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Unformatted text preview: B U Department of Mathematics Math 202 Differential Equations Summer 2003 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. Determine the constants a and b so that μ ( x, y ) = x a y b is an integrating factor for the equation ydx- ( x + x 6 ) dy = 0 Find a one-parameter family of solutions of this equation.(All integrals that may arise should be evaluated.) Solution: ( μM ) y = ( μN ) x : ( x a y b +1 ) y =- ( x a +1 y b + x a +6 y b ) x ⇒ ( b + 1) x a y b =- y b [( a + 1) x a + ( a + b ) x a +5 ] ⇒ a + 6 = 0, a + 1 =- ( b + 1) ⇒ a =- 6, b = 4...
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