MATH 3D Study Guide - Final Guide: Integrating Factor
Document Summary
Final review: solve the following: (a) (ex sin y 2y sin x)dx + (ex cos y + 2 cos x)dy = 0 (b) y(cid:48) = 2y (c) y(cid:48) = (a) my = ex cos y 2 sin x = nx so this equation is exact. F (x, y) such that fx = m , fy = n and f (x, y) = c is an implicit solution for some constant c. therefore. F =ex sin y + 2y cos x + g(y) = fy =ex cos y + 2 cos x + g(cid:48)(y) = ex cos y + 2 cos x. So solutions are given implicitly by ex sin y + 2y cos x = c. (b) letting f (x, y) = 2xy y2 x2 it is seen that f (vx, vy) = f (x, y) so this equation is homo- geneous. Let y = vx so that y(cid:48) = v + v(cid:48)x.
