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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- May 26th 2007, 12:51 AMsatyajitHelp 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 - May 26th 2007, 01:19 AMCaptainBlack
The differential equation is:

$\displaystyle

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

$

divide through by $\displaystyle v$ to get:

$\displaystyle

\frac{d}{dh} h v(h) = \frac{g(H-h)}{v(h)}

$

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

$\displaystyle

\frac{du}{dh} = \frac{g(H-h)h}{u(h)}

$

Which is now of variables seperable type so:

$\displaystyle

\int u\ du = \int g(H-h) h\ dh + Constant

$

RonL