MATH 2214 Midterm: MATH 2214 Virginia Tech 3.8 Exam
Document Summary
Solutions 3. 8: a) the characteristic equation is r2 4 = 0 with roots 2. 2a 4c = 0, i. e. a = 1, b = 0, c = 1/2. c) y = t2 . + c1e2t + c2e 2t: a) the characteristic equation is r2 + 1 = 0 with roots i. Consequently a = 4. c) y = 4et + c1 cos t + c2 sin t: a) the characteristic equation is r2 + 1 = 0 with roots i. So the complementary solution is yc = c1 cos t + c2 sin t. 2b + a = 0, b 2a = 1, i. e. a = 2/5, b = 1/5. c) y = et cos t + 5 et sin t + c1 cos t + c2 sin t: a) the characteristic equation is r2 4r + 4 = 0 with double root 2.
