test1_spring_05

test1_spring_05 - MA-366 Spring 2005 Test...

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Unformatted text preview: MA-366, Spring 2005, Test 1Name:AnswersNote:You may use scratch paper. One sheet (both sides) of notes are allowed. No calculators.Problem 1.(12 points)Solve the initial value problemdydxDx3NUL2yx;y.NUL1/D:and determine the largest interval where the solution is defined.Answer:This is a linear equation. The general solution isy.x/DCx2Cx35.The solution of the IVP isy.x/D15x2Cx35, defined forx<.1MA-366, Spring 2005, Test 12Problem 2.(10 points)Find the general solution to the equation.1Cex/DC2dydxCyDC3D1Answer:This is a linear equation again. The solution isy.x/DCeNULxCeNULxln.1Cex/.MA-366, Spring 2005, Test 13Problem 3. (12 points)Solve the initial value problem and find the largest interval where the solution isdefinedp1Cx2dydxDxy3;y./DNUL1:Answer:Separable equation. Solution:yD NULDLE3NUL2p1Cx2DC1NUL1=2,jxj<p5=2.MA-366, Spring 2005, Test 14Problem 4.(12 points)Consider the equationxDf .x/, wheref .x/is sketched belowFind the equilibrium solutions, classify them by stability and sketch the phase portrait of this equation.Find the equilibrium solutions, classify them by stability and sketch the phase portrait of this equation....
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This note was uploaded on 01/18/2012 for the course MATH 366 taught by Professor Edraygoins during the Fall '09 term at Purdue.

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test1_spring_05 - MA-366 Spring 2005 Test...

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