Ordinary Differential Equations

An ordinary differential equation (ODE) is an equation involving a function of one variable and its derivatives.

$$F(x,y,y^{\prime },y^{\prime \prime },\dots ,y^{(n)})=0$$

where

• $x$ = independent variable
• $y(x)$ = unknown function
• $y^{\prime },y^{\prime \prime },\dots$ = derivatives

An ODE is called:

• first order if the highest derivative is $y^{\prime }$
• nth order if the highest derivative is $y^{(n)}$