quiz_10B - dy dx = 1 y 2 . This is a separable equation, we...

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Math 213 — Quiz 10 Name Solution 1. Find the orthogonal trajectories of the family of curves given by y = ( x + k ) - 1 . First note that k = y - 1 - x . Differentiating and subsituting for k , we find dy dx = - ( x + k ) - 2 = - 1 ( x + y - 1 - x ) 2 = - y 2 . So the orthogonal trajectories satisfy the differential equation
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Unformatted text preview: dy dx = 1 y 2 . This is a separable equation, we can write it as y 2 dy = dx. Integrating both sides, we nd y 3 3 = x + C or y = (3 x + ) 1 / 3 (where = 3 C )....
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This note was uploaded on 05/09/2008 for the course MATH 2130 taught by Professor Dorais during the Spring '08 term at Cornell University (Engineering School).

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