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.