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Unformatted text preview: Math 5525: Spring 2010 Introduction to Ordinary Differential Equations Information on Final Exam: Tuesday, May 11, 2010 Time and place: Tuesday, May 11, 10:30 am –12:30 pm, AmundH 240. There will be 8 problems. No books, no notes. Calculators are permitted, however, for full credit, you need to show stepbystep calculations. The main source is the textbook: R. Agarwal and D. O’Regan , An Intro duction to Ordinary Differential Equations, Springer 2008. Lectures 3–5. Exact equations, Separable equations, Firstorder homoge neous equations, Linear equations, Bernoulli equations. Note that the 1st order homogeneous equations have the form y = dy/dx = f ( y/x ). By substitution v = y/x, y = ( xv ) = v + xv , they are reduced to separable equations xv = f ( v ) v . Lecture * (not in the textbook). Incomplete secondorder equations. The equation y 00 = f ( x,y,y ) or F ( x,y,y ,y 00 ) = 0 is incomplete if it does not de pend explicitly on x or y (or both). They are reduced to firstorder equations(or both)....
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 Spring '08
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 Differential Equations, Equations, Partial differential equation, Lipschitz Uniqueness Theorem

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