midterm one differential equations

Classifications of differential equations:

Ordinary vs. Partial
Single equation vs. system
Order of DE
Linear vs. non-Linear
Homogeneous vs. Non-Homogeneous

Degree

Autonomous DE

Ordinary vs partial

Ordinary: One independent variable, one dependent
Partial: more than one independent

Single equation vs. system of equations

Single: One equation
System: multiple equations

Order of ODE

The degree of the highest derivative

Homogeneous vs. Non-Homogeneous

Homogeneous: right hand side is zero.

Non-homogeneous: anything else

Degree

The exponent of the highest order derivative