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Math Help - Linear Diff. Equ. of Second Order

  1. #1
    Member kjchauhan's Avatar
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    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

    Please help me, 2moro I have to explain it..
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  2. #2
    Super Member craig's Avatar
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    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
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  3. #3
    Member kjchauhan's Avatar
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    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.
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