Find the Laplace Transform. 4.y"-4y"+2y-cosht = 0) where : y"(0) = 0, y'(0) = 2, and...
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
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)
2. Use the Laplace transform to solve Y" – 2y = 2 y(0) = 0, y'(0) = 0
solve the following using laplace transform y" + 4y + 4y = t4e-2t; y(0) = 1, y'(0) = 2 +
17. Use the Laplace transform to solve the initial value problem: y" + 4y' + 4y = 2e-, y(0) = 1, (O) = 3. 18. Use the Laplace transform to solve the initial value problem: 4y" – 4y + 5y = 4 sin(t) – 4 cos(1), y(0) = 0, y(0) = 11/17.
Solve the following IVPs using Laplace Transform: 3) y" + 4y' + 4y = t4e-2t; y(0) = 1, y'(0) = 2
(4 points) Use the Laplace transform to solve the following initial value problem: y" – 2y + 5y = 0 y(0) = 0, y'(0) = 8 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 = 01 Now solve for Y(3) By completing the square in the denominator and inverting the transform, find g(t) =
Some the following DE's using Laplace Transform. 1) <3> y - 2 y = a* (0) = | (<4> Y" + 4y' + 4y = 0; Y(0) = 2 ; Y6u =-| - <s> Y" + 4y = f coszt, y(o)= 0; y(o)=4
Solve using Laplace transform: y"-4y'=5e^x, y(0)=0, y'(0)=1
Page 4 IV. Use the Laplace transform to solve the IVP y' - 2y + y = f(t), y(0) = 1, v/(0) = 1, where (10) 0, t <3 f(t) = t-3, 3 You may use the partial fraction decomposition 16–25+1) 5+(9–1 = (-) + ? + - , but you need to show all the steps needed to arrive to the expression - 022-28+1) in order to receive credit.