What is the difference between ordinary and partial differentiation?
Answers
Ordinary differential equations (ODEs)
ODEs are differential equations involving one or more functions of one independent variable and their derivatives. An example involving only one function f(x) might be represented in either of the following notations:
dfdx=af(x)f′(x)=af(x)
If an ODE is in the particular form of:
A(y)dydx=B(x)
then we say it is separable and it is, usually, relatively simple to solve because you can rewrite it as:
A(y)dy⟹∫A(y)dy=B(x)dx=∫B(x)dx
Partial Differential Equations (PDEs)
As the name might suggest, PDEs are differential equations involving partial derivatives; that is, PDEs contain one or more functions of multiple variables and their partial derivatives. An example involving the 1-D heat equation is given below:
∂u∂t=α∂2u∂x2
with α=Kcρ where ρ represents density, c represents specific heat, and K
gives thermal conductivity. Then we call α the thermal diffusivity.
Answer:
An Ordinary Differential Equation is a differential equation that depends on only one independent variable. A Partial Differential Equation is differential equation in which the dependent variable depends on two or more independent variables.