MATH 307 Midterm: MATH 307 UW 307 Su10 Sol1
Document Summary
Math 307, sections a, b and c, summer 2010, solutions to midterm i: for the di erential equation dy dt. = y2(9 y2), < y0 < , sketch the graph of y versus y2(9 y2), determine the critical (equilibrium) points, and classify each one as asymptotically stable, unstable, or semistable. Draw the phase line, and sketch several graphs of solutions in the ty-plane. Also, nd and show the values of y where concativity changes. The equilibrium points are 3 (stable), 0 (semistable) and -3 (unstable). Concavity changes when f (y) = 0 or when y = 3 2. 2 : solve the initial value problem. 2y cos t + sin4 t = sin t dy dt y(cid:16) . (t) = e r 2 cos t sin t dt = e 2 ln | sin t| = sin2 t y(t) = sin2 tz sin tdt = sin2 t( cos t + c)
