MATH 1005 Study Guide - Integrating Factor

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scarletsnake516

6 Feb 2014

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[6: solve the initial-value problem 2y (cid:1) cos(x) = cos(x) y2 = sin(x) + c y = (cid:1) (cid:1) 2yy y(0) = 2 2 = c c = 4 y = x2 + y2 (cid:1: find the general solution of y sin(x) + 4. sin(x) + c. xy y (cid:1) Solution: (cid:1) u2 = ln|x| + c u = (cid:1) , u = x y y x xy. 2: find the general solution of xy. 2 ln|x| + k y = x (cid:1) = |x|3 = x3, and we may take i(x) = x3. + 3x2y = x3 + x2 (x3y) (cid:1) [6: find an integrating factor which makes the equation x + y2 + xyy (cid:1) P = x + y2, q = xy, py = 2y, qx = y, py (cid:5)= qx, so the equation is not exact. Py qx is a function of x only, so an integrating factor i(x) exists, determined.

Related Questions

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