3 plot the rough solutions of the following differential equations you

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.)