Find the general solution of the ordinary differential equation
d4y/dx4 + 4y = sin2x + 2x + ex.
m4 = −4 =⇒ m = 1 + i, −1 + i, −1 − i, 1 − i.
Thus the complementary solution is
Y(x) = ex (acosx + bsinx) + e−x (ccosx + dsinx).
A particular solution is
