How do I solve complex differential equations involving velocity and time?

[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:

<br /> dV = - \mu V^2 t - \beta t<br />

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:

<br /> dH = \gamma V^2 t - \alpha t<br />

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?

 

[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.

 

[mathwonk]

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

 

[noble24]

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

<br /> dV = - \mu V^2 dt - \beta dt<br />

<br /> dH = \gamma V^2 dt - \alpha dt<br />

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

<br /> \frac {dV} {dt} = - \mu V^2 - \beta<br />

Now what...

 

[dextercioby]

You needn't have done that.U already had separated variables and u only had to integrate.

Daniel.

 

[dextercioby]

EDIT:You've changed your equations a great deal and now the advice goes:SEPARATE VARIABLES...

Daniel.