# Need to solve the following differential equation

1. Apr 28, 2004

### simick1712

Sorry if this is in the wrong section, I wasn't sure where to post it.

Can anyone help me - I need to solve the following differential equation and find the values of c and B.

> k is given as -98.3146.
> v = 55 when t = 9
> v = 50 when t = 10

k(v^2) + B = m.(dv/dt)

Am I right in thinking that by separation of variables and integration I get

arctan(v/sqrt(B/k))=kt/m + c

??

But then if so, how do I find the values of c and B?

Thanks for any help,

Simon.

2. Apr 28, 2004

### krab

Your solution would be OK, except that k is negative. Note that you are taking the square root of k. The proper way to do this gets you an inverse hyperbolic tangent, not an arctan.

Also, your k on the rhs should be sqrt(Bk)

Last edited: Apr 28, 2004
3. Jul 5, 2004

### eJavier

First, I don't see any C in the equation to solve, so I assume it's the constant of integration.
I got:
$$\frac{\sqrt{B}}{\sqrt{k}}\tanh{\frac{\sqrt{B}\sqrt{k}\cdot t+C \sqrt{B}\sqrt{k}\cdot m}{m}}$$

Last edited: Jul 5, 2004
4. Jul 5, 2004

### eJavier

You could also try the "homogeneous + particular" approach.

5. Jul 5, 2004

### HallsofIvy

Staff Emeritus
No, you can't because this is a non-linear equation. The whole point of linear equations is that you can solve separate parts of the problem, then put them together. With non-linear equations you can't do that.

6. Jul 5, 2004

### eJavier

Yes, you're right. :blush: