This yields 2 g1 x y y2 thus one solution is g x

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Unformatted text preview: 2 G2 (x, y, z ) = − x2 + 1 z + g2 (x, y ) . If we apply these to the last equation we get ∂g2 − ∂g1 = y . You can try to set ∂x ∂y g2 to be zero because this is the last equation you need to satisfy. This yields 2 g1 (x, y ) = − y2 . Thus one solution is G (x, y, z ) = y2 z2 − 2xyz − , − x2 + 1 z , 0 . 2 2 Note that G is not unique because if I choose any C 2 function f and ta...
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