Question

# 3. Plot the rough solutions of the following differential equations. You can use your hand (preferably), or wolfram alpha, or you can solve in MATLAB. I just need a rough shape of the plot, no numbers!Only plot the part of the solution for t = 0 to t = 10. But please write the poles for each case. a. ÿ +ỷ + 2y = 2 unit(t), with initial conditions y(0) = 0.5 , y(0) = 1 (under-damped 2nd od.) b. ÿ + ỷ + 2y = 0, with initial conditions y(0) = 0.5 , ý(0) = 1 (under-damped 2nd od.) c. ÿ + ỷ + 2y = 28 (t), with initial conditions y(0) = 0.5 , ý(0) = 1 (under-damped 2nd od.) d. ÿ + ỷ + 2y = 2t, with initial conditions y(0) = 0.5, y(0) = 1 (under-damped 2nd od.) e. ÿ + ỷ + 2y = 2 sin(6t), with initial conditions y(0) = 0.5 , y(0) = 1 (under-damped 2nd od.) f. ÿ - ý + 2y = 2 unit(t), with initial conditions y(0) = 0.5 , ý(0) = 1 (unstable 2nd od.) g ÿ + 2ý + y = 2 unit(t), with initial conditions y(0) = 0.5, y(0) = 1 (critically damped) h. ÿ +3ỷ + y = 2 unit (t), with initial conditions y(0) = 0.5 , ÿ(0) = 1 (overdamped 2nd od.)  Fig: 1  Fig: 2  Fig: 3  Fig: 4  Fig: 5  Fig: 6  Fig: 7  Fig: 8  Fig: 9