# The difference between linear and non linear differential equation

1. Oct 28, 2008

### fabianz

I'm just starting to learn about ordinary differential equation and I'm still
don't know how to find the difference between linear and non linear differential equation.
thank you very much

Last edited: Oct 28, 2008
2. Oct 29, 2008

### mathwonk

its pretty much the difference between ones you can solve and ones you cannot.

3. Oct 29, 2008

### HallsofIvy

Staff Emeritus
Oh, now that's just silly! (Though pretty much true!)

fabianz, do you know the difference between linear and nonlinear functions?

A linear function must be of theform f(x)= ax+ b. Nothing more complicated than multiplying by a number and adding a number. For a function of several variables, "a" and "b" can be any function of the other variables and still be "linear in x". Any thing other than that is "non-linear".

A differential equation if "linear" if it does not involve any non-linear functions of the dependent variable