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TEXAS A&M UNIVERSITY DEPARTMENT OF MATHEMATICS MATH 308-502 Exam 1 version A, 3 Oct 2014 On my honor, as an Aggie, I have neither given nor received unauthorized aid on this work. Name (print): No detailed analytical work — no points. Each question is worth 5 points 1. Find the solution of dy = 6e2x−y , dx y(0) = 0. 2. Find the solution of (1 + x)y 0 + y = cos x, y(0) = 1. 3. Find the general solution (implicit is ok) of (6xy − y 3 )dx + (4y + 3x2 − 3xy 2 )dy = 0. 4. Find the general solutions of 1. y 00 + 6y 0 + 7y = 0, 2. y 00 + 6y 0 + 9y = 0, 3. y 00 + 6y 0 + 10y = 0. 5. Find the solution of y 00 + ω02 y = sin(ω0 t), Points: y(0) = 0, y 0 (0) = 0. /25