MATH 246 Midterm: MATH246 BOYLE-M SUMMER I2005 0101 MID SOL 1

• School: University of Maryland
• Department: Mathematics
• Course: MATH 246
• Professor: All

Document Summary

Math 246-0102 exam 2 solutions boyle. Put a box around the result of a computation. You are allowed one page of notes (both sides): (15 points) find the solution to the initial value problem y + 4y + 13y = 0, y(0) = 1 , y (0) = 16 . The characteristic equation for this di erential equation is r2 + 4r + 13 = 0. The roots of the left side are r = 2 3i. Therefore the general solution for the de has the form y = e 2t[c1 cos(3t) + c2 sin(3t)] . To solve the ivp we determine the values of the constants. Since y(0) = c1, we have c1 = 1. Computing y (t) and setting t equal to zero, we nd that y (0) = 2c1 + 3c2. Since y (0) = 16 and c1 = 1, we have 16 = 2 + 3c2, and therefore c2 = 6.