MATH 0290 Midterm: Math 0290 Exam 1 (0290) 2015 Fall -182
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Show all your work (no work = no credit). Simplify your answers when possible: (10 points) a 0. 25 kg mass is attached to a spring having a spring constant 9 kg/s2. The system is displaced 0. 3 m from its equilibrium position and released from rest. If there is no dumping present, nd the amplitude, frequency, and phase angle of the resulting motion. Find the interval of existence of the solution. Mention type of the given di erential equation. (a) (15 points) y ln y + x y = 0, y(1) = e 2, where y = dy dx (b) (15 points) (x2 + 1)y + 2xy = 6x, y(0) = 1. In the previous problems it was proven that y1 = et, y2 = e 4t solutions of the homogeneous equation y + 3y of the equation form the fundamental set of. Use this result to nd a general solution y + 3y .
