advertisement

Worksheet 1-3: Existence-Exact equations Supplemental Instruction Iowa State University Leader: Course: Instructor: Date: Zaynab Diallo Math 267 D’Alessandro 1/21/16 Existence and uniqueness of solution Let 𝑦 ′ = 𝑥𝑦 2 , 𝑦(0) = 1 Does this initial value problem have a (unique) solution? Please Justify? Hint: continuity of f(x,y) and f’(x,y) Exact Equations 𝑑𝑦 3𝑥 2 + 4𝑥 + 2 = , 𝑦(0) = −1 𝑑𝑥 2(𝑦 − 1) 1) Rewrite this equation in its form 𝑵𝒅𝒚 + 𝑴𝒅𝒙 = 𝟎 𝑜𝑟 2) Identify 𝑵(𝒙, 𝒚)𝒂𝒏𝒅 𝑴(𝒙, 𝒚) 3) Is the differential equation an exact equation? Hint: verify that 𝒅𝑵 𝒅𝒙 = 𝒅𝑴 𝒅𝒚 𝑵𝒅𝒚 𝒅𝒙 +𝑴=𝟎 Problem 1 Find the solution of these differential equations using separable technique and linear genera form 1) 𝑦 ′ = 𝑥 2 𝑦