MAT244H1 Study Guide - Midterm Guide: Integrating Factor
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MAT244H1 Full Course Notes
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Mat244 fall 2016 term test 1. Problem 1 find the solution of the following problem (cid:26) y(cid:48) + 4y = xex y(0) = 1. Problem 2 solve the following problem(cid:26) y(x + y) + (xy + 1)y(cid:48) = 0 y(0) = e given that the equation has an integrating factor of the form = (y). Problem 3 consider the following bernoulli problem (cid:26) y(cid:48) + y = r(x)y2 (cid:26) 1 x 1 y(0) = 1 r(x) = 4 : sketch in the xy-plane the graphs of solution satisfying conditions y(0) = 2, y(0) = 2, and y(0) = 3. Problem 5 solve the following equation (cid:48) y y x y + x + 2. Hint: you can use the axis translation x = x + 1 and y = y + 1. Problem 1 g(x), the integrating factor is (x) = exp(cid:0)(cid:82) q(t)dt(cid:1), so we compute: This is a linear 1st order ode, so we seek an integrating factor.