Find the complete time-domain solutions for the following differential equations using Laplace transforms:

(d) A process is described by two differential equations

If x₁ = e^?t and x₂ = 0, what can you say about the form of the solution for y₁? for y₂?

d'x + 4x = e with x(0) = 6, dx(0) (a) 0, dt d'x(0) -0% di dx (b) - 12x = sin 3t x(0) 0 dx(0) dx (e) + 25x = e- x(0) = 0, di dt