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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 step-by-step calculations. The main source is the textbook: R. Agarwal and D. ORegan , An Intro- duction to Ordinary Differential Equations, Springer 2008. Lectures 35. Exact equations, Separable equations, First-order 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 second-order 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 first-order equations(or both)....
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