4. (2 points) a) Solve the following initial value problem Tư +99 = 1 (t) -...
(2 points) Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function. yy1+(t-4), y(0)0. a. Find the Laplace transform of the solution. Y(s) = L {y(t)) = b. Obtain the solution y(t) C. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t = 4. if 0st<4, y(t) if 4t< o0.
(1 point) Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function. y" + 167²y = 418(t – 4), y(O) = 0, y'(0) = 0. a. Find the Laplace transform of the solution. Y(s) = L {y(t)} = b. Obtain the solution y(t). yt) = c. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t =...
(1 point) Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function a Find the Laplace transform of the solution. b. Obtain the solution y(t) u(t)- C. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution att 1 İf 0 < t < 1, y(t) if 1 t<oo.
5. (11 points) Solve the following initial value problem, y" + 3y + 2y = g(t); y(0) = 0, 7(0) = 1/2 where g(t) = 38(t - 1) + uz(t) Type here to search
Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function.y′+y=7+δ(t−1),y(0)=0.Find the Laplace transform of the solution. Y(s)=L{y(t)}=Obtain the solution y(t). y(t)=Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t=1. y(t)= { if 0≤t<1, if 1≤t<∞.
(1 point) Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function. "8 6(t 1), y(0) = 3, /(0) = 0. a. Find the Laplace transform of the solution. Y(8)= L{y(t)} = | (3s+e^(-s)-24)/(s^2-8s) b. Obtain the solution y(t) y(t)=1/8(e^(8t-8)-1 )h (t- 1 )+6e^(8t)-3 c. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t 1. if...
Please help both questions, thanks (1 point) Let g(t) = e2 a Solve the initial value problem 4 – 2 = g(t), using the technique of integrating factors. (Do not use Laplace transforms.) y(0) = 0, (t) = b. Use Laplace transforms to determine the transfer function (t) given the initial value problem 6' - 24 = 8(t), (0) = 0. $(t) = c. Evaluate the convolution integral (6 + 9)(t) = Sølt – w)g(w) dw, and compare the resulting...
(1 point) Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function. a. Find the Laplace transform of the solution. b. Obtain the solution y(t) y(t) c. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t-5 y(f)- if5<t<oo.
1. (Exercise*) Solve the first order initial value problem y + 2y =t(ui(t) – uz(t)) subject to y(0) = 0.
Use Laplace Transform to solve this problem: Determine the solution of the following initial value problem y"(t) + 3y'(t) + 2y(t) = f(t), y(0) = 0, y'(0) = 0. where f(t) = 1 when t lies between 2n and 2n + 1, and f(t) = 0 when t lies between 2n – 1 and 2n (for non-negative integers n). This is a square-wave forcing term.