First Order Differential

#math

$$y' + p(x)y = r(x)$$

is the general form of a first order differential equation.

The above has the solution of the form

$$\exp\left( \int p(x)dx \right) y(x) = \int r(x) e^{\int^x p(t)dt}dx$$

Where the factor,

$$e^{\int p(x)dx}$$

is called the integrating factor.