# System of non-linear ODE

1. May 30, 2014

### metamathphys

Hello everybody. Solving a problem in Physics I run into a system of equations that I do not know how to solve, I would appreciate some help. Here is the system:

\ddot{x}+4\dot{x}^2=C_1e^{y}

\dot{y}^2=C_2\ddot{x}

The dependent variables are x,y. C_1 and C_2 are some constants. I try to play with the equations to obtain one equation in one unknown but I dont get anywhere...

If someone could tell me where I can learn to write the equations so that they appear in math style that would be awesome as well.

2. May 30, 2014

### DeIdeal

Are you sure you've done everything correctly so far and you're indeed meant to solve this analytically? I put the system in Maple, and the solution is quite ugly. I don't know what "Physics I" consists of, but it sounds like something where you wouldn't need to solve something like this.

You can use [ tex] and [ itex] tags (without the spaces, itex for inline text) to write in LaTeX.

3. May 30, 2014

### metamathphys

I am almost sure the system is setup correctly. I do not need an exact solution but an approximate one i.e. the first few terms in a power series method.

Best

4. May 30, 2014

### the_wolfman

$\ddot{x}+4\dot{x}^2=C_1e^{y}$

$\dot{y}^2=C_2\ddot{x}$

What happens if you assume that $|y| \ll 1$ ?

In this limit what is the Taylor expansion of $e^{y}$ ?