Please answer questions clearly

(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 01 and CZ for the weights, where 01 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. All numerical angles(phases) should be given in radian angles (not degrees). Remember to use u(t) in Webwork answers when the solution is fort z 0. Given the differential equation y\" + 14y' + 45y = 2u(t) . a. Find the functionalwform of the complementary solution, y,,. (t). Yea) = help (formulas) b. Find the particular solution, yp(t). Yp(t) = help (formulas) c. Find the Wditions y(0) = 13 and y' (0) = 8. y(t) = help (formulas) (20 points) This problem is related to Problems 7.1 (3-7.1 8 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. All numerical angles(phases) should be given in radian angles (not degrees). Given the differential equation y" + 7y' + 10y = 6cos(4t + 0.785398)u(t) . a. Find the functional form of the complementary solution, yc (t). yc(t) = help (formulas) b. Find the particular solution, yp(t). yp(t) = help (formulas) c. Find the total solution, y(t) for the initial condition y(0) = 3 and y' (0) = 6. W) = help (formulas) Note the answers are checked to an absolute accuracy of 0.01