QUESTION 3 Use Laplace Transform to solve the initial value problem y" + 9y = f(t)...
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-
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
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>,
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
Find the Laplace transform Y(s)=L{y} of the solution of the given initial value problem. Enclose numerators and denominators in parentheses. For example, (a−b)/(1+n). y" +9y S t, 0<t<1 1, 1<t< , y(0) = 7, y' (0) = 4
Q1) Solve the following DE: (Using Laplace transform is recommended) y" + 5y' – 6y = f(t), y(0) = 0, y'(0) = 0, where 0 <t< 2 f(t) = {-4 t>2 1
(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
(1 point) Consider the following initial value problem: y" +9y (st, o<t<8 y(0) = 0, '(0) = 0 132, ?> 8 Using Y for the Laplace transform of y(t), i.e., Y = C{y(t)} find the equation you get by taking the Laplace transform of the differential equation and solve for Y(8)
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