Problem #9: (a) Given the initial value problem
y' + 3y = 10 sin t, y(0) = 5,
find the Laplace transform of the solution Y(s).
(b) Using the Laplace transform, Y(s), find y(t), the solution to our initial value problem.
*Don't forget: Your answer should be a function of t.
(A) $\frac{5}{s+3} + \frac{4}{s^2+1}$ (B) $\frac{35}{s+3} + \frac{30}{s^2+1}$ (C) $5 + \frac{30}{s+3} + \frac{30}{s^2+1}$ (D) $5 + \frac{1}{s+3} - \frac{s-3}{s^2+1}$ (E) $\frac{5}{s+3} - \frac{s}{s^2+1}$
(F) $\frac{30}{s+3} + \frac{30}{s^2+1}$ (G) $\frac{1}{s+3} - \frac{s-3}{s^2+1}$ (H) $\frac{6}{s+3} - \frac{s-3}{s^2+1}$
