Final answer:
Variation of parameters is a method used to find a particular solution to a non-homogeneous linear differential equation. It involves finding the complementary solution and assuming a particular solution in the form of a linear combination of functions, which are determined through equating terms in the non-homogeneous equation. The final particular solution is obtained by substituting the determined coefficients.
Step-by-step explanation:
Variation of parameters is a method used to find a particular solution to a non-homogeneous linear differential equation. To use this method, you first need to find the complementary solution, which involves solving the associated homogeneous equation. Then, you need to find a particular solution by assuming that it can be written as a linear combination of functions. These functions are chosen such that their derivatives match the terms in the non-homogeneous equation, but with undetermined coefficients. After substituting this assumed solution into the non-homogeneous equation, the coefficients can be determined by equating the terms on both sides of the equation. Finally, the particular solution is obtained by substituting these determined coefficients back into the assumed solution