Having the Hardest Time

1. Feb 11, 2005

noble24

I know at some point, years ago, I could differential equations in my sleep. But now after going through my old math book and reading a number of the threads here, I'm really confused. The problem I am looking to solve looks like this:

$dV = - \mu V^2 t - \beta t$

where mu and beta are constants, t is time and V is horizontal velocity. I want to compute the horizontal velocity at time t given the initial horizontal velocity, mu and beta. My problem gets more complex with the second equation I need to solve:

$dH = \gamma V^2 t - \alpha t$

where gamma and alpha are constants, t is time, V is horizontal velocity and H is vertical velocity. I want to compute the vertical velocity at time t given the initial horizontal velocity. I've been going nuts trying to make this work in my head. They look like rudimentary textbook problems, but I just can't seem to make sense of them. Could someone walk me through the steps?

2. Feb 11, 2005

dextercioby

In both equations the "dt" is missing.I can assume it should be in the RHS,case in which i would advise you to integrate directly both sides of the equations...

Daniel.

3. Feb 11, 2005

mathwonk

yes, the basic rule is balance units: i.e. if one side is a differential, the other is too.

4. Feb 11, 2005

noble24

Oops. Sorry, the t should have been dt. Corrected:

$dV = - \mu V^2 dt - \beta dt$

$dH = \gamma V^2 dt - \alpha dt$

So, how do I integrate these? Let's take the first one and divide by dt. Then I get:

$\frac {dV} {dt} = - \mu V^2 - \beta$

Now what...

5. Feb 11, 2005