Please answer questions clearly

(20 points) Novel problem not in text. The driving function and particular solution that define a second order differential equation U\" + bv' + CD = USU), are given by vs(t) = (Ge4' + 12)u(t), and vp(t) = (3e'4' + 3)u(t) What are the constants b and c? b = help (numbers) c = help (numbers) (20 points) This problem is related to Problems 7.10-7.18 in the text. Instructions for forms of answers in differential equation problems: For second order DEs, the roots of the characteristic equation may be real or complex. If the roots are real, the complementary solution is the weighted sum of real exponentials. Use C1 and CZ for the weights, where C1 is associated with the root with smaller magnitude. If the roots are complex, the complementary solution is the weighted sum of complex conjugate exponentials, which can be written as a constant times a decaying exponential times a cosine with phase. Use C1 for the constant and Phi for the phase. (Note: Some equations in the text give the constant multiplying the decaying exponential as 201. This was done for the derivation. The constant for this problem should be Ct alone.) All numerical angles(phases) should be given in radian angles (not degrees). Given the differential equation y" + 8y' + 25y = 7u(t) a. Write the functional form of the complementary solution, yc (t). yc (t) = help (formulas) b. Find the particular solution, yp(t). J'pU) = help (formulas) c. Find the total solution, y(t) for the initial conditions y(0) = 1 and J/ (0) = 15. y(t) = help (formulas)