Very Tough Nonlinear First Order Differential Equation

[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

thanks for your help in advance

 

[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.

 

[sexycalibur]

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

 

[sexycalibur]

matlab can't solve it.

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

 

[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