General Solution Method for
1st Order Linear Differential Equations
A differential equation is linear if it is a linear function of x, y, y’, y"…and the order is the order of the highest derivative.
A 1st order linear DE can always be written in the form
or rearranged to the form .
The steps to solve such equations are summarized below.
- Put the equation in the standard form. (The equation with P(x) and Q(x) above.)
- Obtain the integrating factor
- Multiply the standard equation by the integrating factor.
- The left-hand side of the equation should simplify to a derivative of the product of the integrating factor and the dependent variable.
- Solve the equation by integrating, using the initial conditions if necessary.