To Rewrite a Higher Order ODE as a System of First Order ODEs
The following equation is an nth order Ordinary Differential Equation:
1. Define variables y0,y1,...yn as follows:
2. Rewrite the nth order ODE in terms of the new variables:
 | This is equivalent to a system of first-order ODEs:  where  |
3. Solve the original equation for yn and substitute the result in a vector of the following form:
| | You can apply the ODE solvers on this vector function. |