## Linear First-Order Differential Equations

A first-order differential equation is linear if it can be expressed as:

where P(x) and Q(x) are functions of x.

The best method of solving a linear first-order differential equation deals with rewriting in standard form (if necessary) and then multiplying both sides by an integrating factor:

After mulitplying both sides by the integrating factor, the differential equation becomes:

Thereafter, it is beneficial to rewrite the equation in the form:

Integrating both sides with respect to x and solving for y will yield solution.

Thereafter, it is beneficial to rewrite the equation in the form:

Integrating both sides with respect to x and solving for y will yield solution.