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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 π¦ ′ = π₯π¦ 2 , π¦(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 ππ¦ 3π₯ 2 + 4π₯ + 2 = , π¦(0) = −1 ππ₯ 2(π¦ − 1) 1) Rewrite this equation in its form π΅π π + π΄π π = π ππ 2) Identify π΅(π, π)πππ π΄(π, π) 3) Is the differential equation an exact equation? Hint: verify that π π΅ π π = π π΄ π π π΅π π π π +π΄=π Problem 1 Find the solution of these differential equations using separable technique and linear genera form 1) π¦ ′ = π₯ 2 π¦