# Very Tough Nonlinear First Order Differential Equation

1. Sep 25, 2008

### sexycalibur

1. y' = a*(y^n) + c

a, n and c are constants. Any idea about this problem ? How can it be solved ?

i think there is no analytic solution

2. Sep 25, 2008

### nughret

There are a couple of ways to solve this; power series method if you only need to solve to a specified power. Otherwise use the fact that the diff eqn is seperable and you get left with dy/(a*y^n + c) = dx , not an easy integral but if you are given specific values of your constants you will have a better chance.

3. Sep 25, 2008

### sexycalibur

yes it is seperable. But this integral is tought too :)

4. Sep 25, 2008

### sexycalibur

matlab cant solve it.

Should i trust matlab and not keep on trying to solve this ??

5. Sep 25, 2008

### nughret

As i said with arbitary n the integral is very difficult and you won't get very far with a pen and paper (if you want an exact solution).
I plugged this into the integrator and it gave me a solution, i haven't got access to matlab to try on that