MATH 251 Midterm: MATH 251 PSU s251Exam 1(fa02)
Document Summary
Midterm exam 1: (i) linear, homogeneous, oder 2. (ii) nonlinear, order 1. (iii) linear, nonhomogeneous, order 3, (a) (b, (a) (b) y 4y + 13y = 0. 1,2 = 2 3i y(t) = c1e2t cos 3t + c2e2t sin 3t y + 2y + y = 0. 1,2 = 1 y(t) = c1e t + c2te t y = cos t + 1 y(0) = 3 y ydy = (cos t + 1)dt y2. = sin t + t + const ( 3)2. = sin 0 + 0 + const const = 2 y(t) = +s2(cid:18)sin t + t + 2(cid:19) ty + 3y = 3, y(1) = 2 y + (t)er 3 t dt t dt = e3 r = t3 t3 + const. = 1 + const t3 y(t) = r t3 3 t3 t3 const. 13 const = 1 y(t) = 1 +
