1. ## 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!

2. ## 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

3. ## Re: Separable ODE

Thanks, my lecture notes said it was separable, but I'm pretty sure it's actually not!

4. ## 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

$\displaystyle \frac{1}{K+1}\ln (1+(K+1)v)=t+C.$

5. ## Re: Separable ODE

Lol can't believe I missed that. I've recently been doing a lot of problems with the more complicated method.