Solve the differential equation using the method of undetermined coefficients

a) 4y" - 4y'-3y = cos2x

First: the homogeneous solutions: the characteristic equation is4r^2 - 4r - 3 = 0which has roots r = 3/2, - 1/2 hence the homogeneous solution isy = c1. exp (-x/2) + c2. exp (3x/2)

next you need the general form for the guess for yp and that isyp = A1cos (2x) + A2sin (2x)

Now substitute that into the equation and solve for A1, A2.