MATH 3400 Final: Math3400 Final Exam Solution
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The rst 20 (multiple-choice) problems are 5 points each, the remaining 5 (essay) problems are 10 points each (show all work to get full credit on the essay problems): (circle all that apply!) The di erential equation x dy dx (a) separable, (b) linear, (c) homogeneous, (d) exact. Answer: (b), (c), (d: the general solution of the equation x + 5x = 3 is (a) x(t) = 3. 5 + e 5t (b) x(t) = 3 + c sin 5t (c) x(t) = 3. Answer: (d: a solution of the initial value problem y + 8y = 1 + e 6t is. 8 e 8t (c) x(t) = 4 e2t + 3e8t (d) x(t) = 4 e 2t + 3e 8t. Answer: (b: two linearly independent solutions of the equation y + y 6y = 0 are (a) e 3x and e2x, (b) e 2x and e3x, (c) e x and e6x, (d) e 6x and ex.
