(3) - Assignment Solutions

(3) - Assignment Solutions - McGill University Math 315...

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McGill University Math 315: Diferential Equations Written Assignment 3: Due on April 14, 2010, Not hand in 1. (a) Find the Laplace trans±orm L ( f ), ±or the ±unction: ( i ) f ( t )= sin t t ;( ii ) f ( t ± cos t 0 t< 2; t, t 2 . (b) Find the inverse Laplace trans±orm F ( s ), ±or the ±unction: F ( s )=ln s 2 +1 s 2 +4 (c) Find a non-trivial solution ±or the ±ollowing EQ., such that y (0) = 0: ty ± - ( t - 2) y ± + y = 0. 2. Give EQ’s: (i) x 2 y ± +(2 x 2 - 3 x ) y ± - 2 y = 0; (ii) xy ± + y ± - xy = 0; (a) Determine the regular singular point o± the equation;
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