## Partial Differential Equations

A partial differential equation (PDE) is a type of differential equation involving unknown function(s) of several independent variables, in addition to partial derivatives with respect to those variables.

In PDEs, it is common to denote partial derivatives using subscripts. For example:

If a function u(x,y) is sufficiently differentiable, separation of variables and basic integration serve as two methods of solving them.

Example #1:

Using basic integration, find the general solution of u

_{x}= x for u(x, y) with u(0, y) = 3y

Solution #1:

Using basic integration, find the general solution of u

Example #2:

Using basic integration, find the general solution of u

_{xy}= xy for u(x, y)

Solution #2: