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:
$\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