\left. \begin{array} { r } { ( 3 x ^ { 2 } y + 8 x y ^ { 2 } ) d x + ( x ^ { 3 } + 8 x ^ { 2 } y + 12 y ^ { 2 } ) d y = 0 } \\ { y ( 2 ) = 1 } \end{array} \right.
Solve for x, y
\left\{\begin{matrix}\\x=-\frac{\sqrt[3]{9\sqrt{209}+145}}{6}-\frac{\sqrt[3]{145-9\sqrt{209}}}{6}-\frac{2}{3}\approx -2.160653764\text{, }y=\frac{1}{2}=0.5\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }y=\frac{1}{2}=0.5\text{, }&d=0\end{matrix}\right.
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