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Unformatted text preview: and the diFerential equation y = x/y on the same interval , we see that x 2 + y 2 = 6 does not dene an implicit solution to the diFerential equation. 11. DiFerentiating the equation e xy + y = x 1 implicitly with respect to x yields d dx ( e xy + y ) = d dx ( x 1) e xy d dx ( xy ) + dy dx = 1 e xy y + x dy dx + dy dx = 1 ye xy + dy dx ( xe xy + 1) = 1 dy dx = 1 ye xy 1 + xe xy = e xy ( e xy y ) e xy ( e xy + x ) = e xy y e xy + x . 5...
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This note was uploaded on 03/29/2010 for the course MATH 54257 taught by Professor Hald,oh during the Spring '10 term at University of California, Berkeley.
 Spring '10
 Hald,OH
 Math, Differential Equations, Linear Algebra, Algebra, Equations

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