Method of Undetermined Coefficients (Second Order Non-Homogeneous Equations)

This ordinary differential equations video explains the method of undetermined coefficients for solving linear non-homogeneous second order equations with constant coefficients. We show the most common forms for the particular function that students new to the method will encounter at first. We introduce the superposition approach to the undetermined coefficients method and solve several examples with different particular functions, including a constant function, linear polynomial, quadratic polynomial, cosine function, and exponential function. Finally, we remind to check for linear independence with the complementary function when choosing the particular function.
0:00 Introduction
1:45 Common Particular Function Forms
2:44 Constant Function Example
5:43 Linear Polynomial Example
9:02 Quadratic Polynomial Example
13:44 Sine/Cosine Example
20:38 Exponential Example
23:07 Linear Independence
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