MATH 0290 Final: Math 0290 Final Exam (0290) 2017 Sping -198
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Show all your work (no work = no credit). Simplify your answers when possible: consider the following ordinary di erential equation (ode) y + Page 2: (15 points) find the solution to the previous ode y + y = 2 sin t that satisfy the initial conditions y(0) = 0, y (0) = 1. 1 s2 (s2 + 1)2 = d ds (cid:18) s s2 + 1(cid:19) (cid:21) Page 3: for the system of nonlinear di erential equations x = x(3 x y) y = x 2y (a) (5 points) find x-nullcline and y-nullcline. Draw a plot. y x (b) (5 points) find equilibrium points. Page 4 (c) (5 points) find jacobian matrix at every equilibrium point. Determine types of all equilibrium points of the given nonlinear system. If the type cannot be determined, explain why. (d) (5 points) for the most left equilibrium point nd eigenvalues of the corresponding linear system and its eigenvectors.
