# Non-linear ODE's

1. Aug 3, 2008

### robousy

Hey folks,

Does anyone have any experience with how to solve non-linear ODE's numerically, perhaps in mathematica??

I am trying to solve the following equations:

$$3H_a^2+3H_aH_b=K_1$$
$$\dot{H}_a+3H_a^2+H_aH_b=K_2$$
$$\dot{H}_b+3H_a^2+3H_aH_b=K_3$$

Where $$H_a$$ and $$H_b$$ are both functions of time and the K's are just constants.

Any help appreciated!

2. Aug 4, 2008

### Defennder

Well it would be a lot easier to read if you had used the familiar general x,y algebra symbols instead of Ha, Hb.

So this reduces to:
$$3x^2 + 3xy = K_1$$
$$x' + 3x^2 + xy = K_2$$
$$y' + 3x^2 + 3xy = K_3$$

You can express xy in the first equation in terms of x and substitute it into the second equation and then you can simply separate the variables before integrating directly.

Once you have x(t), just substitute it into the 3rd equation. You should be able to find an integrating factor now. I don't think there's a need for numerical solutions.

Last edited: Aug 4, 2008
3. Aug 4, 2008

### robousy

You are right, I should have simplified it into more recognizable variables. I think this is a lot easier than I first though, thanks for pointing that our Defennder!