6 (5) Solve the differential equation using a Laplace Transform: y 3y' +2y t y(0) 0,...
3. Using Laplace transform, solve the differential equation y" +2y' +y=te* given that y(0) = 1, y'(0)= -2.
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) +
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)
4. Solve the given differential equation (i.e., find y(t)) using Laplace transform method: and subject to the conditions that yo) = 0 and y” + 2y'+y=0 y’0) = -2. 21
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
(6 points) Use the Laplace transform to solve the following initial value problem: y" + 3y' = 0 y(0) = -3, y'(0) = 6 First, 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 = 0 = = + Now solve for Y(s) and write the above answer in its partial fraction decomposition, Y(s) where a <b Y(S) B s+b sta + Now...
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
Q- Solve the problem by Laplace transform, y + 3y = 6, given that at t=0, y=1, then take inverse Laplace transform to get y(t).
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 using the method of the laplace transform. y"-4y'+3y=e^t,y(0)=0,y'(0)=5