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Unformatted text preview: B U Department of Mathematics Math 202 Differential Equations Summer 2001 First Midterm This archive is a property of Bo˘gazi¸ ci University Mathematics Department. The purpose of this archive is to organise and centralise the distribution of the exam questions and their solutions. This archive is a non-profit service and it must remain so. Do not let anyone sell and do not buy this archive, or any portion of it. Reproduction or distribution of this archive, or any portion of it, without non-profit purpose may result in severe civil and criminal penalties. 1. Find one-parameter family of solutions of the differential equation: y = 1 + x- (1 + 2 x ) y + xy 2 Solution: This is a Ricatti eqn., y = 1 is a solution. Let y = 1 + 1 z DE ⇒ z- z =- x (a linear DE) Integrating factor μ = e- x ( e- x z ) =- xe- x , z = 1 + x + ce x y = 1 + 1 1 + x + ce x ( c ∈ R ) 2. a) Show that the equation: ( x 2 + y 2 ) dx +2 xy dy = 0 is exact and find a one-parameter family of solutions....
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- Winter '11
- Equations, real solutions