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Unformatted text preview: 1 THE UNIVERSITY OF BRITISH COLUMBIA Sessional Examinations April 2009 MATHEMATICS 215 TIME: 2.5 hours NO AIDS ARE PERMITTED. Note that the maximum number of points is 110. A score of N/110 will be treated as N/100. Also note that this exam has three pages. (15) 1. Consider the differential equation . 2 y x dx dy- = (*) (a) Find the general solution of (*). (b) Find a particular solution (is there only one?) of (*) satisfying the initial condition y (0) = - 2. (c) Sketch the solution curves of (*). (10) 2. Find the inverse function f ( t ) of the Laplace transform for (a) ; 2 ) ( 2-- = s s s s F (b) [ ] . ) ( 1 ) ( 2 2 2 s s e s s e s s F-- +- = . In each case, evaluate f (3). (15) 3. Solve the initial value problem: . ) ( ) ( , cos 4 = = = + y y t y y (15) 4. Solve the following initial value problem for t > 0 and sketch its solution: ) ( , 1 ) ( ), ( = =- = - y y t y y ....
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