Answers to 2250 midterm 1, first 4 problems, Spring 2003

1. y = x^5/60 + 5x^2/24 + x/4 -65/432
       +x exp(-2x)/8 +3 exp(-2x)/16 -cos(3x)/27

2. Equil sols y = 1/4, y = -1/4. Non-equil sol
   y = (1/4)(top/bot), 
       top = A exp(4 sin x) - sin^4(x), 
       bot = A exp(4 sin x) + sin^4(x)

3. y = x^(-5/2)[[ -x^2/4 -x/4 -1/8]exp(-2x) + c]
       c = 4 + 5exp(-2)/8

4. (6/13) y^(13/6) = At+c, 
   c = (6/13) (20)^(13/6),
   1.25 A = (6/13)(12)^(13/6)-c
   t = 37 minutes or 0.61 hours
   Sanity: it drains to 12 ft in 1.25 hours, likely 1/2 that to finish.