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Unformatted text preview: C 1 2 y + sin 2 y = 4 arctan x + C. The last equation denes implicit solutions to the given diFerential equation. 13. Writing the given equation in the form dx/dt = x x 2 , we separate the variables to get dx x x 2 = dt . Integrate (the left side is integrated by partial fractions, with 1 / ( x x 2 ) = 1 /x + 1 / (1 x )) to obtain: ln  x  ln  1 x  = t + c ln x 1 x = t + c x 1 x = e t + c = Ce t , where C = e c x = Ce t xCe t x + xCe t = Ce t 28...
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 Spring '10
 Hald,OH
 Math, Differential Equations, Linear Algebra, Algebra, Equations

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