Part B (5 points each] An initial value problem y' + 2y = f(©),y(0) = 0...
Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below. y'' + 2y = 2t4, y(0) = 0, y'(0) = 0 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. Y(s) = Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below. y" -7y' + 12y = 3t e 3t, y(0) = 4, y'(0) = -1 Click...
a) Find the general solution of the differential equation Y'(B) + 2y(s) = (1)3 8>0. b) Find the inverse Laplace transform y(t) = --!{Y(s)}, where Y(s) is the solution of part (a). c) Use Laplace transforms to find the solution of the initial value problem ty"(t) – ty' (t) + y(t) = te", y(0) = 0, y(0) = 1, fort > 0. You may use the above results if you find them helpful. (Correct solutions obtained without Laplace transform methods...
(5 points) Consider the following initial value problem: Y" - 2y - 35y = sin(4t) y(0) = 3, y'(0) = -4 Using Y for the Laplace transform of y(t), i.e., Y = L{y(t)}, find the equation you get by taking the Laplace transform of the differential equation and solve for Y(S) = (35+2)/(s^2-25-35)+4/((s^2-28-35)*(s^2+16))
Consider the initial value problem for function y, y" – ' - 20 y=0, y(0) = 2, 7(0) = -4. a. (4/10) Find the Laplace Transform of the solution, Y(8) = L[y(t)]. Y(8) = M b. (6/10) Find the function y solution of the initial value problem above, g(t) = M Consider the initial value problem for function y, Y" – 8y' + 25 y=0, y(0) = 5, y(0) 3. a. (4/10) Find the Laplace Transform of the solution. Y(s)...
Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below. y" +2y = 2+2 -7,y(0) = 0, y'(0) = - 3 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. Y(s)-
1. (5 points) Use a Laplace transform to solve the initial value problem: y' + 2y + y = 21 +3, y(0) = 1,5 (0) = 0. 2. (5 points) Use a Laplace transform to solve the initial value problem: y + y = f(t), y(0) = 1, here f(0) = 2 sin(t) if 0 Str and f(0) = 0 otherwise.
Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below. y'' + 2y = 562 - 6, y(0) = 0, y'(O) = - 6 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. Y(s) = 1
Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below. y" +2y = 62 -9, y(0) = 0, y'(0) = -6 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. Y(s) =
(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...
Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below y+2yt22, y(0) = 0, y'(0) = - 2 Click here to view the table of Laplace transforms Click here to view the table of properties of Laplace transforms Y(s)= Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below y+2yt22, y(0) = 0, y'(0) = - 2 Click here to view the table of Laplace transforms Click here...