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Unformatted text preview: x 2 y 2 + g ( y ) . Substituting N ( x, y ) (given in part (b)) for F/y , we can now solve for g ( y ) to obtain N ( x, y ) = x 2 y 2 = x 2 y 2 + g ( y ) g ( y ) = 0 . The integral of g ( y ) will yield a constant and the choice of the constant of integration is not important so we can take g ( y ) = 0. Hence we have F ( x, y ) = x + x 2 /y and the solution to the equation is given implicitly by x + x 2 y = C . Solving the above equation for y , we obtain y = x 2 C x . 67...
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 Spring '10
 Hald,OH
 Math, Differential Equations, Linear Algebra, Algebra, Equations

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