us your working so far and we will help you through where you get stuck.

Thank you

3. Method of transforming the independent variables, I took $\displaystyle z=\int e^{-\int Pdx} \; dx$
But I didn't gt it properly.. and $\displaystyle Q_1 \ne constant$

I also supposed $\displaystyle Q_1=constant$, but in this case I also didint get it.