EN.550.291 Midterm: Exam 1 Solutions Fall 2013
14 Mar 2019
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Exam 1, linear algebra & di erential equations 550. 291, fall 2013. The only permitted calculators are ti-30x iis, ti-30xa, and ti-30x iib. (in particular, ti-30x pro is not permitted. ) Problem 1: (10 points) solve the di erential equation dy dx + 1 x y = ex2 where x, y > 0. Solution: this is a rst order, linear de. So we have (yx) = y x + y = x(y + 1 that is y = 1 dx = eln x = x. , and integrating this yields that yx = 1 x y) = xex2 x. Problem 2: (10 points) solve the di erential equation ex +2xy +4x3y3 +(cid:16)3x4y2 + x2 + ey(cid:17) dy dx = 0. Solution: this de is exact since, for m = ex + 2xy + 4x3y3 and n = 3x4y2 + x2 + ey, we have that m.
