10. Use the Laplace transform to solve y" - 3y' +2y f(t), y(0)-0,'(0) 0, where (t)-(0...
2. Use the Laplace Transform to solve the initial value problem y"-3y'+2y=h(t), y(O)=0, y'(0)=0, where h (t) = { 0,0<t<4 2, t>4
Page 4 IV. (10) Use the Laplace transform to solve the IVP y" - 2y + y = f(t), y(0) = 1, 7(0) = 1, where t<3 f(t) = t-3, t3 You may use the partial fraction decomposition 70-28+1) -1,2 = (+*++* - , but you need to show all the steps needed to arrive to the expression (+28+1) in order to receive credit.
Page 4 IV. Use the Laplace transform to solve the IVP y' - 2y + y = f(t), y(0) = 1, v/(0) = 1, where (10) 0, t <3 f(t) = t-3, 3 You may use the partial fraction decomposition 16–25+1) 5+(9–1 = (-) + ? + - , but you need to show all the steps needed to arrive to the expression - 022-28+1) in order to receive credit.
Use the Laplace transform to solve the given initial-value problem. so, 0 <t< 1 y' + y = f(t), y(0) = 0, where f(t) 17, t21 y(t) = + ult-
So, 0St<4 6. Define f(t) = 34 Use the Laplace transform to solve th /' + 2y + y = f(t), t€ (0,00) | M(0) = 0 7(0) = 0
Use the Laplace transform to solve the given initial-value problem. 0 st<1 t 1 y' y f(t), y(0) 0, where f(t) (4, ae-1 -(1-1) 4 y(t) X Use the Laplace transform to solve the given initial-value problem. 0 st
QUESTION 3 Use Laplace Transform to solve the initial value problem y" + 9y = f(t) ,y(0) = 1, y'(0) = 3 where 6, f(t) 0 <t<nt i < t < 0
3. Find the Laplace transform off, where f(t) = 3 + 2 if Ost <3, f(t) = 0 if 3 st < 6 and f is periodic with period 6. 4. Solve y" - 16y = 40e4t y(0) = 5, y(0) = 9 using the Laplace transform.
6 (5) Solve the differential equation using a Laplace Transform: y 3y' +2y t y(0) 0, y'(0) 2
Use the Laplace transform to solve the initial value problem: y" - 3y' + 2y = 4t + ezt, y(0) = 1, y'(0) = -1