QUESTION 1 Determine the Laplace transform (Y(s) ) for the differential equation below: y"(t)2y'(t)3y(t) 32, y(0)...
Determine the Laplace transform (Y(s)) for the differential equation below: 2y () + Зу() — 32, у(0) — 0, у'(0) — 0, у" (0) — 0 У"(). Y(s) (32) (s^3 +2*s^2 +3s + 0) O Y(s) = (2) /(s^3 s^2 + 2s + 3) Y(s) (3*sA2 + 8"s^1 +15) / (s^3 + s^2 + 2s + 3) = Y(s) (32)/ (s2 2s3) +
6 (5) Solve the differential equation using a Laplace Transform: y 3y' +2y t y(0) 0, y'(0) 2
3. Using Laplace transform, solve the differential equation y" +2y' +y=te* given that y(0) = 1, y'(0)= -2.
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...
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)
1. Use the Laplace transform to convert the following differential equation into s-space and then solve for Y(s): vy(t) +14y(t) = sin(3) + cos(54) (1) 2. Use the Laplace transform to convert the following differential equation into s-space and then solve for Y(s): "(t) + 3y(t) = 2)
3. (30 points). Determine function y(t) from the following differential equation using the Laplace transform d?y dt2 dy. +42 + 3y = 3 dt y(0) = 2, y'(O) = 0
1. Use the Laplace transform to convert the following differential equation into s-space and then solve for Y(s): 1/(t) + 14y(t) = sin(34) + cos(5t). 2. Use the Laplace transform to convert the following differential equation into 8-space and then solve for Y(): y") + 3y(t) = (2)
Q4. Laplace Transforms a) (20 points) Solve the differential equation using Laplace transform methods y" + 2y + y = t; with initial conditions y(0) = y(O) = 0 |(s+2) e-*) b) (10 points) Determine L-1 s? +S +1
2. Use the Laplace Transform to solve the initial value problem y"-3y'+2y=h(t), y(O)=0, y'(0)=0, where h (t) = { 0,0<t<4 2, t>4