Nonhomogeneous Linear Equations

Consider the nonhomogeneous linear equation


We have seen that the general solution is given by


where tex2html_wrap_inline28 is a particular solution and tex2html_wrap_inline30 is the general solution of the associated homogeneous equation. We will not discuss the case of non-constant coefficients. Therefore, we will restrict ourself only to the following type of equation:


Using the previous section, we will discuss how to find the general solution of the associated homogeneous equation


Therefore, the only remaining obstacle is to find a particular solution to (NH). In the second order differential equations case, we learned the two methods: Undetermined Coefficients Method and the Variation of Parameters. These two methods are still valid in the general case, but the second one is very hard to carry.

[Differential Equations] [First Order D.E.] [Second Order D.E.]
[Geometry] [Algebra] [Trigonometry ]
[Calculus] [Complex Variables] [Matrix Algebra]

S.O.S MATHematics home page

Do you need more help? Please post your question on our S.O.S. Mathematics CyberBoard.

Author: Mohamed Amine Khamsi

Copyright 1999-2023 MathMedics, LLC. All rights reserved.
Contact us
Math Medics, LLC. - P.O. Box 12395 - El Paso TX 79913 - USA
users online during the last hour