# Separable ODE

• Apr 13th 2013, 11:12 AM
Ant
Separable ODE
Hi,

I'm sure this is straight forward I'm just having a mental block:

I'm trying to solve:

$\displaystyle \frac{dv}{dt}=1+(K+1)v$

should only need the first step or a hint!
• Apr 13th 2013, 12:10 PM
Shakarri
Re: Separable ODE
There might be a simpler method but you can solve it like in the example here Examples of differential equations - Wikipedia, the free encyclopedia
Where p(x)= -(k+1) and q(x)= 1
• Apr 13th 2013, 12:30 PM
Ant
Re: Separable ODE
Thanks, my lecture notes said it was separable, but I'm pretty sure it's actually not!
• Apr 13th 2013, 01:23 PM
BobP
Re: Separable ODE
The equation can be solved by the variables separable method,

write it as $\displaystyle \int \frac{dv}{1+(K+1)v}=\int dt.$

It integrates directly to

$\displaystyle \frac{1}{K+1}\ln (1+(K+1)v)=t+C.$
• Apr 13th 2013, 03:23 PM
Shakarri
Re: Separable ODE
Lol can't believe I missed that. I've recently been doing a lot of problems with the more complicated method.