Variation of Parameters

The Variation of Parameters is a method used to solve non-homogeneous differential equations. It is particularly useful when the non-homogeneous term is not easily solvable using other techniques like the method of undetermined coefficients.

The Variation of Parameters method involves finding a particular solution to the non-homogeneous equation by replacing the constants in the complementary solution (obtained from the corresponding homogeneous equation) with functions of the independent variable. Once these functions are found, the general solution is obtained by adding the complementary and particular solutions. This technique can be applied to both linear and nonlinear differential equations and can be extended to higher-order differential equations as well.