Self-Quiz Solutions 1 | Introduction to Differential Equations | MATH 220, Quizzes of Differential Equations

Download Self-Quiz Solutions 1 | Introduction to Differential Equations | MATH 220 and more Quizzes Differential Equations in PDF only on Docsity! MATH 220 Self-quiz 1 1. Show that an implicit solution of the differential equation: y′ = −x y is given by: x2 + y2 = C Solution: We begin with the given relation and we differentiate both sides of it. While doing so, we take into consideration that y is a function of x: 2x + 2yy′ = 0 By solving for y′, we get our differential equation. This implies that the given implicitly defined function satisfies our differential equation. 2. Check that y = sin x + cos x is an explicit solution of the differential equation: y′′ + y = 0 Solution: We compute: y′ = cos x− sin x and