Find the function that satisfies the following differential

Question

Repeat given Problem for v_S(t) = 1000e^-200t u (t)V. Plot your result using MATLAB.

Problem

Find the function that satisfies the following differential equation and the initial condition for an input v_S(t) = 10 cos 250 (t) V:

dv(t)/dt + 50v(t) = v_s(t), v(0) = 0V