Consider the following nonhomogeneous linear differential equation, y" +y' +y = 4e4" (cos(x) – sin(x) Find the particular solution satisfying the equation, if the particular integral is y, = 2e"...

Extracted text: Consider the following nonhomogeneous linear differential equation, y" +y' +y = 4e4" (cos(x) – sin(x) Find the particular solution satisfying the equation, if the particular integral is y, = 2e" cos(x) and the initial conditions are y(0) = 0 and y' (0) = 1.