MATH 3D Study Guide - Quiz Guide: Product Rule, Jyj
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Math 3d quiz 1 morning - january 24th. Please put name on front & id on back for redistribution! *there is a question on the back side: consider the following ode with initial condition: x2y(cid:48) = y xy and y( 1) = 1. (a) [3pts] prove that this ode has a unique solution. (hint: section 1. 2 material). Here, x2 y. x2 f (x, y) = (1 x) 1 x y, fy(x, y) = x2: f is continuous as long as x is away from 0. Since the assumptions of picard"s theorem are satis ed, we conclude there exists a solution, and that it is unique by picard"s theorem. , and (x0, y0) = ( 1, 1). (b) [7pts] find the exact solution for y. Reminder: address what the domain of validity is. From (a) how we wrote y(cid:48) = 1 x x2 y, we separate and integrate. With leibniz notation, dy y dx = ln|y| = 1 x.