1. (18 pts) Find the suitable form for the general solution y(t) if the method of undermined coefficients is to be used. YOU DON'T NEED TO FIND THE COEFFICIENTS. (a) y"+2y=3t2 + 4te-2t, (b) y" + 2y +5y=7e- sin 2t+ 3te cos 2t. 2. Determine the constant. (a) (4 pts) Find the value of k given that the period is 57 for the motion described by 25y"+ky = 0. (b) (4 pts) Find the value of 7 for the critically damped motion described by 4y"+y+9y=0. (c) (4 pts) Find the value of w such that the solution to the following equation exhibits resonance 3u"+75u8 cos wt.