MATH 251 Midterm: MATH 251 PSU s251Exam 2(su12)
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July 24, 2012 (cid:1)(cid:2)(cid:3) (cid:4)(cid:5) (cid:3) (cid:6)(cid:2) (cid:7)(cid:2) (cid:8)(cid:2) (cid:9)(cid:2) Answer key (form a) y = c1 + c2 t + c3 t2 + c4 cos 4t + c5 sin 4t x. 9cos (a) u + 20u + 100u = 0 (c) 20 tx. 5 cos t sin2 t cos t (b) critically damped (d) k = 144. 2 cos t sin5 t sin t (a) improper node, unstable (c) spiral point, unstable (e) proper node (star point), asymptotically stable (b) node, asymptotically stable (d) center, stable (a) f t t e. 2 (cid:11)(cid:2)(cid:3) (cid:3) (cid:12)(cid:2) (cid:1)(cid:13)(cid:2) (cid:3) t y (a) (b) y(2 ) = 2 3 + 3cos(2 4) 6 te (b) saddle point, unstable (a) (0, 2) and ( 1, 2) (b)
