QUESTION 12 Apply Laplace Inverse to find f(t): s +7 F(s) = 5(52 + 4s +3)…

QUESTION 12 Apply Laplace Inverse to find f(t): s +7 F(s) = 5(52 + 4s +3) Choose the correct answer: L-‘[F(s)] = f() 1) f(1) = 4t’e-31 – 3e-+ + 7t 2) f(t) = 5t? – 3e-4 3) f(0) =2-31 – 3e– + 4) f() = 6e-6 – e-31 +} QUESTION 13 Solve the ODE: 2 2 + 3ź – 2z = te-2 z(0) = 0 & ż(0) = -2 Choose the correct answer: 1) z(t) = -0.768 0.5t – 0.1t2e-2t 2) z(t) = -0.768 0.5t + 0.768 e-2t – 0.08 te-2 – 0.1t?e-2 3) z(t) = 0.768 e-2t – 0.1t²e-2t 4) z(t) = -0.382 0.5t + 0.768 -2t + 12 t3e-2t – 0.1t2e-2t 5) z(t) = -0.78 e-+ – 0.08 te-3t -0.102e-2t