Undetermined Coefficients

The method of undetermined coefficients is a technique used to solve non-homogeneous linear differential equations with constant coefficients. It is applicable when the non-homogeneous term is a simple function such as a polynomial, exponential, or sinusoidal function.

This method involves assuming a particular solution for the non-homogeneous equation with undetermined coefficients, which are then determined by substituting the assumed solution into the differential equation and solving for the coefficients. Once the coefficients are found, the general solution is obtained by adding the complementary solution (from the corresponding homogeneous equation) and the particular solution.

It’s important to note that the method of undetermined coefficients is not applicable for all non-homogeneous equations. In cases where it is not suitable, other techniques like the variation of parameters method may be used instead.