MATH 263 Study Guide - Midterm Guide: Integrating Factor, Talking Lifestyle 1278, Hit106.9 Newcastle

• School: McGill University
• Department: Mathematics and Statistics
• Course: MATH 263
• Professor: All

Document Summary

Solutions for mid-term test - 22 october, 2009: solve the initial value problem dy dx. Solution : the di erential equation can be written as (2y + 3)dy = (3x2 + 2x + 3)dx. Integrating the left side with respect to y and the right side with respect to x gives y2 + 3y = x3 + x2 + 3x + c, where c is an arbitrary constant. To determine the solution satisfying the prescribed initial condition, we substitute x = 0 and y = 1, obtaining c = 4. Hence the solution of the initial value problem is given implicitly by y2 + 3y = x3 + x2 + 3x + 4. Since x = 0, y = 1, we get. 2: solve the di erential equation (5xy + 2y2) + (x2 + xy)y(cid:48) = 0. On computing the quantity (my nx)/n, we nd that. 5x + 4y (2x + y) x2 + xy.