# Classification of ODE's

1. Feb 28, 2012

### Lengalicious

When classifying an ODE do I just say whether its linear / non-linear and what order it is?

EDIT: Example: x2x'' + e-xx = t3 where x is function of t.

is this 2nd order, non linear and heterogeneous?

Also, would dx/dt = logte-x be homogeneous because both terms contain the dependant variable 't'?

Last edited: Feb 28, 2012
2. Feb 28, 2012

### bigfooted

There are some more classifications for (second order) odes, mostly based on the fact that the ode is solvable (or not) when it is of a certain class. I like the choice of the Maple software, which is pretty classic. The online description of odeadvisor giving you a classification is here:

Your first order ode is homogeneous, because it does not have a term that only depends on t. dx/dt=a(t)*x+b(t) is not homogeneous, but dx/dt = a(t)*x is. Your example is also separable, which means it can be solved using separation of variables.

3. Feb 28, 2012

### Lengalicious

so if dx/dt = logte-1, would that now mean that this was no longer homogeneous? Thanks for the help by the way.

4. Feb 28, 2012

### alan2

Your equation is not homogeneous because of the t cubed term.