Coefficient Cancelation on Particular Solution

1. Why do we use undetermined coefficients?
2. What is the difference between general solution and particular solution?
3. How do you find the YP of a differential equation?

Why do we use undetermined coefficients?

In mathematics, the method of undetermined coefficients is an approach to finding a particular solution to certain nonhomogeneous ordinary differential equations and recurrence relations.

What is the difference between general solution and particular solution?

The general solution includes all possible solutions and typically includes arbitrary constants (in the case of an ODE) or arbitrary functions (in the case of a PDE.) A solution without arbitrary constants/functions is called a particular solution.

How do you find the YP of a differential equation?

ay + by + cy = 0 and yp is the particular solution. To find the particular solution using the Method of Undetermined Coefficients, we first make a “guess” as to the form of yp, adjust it to eliminate any overlap with yc, plug our guess back into the originial DE, and then solve for the unknown coefficients.