Find a particular solution of the differential equation -(5/4)y" + 2y' + y = 3x*e^(3x)
using the Method of Undetermined Coefficients (primes indicate derivatives with respect to x).
Find the following particular solution
yp= ?

Note that the characteristic solutions to this ODE are and , so we can safely assume a particular solution of the form

with derivatives

Substitute these expressions into the ODE and solve for a and b. Notice that each term on either side contains a factor of , which we can cancel.

So the particular solution is

1 + (6 / x - 1)

step-by-step explanation:

divide using polynomial division.