P1_1030 - exists. y = 1-2 x y , y > with y (1)...

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Math 415.01 - Dr. Huseyin Coskun - Exam 1 Practice Problems - 10:30 recitation (Vutha) January 18, 2011 The following list of problems is meant to serve as an extra resource for your preparations for Exam 1. This list is in by no means exhaustive, nor is it meant to predict the questions in the exam. Instead it can be used as a tool to assess how well prepared you may be, and to highlight problems that you might face. Pay careful attention to your timing – as this is something that can greatly affect the outcome of your exam. The only way to guarantee success for yourself is to work out as many problems as possible from the text. ( Note : Questions from Secs. 1.1, 1.2, 1.3, 2.5 and 2.6 are not in this sheet but can be on the exam ) (2.2.10) Solve the given initial value problem and find the largest interval on which the solution
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Unformatted text preview: exists. y = 1-2 x y , y > with y (1) =-2 (2.2.16) Solve the given initial value problem and nd the largest interval on which the solution exists. y = x ( x 2 + 1) 4 y 3 with y (0) =-1 2 (2.1.20) Solve ty + (1 + t ) y-t = 0 , y (ln 2) = 1 , t > (2.2.34) Solve y =-(4 x + 3 y ) (2 x + y ) 1 (2.1.1) Solve y + 3 y = t + e-2 t (7.2.13), (7.2.14) Find the inverse of (a) A = 1 1-1 2-1 1 1 1 2 (b) A = 1 2 1-2 1 8 1-2-7 (7.3.16) Find all eigenvalues and eigenvectors of A = 3-2 4-1 (7.3.4) Completely solve the given system of equations x 1 + 2 x 2-x 3 = 0 2 x 1 + x 2 + x 3 = 0 x 1-x 2 + 2 x 3 = 0 (2.3.3) Refer text. (2.3.24) Refer text. (2.4.2) Find intervals of existence of solution of t ( t-4) y + y = 0 , y (2) = 1 2...
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P1_1030 - exists. y = 1-2 x y , y > with y (1)...

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