CHE 321 Midterm: CHE 321 SBU CHE321 Exam 2 15
Document Summary
Hint: you need to sketch two di erent phase-plane portraits. Problems 3 and 4 are on the back (a; 20pts) find the general solution (x, y) = (x(t), y(t)) to the system of odes. Problem 3 (30pts) (x = 4y x y = x + 2y (b; 8pts) sketch the phase-plane portrait, in the xy-plane, for the system of odes in (a). In particular, indicate the slope of every relevant line, the ow directions, and the asymptotic behavior of the solution curves. You may want to state some of this information next to the sketch. Sketch at least two solution curves in each region cut out by the half-line solutions. (c; 2pts) determine whether the origin is a stable, asymptotically stable, or an unstable equilibrium point. Explain why. (a; 12pts) let a be a square matrix. Write down the power-series de nition of ea and use it to show that. Problem 4 (30pts) if b =(cid:18) 0 0.
