Express the solution of the initial value problem in terms of a convolution integral. (Do not...
Question 5: (17 points) Use Laplace transform to solve the initial value problem V" - 4y + 4y = 2.814 -- 3)y(0) = 1, (0) = 2 (If you use convolution theorem for an inverse Laplace transform, you need to compute the integral to express your answer explicitly in terms of t.)
Use the convolution theorem to obtain a formula for the solution
to the initial value problem.
y ′′ + y = g, y(0) = 0, y′ (0) = 1 , where g = g(t) is a given
function.
1. (10 pts) Use the convolution theorem to obtain a formula for the solu- tion to the initial value problem y"+y=g, y(0) = 0, y'(0) = 1, where g = g(t) is a given function.
2. Consider the following initial value problem i-6 8 2e-3t. (0)0, (0) = 0. = (a) Using Laplace transforms find the Green's function g(t) of the initial value problem (b) Hence write down the solution to the initial value problem as a convolution integral Do not evaluate the convolution integral
2. Consider the following initial value problem i-6 8 2e-3t. (0)0, (0) = 0. = (a) Using Laplace transforms find the Green's function g(t) of the initial value problem (b)...
Express the solution of IVP of the function in terms of a convolution integral
(t)= . Use the Laplace transform to solve the following initial value problem: 44" + 2y + 18y = 3 cos(3+), y(0) = 0, y(0) = 0. 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)}. Do not perform partial fraction decomposition since we will write the solution in terms of a convolution integral. L{y(t)}(s) b. Express the solution y(t) in terms of a...
Please show work, thanks.
(2) Express the solution of the given initial-value problem in terms of an integral-defined function. 3,94 + (6 cosa)y=f, y0)=1
Use the Laplace transform to solve the following initial value problem: 44" + 2y + 18y = 3 cos(3t), y(0) = 0, y(0) = 0. 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)}. Do not perform partial fraction decomposition since we will write the solution in terms of a convolution integral. 3s L{y(t)}(s) = (452 + 25 +2s + 18)(52+9) b. Express the...
(1 point) Let g(t) = e2t. a. Solve the initial value problem y – 2y = g(t), y(0) = 0, using the technique of integrating factors. (Do not use Laplace transforms.) y(t) = b. Use Laplace transforms to determine the transfer function (t) given the initial value problem $' – 20 = 8(t), $(0) = 0. $(t) = c. Evaluate the convolution integral (0 * g)(t) = Só "(t – w) g(w) dw, and compare the resulting function with the...
convolution
3. Find a formula for the solution of the initial value problem. (d) y" + k2y: y'(0) f(t), y(0) 1, -1
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...