We must solve v xv v 1 we must solve xv dv dx we

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Unformatted text preview: t solve v (xv + v ) + 1 = We must solve xv dv = dx We must solve v√ 1 + v2. 1 + v 2 − v 2 − 1. dx dv = . x 1 + v2 − v2 − 1 Integrate both sides. Let w = 1 + v 2 . It follows that dw = 2vdv . We must solve 1 2 √ dw = ln |x| + C. w−w We have ln |x| + C = 1 2 √ √ Let u = w . We have du = 1 w−1/2 dw . 2 We have ln |x| + C = = − ln 1 − 1+ dw √. w(1 − w) √ du = − ln |1 − u| = − ln |1 − w| = − ln |1 − 1−u y x 2 = − ln x− x2 + y 2 = − ln x − x 1 + v2 | x2 + y 2 + ln |x|. 2 Subtract ln |x| from both sides...
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This document was uploaded on 03/23/2014 for the course MATH 242 at South Carolina.

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