How Do You Solve a 2nd Order Inhomogeneous ODE with Given Initial Conditions?

[andrey21]

1. Using the complementary function and particular integral method find the solutio of the differential equation.

d2y/dx^2 + 3 dy/dx +2y = 20cos2x

Which satisfies y(0) = 1 y'(0) = 0

Homework Equations

The Attempt at a Solution

 

[Roni1985]

there are different ways to solve this differential equation.
I know you can solve it with the method of undetermined coefficients OR Variation of Parameters.

 

[andrey21]

I have already found the complementary function to be:

y = Ae^(-t) + Be(-2t)

Im just not sure how to find the particular integral!

 

[Mark44]

Try y_p = Ccos(2x) + Dsin(2x) for your particular solution.

Minor note: The independent variable should be x, not t, since x is the independent variable in your differential equation.