For each of the non-homogeneous linear DEs in Problems
(a) Verify that the given y1, y2, y3 satisfy the corresponding homogeneous equation.
(b) Use the Superposition Principle, with appropriate coefficients, to state the general solution Yh (t) to the corresponding homogeneous equation.
(c) Verify that the given Yp(t) is a particular solution to the given non-homogeneous DE.
(d) Use the Non-homogeneous Principle to write the general solution y(t) to the non-homogeneous DE.
(e) Solve the /VP consisting of the non-homogeneous DE and the given initial conditions
y"' - y" - y' + y = 2t - 1 + 3e2t
y1 (t) = et, y2 (t) = tet, y3 (t) = e-t
yp(t) = 2t + l + e2t
y(0) = 4. y'(0) = 3, y"(0) = 4