## Mathematical Analysis## Differential Equations |

## What is a nonlinear differential equation? |

From above, we know that linear equations have specific rules; for example, the unknowns *y, y*', and so on, will never be raised to a power more than 1; they will not be in the denominator of a fraction; *y* times *y*' is never allowed (because two unknowns multiplied together is, in a sense, a power 2 of unknowns); and they won’t be inside another function (such as a sine).

But a nonlinear equation is much different, allowing for powers of 2(*y*' = *y*^{2}), multiplying differences (*y × y'* = *x*); and even being inside another function (*y*' = *x* *sin y*).

Thus, the nonlinear equations are not as easy to solve as linear differential equations. But that does not mean they lack importance. In fact, because nonlinear equations are more realistic in describing real-life problems, they are much more interesting (and challenging) to mathematical and scientific researchers in many fields.