Use the Laplace transform to solve the given initial-value problem. so, 0 <t< 1 y' +...
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
So 0<t<5 Using the Laplace transform, solve the initial value problem y' + y = 3 t5 y'(0) = 0. 9
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
Solve the following ode using Laplace transform: y' - 5y = f(t); y(0) - 1 t; Ost<1 f(t) = 0; t21
4. Use the Laplace transform to solve the initial value problem y" + y = f(1) = -2, ost<2 13t+4, 122 y(0) = 0, y'(0) = -1
Find the Laplace transform Y(s) = L{y} of the solution of the given initial value problem: 1, y' + 9 = 0<t<T 0,7 <t< y(0) = 5, y'(0) = 4
Use the Laplace Transform to solve each of the following initial-value problem (b) y'(t) + 16y(t) = f(t), y(0) = 2, y'(0) = 1. where f(t) is defined by (t) = , 1, 0 <t<, 10, t>,
10. Use the Laplace transform to solve y" - 3y' +2y f(t), y(0)-0,'(0) 0, where (t)-(0 for 0 st < 4; for t 2 4 No credit will be given for any other method. (10 marks)
(1 point) Take the Laplace transform of the following initial value problem and solve for Y(8) = L{y(t)}; ſ1, 0<t<1 y" – 6y' - 27y= { O, 1<t y(0) = 0, y'(0) = 0 Y(8) = (1-e^(-s)(s(s^2-6s-27)) Now find the inverse transform: y(t) = (Notation: write uſt-c) for the Heaviside step function uct) with step at t = c.) Note: 1 | 1 s(8 – 9)(8 + 3) 36 6 10 + s $+37108 8-9
Find the Laplace transform Y (8) = L {y} of the solution of the given initial value problem. St, 0<t<1 y" + 4y = {i;isica , y0 = 8, Y' (0) = 6 Enclose numerators and denominators in parentheses. For example, (a - b)/(1+n). Y (3) = QE