Question

Difference between ordinary differential equation and partial differential equation with example

Answer 1

Ordinary Differential Equations (ODE)

An Ordinary Differential Equation is a differential equation that depends on only one independent variable.

For example

dydx=ky(t)

is an Ordinary Differential Equation because y depends only on t(the independent variable)

Partial Differential Equations (PDE)

A Partial Differential Equation is differential equation in which the dependent variable depends on two or more independent variables.

For example

The Laplace's equation

δ2fδx2+δ2fδy2=0

is a Partial Differential Equation because f depends on two independent variables x and y.

Answer 2

Answer:

Differential equations are in dynamic form where as partial dfes are in static form. ... An ordinary differential equation (ODE) has 1 independent variable but a partial differential equation (PDE) has more than 1 independent variable. An ODE is therefore a special case of a PDE