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$$ x^3 + y^3 = 18 x y $$ $$ 3x^2 +3y^2y' = 18 x y $$ $$ 3(x^2 +y^2y') = 18 x y $$ $$ 3(x^2 +y^2y') = 18xy' - 18y $$ $$ x^2 +y^2y' = 6xy' - 6y $$ $$ y^2y' - 6xy'= - 6y - x^2 $$ $$ y'(y^2 - 6x) = - 6y - x^2 $$ $$ y' = - \frac{6y - x^2}{y^2 - 6x} $$
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Thu, 01 Nov 2018 02:12 GMT