Problem 1: Find the time-domain solution for the following differential equation using Laplace transforms: dt2d2x+5dtdx+6x=u(t);dtdx(0)=x(0)=0 where u(t) is the unit ramp function. Before you invert, comment on the qualitative nature of the solution asymptotically in terms of possible oscillatory, convergent or divergent behavior and calculate the final value. Problem 2: Find the time-domain solution for the following differential equation using Laplace transforms: dt4d4x+dt3d3x=cost;x(0)=dtdx(0)=dt3d3x(0)=0,dt2d2x(0)=1 Before you invert, comment on the qualitative nature of the solution asymptotically in terms of possible oscillatory, convergent or divergent behavior and calculate the final value