4. A DC voltage v(t) = u(t) Volt is applied to a circuit, and a current i(t) = sin(wt) u(t) Amperes results. u(t) denotes the unit-step function. What is the circuit? Hint: Think in the Laplace transform domain.

Use integration to find the Laplace Transform of the following time domain func-tions. Simplify your answers to have a common denominator.

The Laplace Transform can be used to solve differential equations using a four step process. 1.Take the Laplace Transform of the differential equation using the derivative property (and, perhaps, others) as necessary.2.Put initial conditions into the resulting equation.3.Solve for the output variable.4.Get result from Laplace Transform tables which in the picture.  If the result is in a form that is not in the tables, you'll need to use the Inverse Laplace Transform. Solve the following DE using Laplace Transform Method:1. f(x) = e-2x (1-2x)

LAPLACE TRANSFORM ( NEED ONLY HANDWRITTEN SOLUTION PLEASE OTHERWISE DOWNVOTE).