4) Use Laplace Transform to solve the DE y' +6y=4et where y(0) = 2

Use Laplace transform technique to solve y"+2y +2y=e-t, y(0) = - 4, y'(0) = -2

use Laplace transform to solve IVP a) y'-3y = 4, y(0) = 0

-Obtain the Fourier transform of f(t) = sin (3t) -t²+7it+12

Solve the problem using Laplace transform

Find the fourier transform for the known function |A(sinh ot + cos wt) f (t) = { if -astsa %3D otherwise

Use the Laplace transform to solve the initial value problem ty''+(4t-2)y'+(13t-4)y=0,y(0)=0,y'(0)=0

Use Laplace transforms to solve the IVP y''-y=0, y(0)=2, y'(0)=3. Show the complete solution.

Use convolution and Laplace transform to evaluate y''+y=sin(t) , y(0)=1 , y'(0)=-1

h(t)=t^2sin(3t) laplace transform