MATH 0290 Midterm: Math 0290 Exam 1 (0290) 2014 Sping Solution -179

• School: Pitt
• Department: Mathematics
• Course: MATH 0290
• Professor: All

Document Summary

S o l u t i o n s: solve the initial-value problem. Mention a type of the given di erential equation. (a) (10 points) y . = x2y, y(0) = 8, where y = dy dx. = 3x2 dx, ln |y| = x3 + c1, , c = ec1. y(0) = c = 8, y = 8ex3 (b) (10 points) ty = 2y + t3, y( 1) = 3. It is a rst order linear di erential equation. y . I(t) = er 2 t dt = e 2 ln |t| = t 2. It is a second-order linear homogeneous di erential equation. Its characteristic equation r2 + 6r + 9 = 0 has one root r = 3. The general solution is y(t) = e 3t (c1 + c2t) The air resistance force is given by r(v) = 2v. The equation v = g 2v is separable. Its solution is v(t) = ce 2t g.