The current I=-10e^-2t,Find the voltage of the source Vs?
In using 1/s for the capacitor, you've forgotten about initial conditions.

At t=0 the voltage across the capacitor is -10V. Either that voltage has been generated by V(s) (unlikely, if not impossible), or the capacitor has an initial condition of -10V. Try including this in your Laplace formulation.

In this problem you have been told the I.C. implicitly by being given the current through R, and consequently the voltage across C, so the I.C. is already taken care of in the differential equation solution.