ODE No. 787

2.787 ODE No. 787

$y^{'} (x) = \frac{x (2 x^{4} - 2 x^{2} y (x) + x^{2} - x - 1)}{(x + 1) (x^{2} - y (x))}$ ✓ Mathematica : cpu = 27.2233 (sec), leaf count = 484

$Solve [\frac{2 2^{2 / 3} (2 - \frac{x (x^{2} - x - 1) (2 x^{2} - 2 y (x) + 3)}{\sqrt[3]{x^{3} {(x^{2} - x - 1)}^{3}} (x^{2} - y (x))}) (\frac{x (x^{2} - x - 1) (2 x^{2} - 2 y (x) + 3)}{\sqrt[3]{x^{3} {(x^{2} - x - 1)}^{3}} (x^{2} - y (x))} + 4) ((1 - \frac{x (x^{2} - x - 1) (2 x^{2} - 2 y (x) + 3)}{2 \sqrt[3]{x^{3} {(x^{2} - x - 1)}^{3}} (x^{2} - y (x))}) \log (\frac{2 - \frac{x (x^{2} - x - 1) (2 x^{2} - 2 y (x) + 3)}{\sqrt[3]{x^{3} {(x^{2} - x - 1)}^{3}} (x^{2} - y (x))}}{\sqrt[3]{2}}) + (\frac{x (x^{2} - x - 1) (2 x^{2} - 2 y (x) + 3)}{2 \sqrt[3]{x^{3} {(x^{2} - x - 1)}^{3}} (x^{2} - y (x))} - 1) \log (\frac{\frac{x (x^{2} - x - 1) (2 x^{2} - 2 y (x) + 3)}{\sqrt[3]{x^{3} {(x^{2} - x - 1)}^{3}} (x^{2} - y (x))} + 4}{\sqrt[3]{2}}) - 3)}{9 (- \frac{{(2 x^{2} - 2 y (x) + 3)}^{3}}{{(x^{2} - y (x))}^{3}} + \frac{12 x (x^{2} - x - 1) (2 x^{2} - 2 y (x) + 3)}{\sqrt[3]{x^{3} {(x^{2} - x - 1)}^{3}} (x^{2} - y (x))} - 16)} = c_{1} + \frac{4 2^{2 / 3} {(x^{3} {(x^{2} - x - 1)}^{3})}^{2 / 3} (x (x^{2} - 3 x + 3) - 3 \log (x + 1))}{27 x^{2} {(- x^{2} + x + 1)}^{2}}, y (x)]$

✓ Maple : cpu = 0.335 (sec), leaf count = 191

${y (x) = 1 (4 x^{2} e^{R o o t O f (8 x^{3} e^{_Z} - 24 x^{2} e^{_Z} - 36 x^{3} + 6 \ln (\frac{2 e^{_Z} - 9}{{(1 + x)}^{4}}) e^{_Z} + 18_C 1 e^{_Z} - 6_Z e^{_Z} + 24 x e^{_Z} + 108 x^{2} - 27 \ln (\frac{2 e^{_Z} - 9}{{(1 + x)}^{4}}) - 81_C 1 + 27_Z - 108 x + 27)} - 18 x^{2} - 9) {(4 e^{R o o t O f (8 x^{3} e^{_Z} - 24 x^{2} e^{_Z} - 36 x^{3} + 6 \ln (\frac{2 e^{_Z} - 9}{{(1 + x)}^{4}}) e^{_Z} + 18_C 1 e^{_Z} - 6_Z e^{_Z} + 24 x e^{_Z} + 108 x^{2} - 27 \ln (\frac{2 e^{_Z} - 9}{{(1 + x)}^{4}}) - 81_C 1 + 27_Z - 108 x + 27)} - 18)}^{- 1}}$

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