x = x ^ { 2 } \frac { d ^ { 2 } y } { d x ^ { 2 } } - 2 y = x ^ { 2 } + \frac { 1 } { x }
Evaluate (complex solution)
x=-2y\text{ and }-2y=x^{2}+\frac{1}{x}
Solve for y
y = \frac{2 ^ {\frac{2}{3}} {(\sqrt[3]{3 \sqrt{69} + 25} + \sqrt[3]{25 - 3 \sqrt{69}} - \sqrt[3]{2})}}{12} = 0.37743883312334586
x=-\frac{2^{\frac{2}{3}}\sqrt[3]{3\sqrt{69}+25}}{6}-\frac{2^{\frac{2}{3}}\sqrt[3]{25-3\sqrt{69}}}{6}+\frac{1}{3}
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