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Unformatted text preview: Be sure that this examination has three pages. The University of British Columbia Final Examinations December 2006 Mathematics 215 Elementary Differential Equations I Mathematics 255 Ordinary Differential Equations Time: 2 1 2 hours Special instructions: (1) One 8 1 2 00 11 00 page of notes may be used, but no other aids are permitted. In particular, calculators and cell phones are not allowed . (2) Answers must be justified to receive full credit. (3) A table of Laplace transforms is attached. Marks 1. (a) Find the general solution of the equation  dy dt = t 2- y t . (b) Find all values of the constants a and b so that the differential equation dy dx =- y a 2 xy + 2 bxy 2 is exact, then for these values of a and b find the solution of the equation that also satisfies the initial condition y (1) = 1. 2. Consider the autonomous equation  dy dt = ( y- 1)( y- 5) ,- < y < + ....
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