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Unformatted text preview: f x = ( x-1 + x-2 y 3 ) and integrating by x , we get f ( x,y ) = log x-x-1 y 3 + ( y ) . Dierentiating by y , we have f y =-3 x-1 y 2 + ( y ), which must equal-3 x-1 y 2 . Hence we must have ( y ) = 0, so we can take ( y ) = 0. The solution to the dierential equation is simply f ( x,y ) = C , so log x-x-1 y 3 = C. Using the initial condition y (1) = 8, we have-8 3 = C , so the solution to the initial value problem is log x-x-1 y 3 =-8 3 . 1...
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- Spring '07