Question 13 13. If y(t) satisfies DE:y" - 3y' = 4 with IC:y(0) = 0, y'(0)...
QUESTION 1 Determine the Laplace transform (Y(s) ) for the differential equation below: y"(t)2y'(t)3y(t) 32, y(0) = 15, y'(0) 1, y"(0) = 0 Y(s) = (15*s^1 + 63) (SA3S^2 2s + 3) Y(s) (15sA2 + 31 s^1 + 32) /(sA3 + s^2 + 3s + 0) Y(s) (s^2 6*s^1 15) / (s^2 2s 3) 63) / (s^2 2s Y(s) (15*s^1 3) +
Consider the IVP y'' + 3y' + 3y = (1 − u(t − 4)) with y'(0) = 0 and y(0) = 0. Solve the differential equation, and if possible, provide a graph
(1 point) Consider the initial value problem y' + 3y = 0 if 0 <t <3 9 if 3 < t < 5 0 if 5 <t< oo, y(0) = 3. (a) Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of y by Y. Do not move any terms from one side of the equation to the other (until you get to part (b) below). y(s)(5+6)...
Solve: y' – 4y' + 3y = 9t – 3 y(0) = 3, y'(0) = 13 y(t) = Preview
Solve the differential equation below using Laplacian Transformations: Y' – 3y = f(t); y(0) = 0, y (0) = 1 where f(t) = 2, 0 < t <3 13, t > 3 {
Solve the initial value problem y" + 3y' + 2y = 8(t – 3), y(0) = 2, y'(0) = -2. Answer: y = u3(t) e-(-3) - u3(t)e-2(1-3) + 2e-, y(t) ={ 2e-, t<3, -e-24+6 +2e-l, t>3. 5. [18pt] b) Solve the initial value problem y' (t) = cost + Laplace transforms. +5° 867). cos (t – 7)ds, y(0) – 1 by means of Answer:
9. Solve the initial value problem using the Laplace transform y" + 3y = f(t), y(0) = 0, y(0) = 1, where f(t) = { ( 1 home s 2, if 0 <t<5 1, if t > 5 (6
Solve the initial value problem. y'" – 3y" - y' + 3y = 0; y(0)=5, y'0) = -3. y'(0)=5 The solution is y(t) =
10. Use the Laplace transform to solve y" - 3y' +2y f(t), y(0)-0,'(0) 0, where (t)-(0 for 0 st < 4; for t 2 4 No credit will be given for any other method. (10 marks)
The functions (t), y(t) satisfy the system of equations dt d v052(01(0 3y(t) and the initial conditions (0)1 and y(0)4 Suppose that the Laplace transforms of z(t), y(t) are respectively X(s), Y(8). By forming algebraic equations in X(s), Y(8). find and the enter the function X(s), Y(8) below syntax. X(s) Y(s)