# Differential Equations

Differential equation is any equation that involves derivatives or differential coefficient or differentials. In mathematics differential equation shows the relationships between physical quantities which appear in mathematical form.

One very common differential equation is Newton’s second law of Motion.

If an object of mass m moving with acceleration a is acted upon with a force F then Newton’s second law says:

$F = ma$

Acceleration can be written as a first derivative of velocity F = $\frac{dv}{dt}$ or as a second derivative of displacement F = $\frac{d^2 s}{d^2 t}$

m$\frac{dv}{dt}$ = F(t, v)…………(1)

m$\frac{d^2 u}{dt^2}$ = F(t, u, $\frac{du}{dt}$)………(2)

Order of differential equation is the largest derivative present in the given equation. In the differential equation shown above (1) [with $\frac{dv}{dt}$] is first order differential equation., (2) is second order equation (with $\frac{d^2 s}{d^2 t}$).