Ordinary Differential Equation

Differential equations are equations that involve derivatives
Ordinary differential equations only involves only ordinary derivatives

Ordinary: Not involving Partials

When solving for ODEs the whole solution set must be found
Solutions for ODEs must include an arbitrary constant

For example, is a valid solution to the ODE

However the solution is only valid for

Equilibrium Solutions

Consider gravity and a drag force affecting a ball

If the net force is , the system will be in equilibrium, therefore the equation becomes

This implies that velocity is constant and is independent of

Initial Value Problems

Initial value problems (IVP) have a given differential and an initial condition

IVPs solves for the arbitrary constant
Can be solved by find the Integral Curve that passes the initial condition

Type of Problem Time Dependent Arbitrary Constant
Equilibrium No No
General Yes Yes
Initial Value Yes No

Methods