First Order Linear Equations
A first order linear differential equation has the
The general solution is given by
called the integrating factor. If an initial condition is given, use it to find the constant C.
Here are some practical steps to follow:
- If the differential equation is given as
rewrite it in the form
- Find the integrating factor
- Evaluate the integral
- Write down the general solution
- If you are given an IVP, use the initial condition to find
the constant C.
Example: Find the particular solution of:
Solution: Let us use the steps:
Note that you may not have to do the last step if you are asked to
find the general solution (not an IVP).
- Step 1: There is no need for rewriting the differential
equation. We have
- Step 2: Integrating factor
- Step 3: We have
- Step 4: The general solution is given by
- Step 5: In order to find the particular solution to the given
IVP, we use the initial condition to find C. Indeed, we have
Therefore the solution is
If you would like more practice, click on
S.O.S MATHematics home page
Do you need more help? Please post your question on our
S.O.S. Mathematics CyberBoard.
Copyright © 1999-2017 MathMedics, LLC. All rights reserved.
Math Medics, LLC. - P.O. Box 12395 - El Paso TX 79913 - USA
users online during the last hour