# Math Help - Help solve a differential equation

1. ## Help solve a 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

2. Originally Posted by satyajit

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:

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

divide through by $v$ to get:

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

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

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

Which is now of variables seperable type so:

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

RonL