Mathematica Tutorial

Nonlinear Systems of ODEs

Following are two examples of nonlinear systems of ODEs that can be solved symbolically using DSolve.

The first three equations in this system of four nonlinear ODEs can be solved independently because none of their right-hand sides depend on p, q, r, or s.

This system of two nonlinear ODEs is autonomous, in the sense that the right-hand sides of the equations do not depend on x.

The previous two examples demonstrate that the solutions to fairly simple systems are usually complicated expressions of the independent variable. In fact, the solution is often available only in implicit form and may thus contain InverseFunction objects or unevaluated Solve objects.