MATH 2552 Midterm: MATH 2552 GT 2 2017
Document Summary
This exam covers chapters 1 and 2 of brannon and boyce. Everything on the exam pertains to a single rst order equation. It can also be summarized under four headings: single rst order equations, modeling, numerical methods, existence/uniqueness. Name and section: (17 points) (1. 2. 9) solve the following ode for y = y(t): Solution: this is a linear rst order equation y +p(t)y = 3t/2. Integrating both sides from t0 to t, we get factor = exp(r t p) = exp(t/2), we write (cid:0)yet/2(cid:1) . 2"(cid:0)2 e /2(cid:1)(cid:12)(cid:12) yet/2 y(t0)et0/2 = t0. Name and section: (cid:26) y = (1 2x)/y y(1) = 2. Solution: this is a separable equation yy = 1 2x. Integrating both sides from 1 to x, we nd. 2 y2 2 = x 1 x2 + 1 = x x2. Name and section: (17 points) (2. 2. 4) a tank contains 200 gallons of water with 100 lbs of salt in solution.
