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Math Help - Help solve a differential equation

  1. #1
    satyajit
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    Help solve a differential equation

    Please help me solve this differential equation:

    v(sqr.) + hv.dv/dh = g(H-h)

    Here H,g are constants and the variables are v & h.

    please solve the eqn. for v = f(h).

    Satyajit S. Patil
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by satyajit View Post
    Please help me solve this differential equation:

    v(sqr.) + hv.dv/dh = g(H-h)

    Here H,g are constants and the variables are v & h.

    please solve the eqn. for v = f(h).

    Satyajit S. Patil
    The differential equation is:

    <br />
v^2 + h v \frac{dv}{dt} = g(H-h)<br />

    divide through by v to get:

    <br />
\frac{d}{dh} h v(h) = \frac{g(H-h)}{v(h)}<br />

    and set u(h) = h v(h) then the diffrential equation becomes:

    <br />
\frac{du}{dh} = \frac{g(H-h)h}{u(h)}<br />

    Which is now of variables seperable type so:

    <br />
\int u\ du = \int g(H-h) h\ dh + Constant<br />

    RonL
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