APPM 2360 Midterm: appm2360spring2014exam1_sol
Document Summary
On the front of your bluebook write: (1) your name, (2) your student id number, (3) recitation section (4) your instructor"s name, and (5) a grading table. Text books, class notes, and calculators are not permitted. Problem 1: (30 points) consider the following di erential equation dy dt (1 y2)1/3. In a small region around (t, y) = (0, 1) the function f (t, y) = (1 y2)1/3 is well de ned and continuous which gives us existence by picard"s theorem. Taking a derivative with respect to y gives: df dy. 1 t which is unde ned for y = 1. This means that picard"s theorem does not guarantee uniqueness. Solution 2: (a) solution to part (a) (i) the solution to the homogeneous equation is given by y 6t2y = 0 y. = z 6t2 dt ln |y| = 2t3 + c1 yh(t) = ce2t3 (ii) let yp(t) = v(t)e2t3.
