In problems 1 to 3 solve the given differential equations by writing the general solution. Write all steps of the solution. 3. y" + 8y' + 16y = e + (t° + 5) e*

A ball is dropped from a height of 16 feet. Each time it drops h feet, it rebounds 0.64h feet. The ball takes the following times for each fall. S1 = -16t + 16, S1 = 0 when t = 1 s2 = -16t2 + 16(0.64), S3 = -16t2 + 16(0.64)², S4 = -16t2 + 16(0.64)³, S2 = 0 when t = 0.8 S3 = 0 when t = (0.8)2 S4 = 0 whent = (0.8)3 Sn = -16t2 + 16(0.64)" - 1, Sn = 0 whent = (0.8)" - 1 Beginning with s2, the ball takes the same amount of time to bounce up as it does to fall, and so the total time elapsed before it comes to rest is given by t = 1 + 2 (0.8)". n = 1 Find this total time. sec

5. Solve: 4(x-x)=-7.

Why  is Y1 not multiplied by 2/(s+7) when solving for Y2