Find the solution of the following Initial Value Problem by using the Laplace Transform. In your...
Find the solution of the following Initial Value Problem by using the Laplace Transform. In your answers, always write y(t) or Y(s), not just y or Y. If you need a Heaviside function, write U(t) or U(t-a). y"(t) – 6 y'(t) + 9 y(t) = S(t-4) y(0) = 2 y'(0) = 3 L(y(t)) = Y(s) (y(t)) = LTY"(t)) = (52 - 6 5 + 9) Y(s) = Set up and solve the partial fraction decomposition of y(s) Y(s) = 2^3...
-16 points 17. Find the Laplace transform Y(s) of the solution of the given initial value problem. Then invert to find y(t). Write u for the Heaviside function that turns on at cnot u(t y"36y = e-2u y(0) 0 y'(O) = 0 Y(s) y(t) Submit Answer Save Progress Practice Another Version -16 points 17. Find the Laplace transform Y(s) of the solution of the given initial value problem. Then invert to find y(t). Write u for the Heaviside function that...
Find the Laplace transform y(s) of the solution of the given initial value problem. Then invert to find y(t). Write uc for the Heaviside function that turns on at c. not uc(t). S1, y" + 4y = ost< 2, y(0) = 6, 7(0) = 8 lo, 2 St<00; Y(s) = y(t) =
(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
Question (2): Laplace Transformsa) Find the Laplace Transform of the following using the Laplace Transform table provided in the back:$$ f(t)=\frac{1}{4}\left(3 e^{-2 t}-8 e^{-4 t}+9 e^{-6 t}\right) u(t) $$b) Find the inverse Laplace Transform \(F(s)\) of the following function \(f(t)\) using the table:$$ f(t)=\frac{12 s^{2}(s+1)}{\left(8 s^{2}+5 s+800\right)(s+5)^{2}(10 s+8)} $$
where h is the Use the Laplace transform to solve the following initial value problem: y"+y + 2y = h(t – 5), y(0) = 2, y(0) = -1, Heaviside function. In the following parts, use h(t – c) for the shifted Heaviside function he(t) when necessary. a. First, take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation and then solve for L{y(t)}. L{y(t)}(s) = b. Express the solution y(t) as the...
Find the Laplace transform Y(s) Ay) of the solution of the given initial value problem. A method of determining the Problems 21 through 24 in Section 6.1. Y"+9 = {1, isted y(0) = 8, y(0) = 3 Y(s) =
Solve initial value problem using Laplace transform Problem 4 Solve the initial value problems given below --ез, y(0) 2. a. b. f ty 3 cos t, y(0)-
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
Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below. y" - 25y = g(t), y(0) = 1, y'(0) = 4, where g(t)= [ t, t>2 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. Y(s) (Type an exact answer in terms of e.)