Problems 18 Solve the following ODEs using Laplace transforms: (a) + 23(t) _ у(t) _ 2y(t)' 0 give...
Using Laplace transforms, solve the initial value problem y' = 2y + 3e-t, y(0) = 4, where y' = Note: to check your work, this equation is linear so it is possible to solve using integrating factors also. 17 Marks) Y
SOLVE #3 AND #4 PLEASE
Use the Laplace transformation to solve the IVP. 1. y"-6y' + 9y-24-9t, y(0)-2, y, (0)-0 2. 9y" - 12y'4y50ey(0)--1,y'(0)2 3. У"-2y'--. 1 2 cos(2t) + 4 sin(2t),y(0)-4,y'(0)-0
Use the Laplace transformation to solve the IVP. 1. y"-6y' + 9y-24-9t, y(0)-2, y, (0)-0 2. 9y" - 12y'4y50ey(0)--1,y'(0)2 3. У"-2y'--. 1 2 cos(2t) + 4 sin(2t),y(0)-4,y'(0)-0
problem 20
18-27 IVPs, SOME WITH DISCONTINUoUS INPUT Using the Laplace transform and showing the details, solve 18. 4y"-12y' + 9y-0, y(0)-2/3, y,(0) | 20. у', + IOv, + 24y 14412, y(0) 19/12. y (0)5 th Ze 22. y" +3y' + 2-4t İf 0 < t < 1 and 8 if t > 1; y(0) = 0, y'(0) = 0 23. y" + y,-2y-3 sin t-cos t, (0 < t < 2π), and 3 3 sin 2t - cos 2t,...
III. Solve each of the following IVPs using Laplace Transforms 1, y'+2y = 4-u2(t), y(0) = 1. 2、 y', _ y = 2t, y(0) = 0, y'(0) = a 3· y', _ y =-206(t-3), y(0) = 1, y'(0) = 0. 4· y', + 2y' + 2y = h(t), y(0) = 0,必))-1.
4. Solve the following differential equation by using Laplace Transforms. Y" + 2y' +y = 0, y(0) = 0, y'(0) = 1
Solve the initial value problem below using the method of Laplace transforms. y" - 2y' - 3y = 0, y(0) = -1, y' (O) = 17 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms y(t) = 1 (Type an exact answer in terms of e.)
(1 point) Solve the differential equation -1, y (0)2 y-4y -5t263 (t) y(0) using Laplace transforms. for 0 t3 The solution is y(t and y(t) for t>
(1 point) Solve the differential equation -1, y (0)2 y-4y -5t263 (t) y(0) using Laplace transforms. for 0 t3 The solution is y(t and y(t) for t>
#32
U. + 2y + y + 1 -e: y(0) = 0, y'(o) - 2 In Problems 31-36, determine the form of a particular solution for the differential equation. Do not solve. 31. y" + y = sin : + i cos + + 10' 32. y" - y = 2+ + te? + 1221 x" - x' - 2x = e' cos - + cost y" + 5y' + 6y = sin t - cos 2t 35. y" –...
Solve listed initial value problems by using the Laplace Transform: 7. yll − yl − 2y = 3 e2t y(0) = −1, yl(0) = 5
Solve the initial value problem below using the method of Laplace transforms. y" + 2y-3y® 0, y(0)-2, y'(0)-6