ODE No. 758

2.758 ODE No. 758

$y^{'} (x) = \frac{y (x) (x^{3} y (x) + 2 x + 2)}{(x + 1) (\log (y (x)) + 2 x - 1)}$ ✓ Mathematica : cpu = 0.930356 (sec), leaf count = 459

${{y (x) \to \frac{6 W (- \frac{1}{6} \sqrt[6]{e^{- 12 x} (6 c_{1} + 2 x^{3} - 3 x^{2} + 6 x - 6 \log (x + 1))^{6}})}{6 c_{1} + 2 x^{3} - 3 x^{2} + 6 x - 6 \log (x + 1)}}, {y (x) \to \frac{6 W (\frac{1}{6} \sqrt[6]{e^{- 12 x} (6 c_{1} + 2 x^{3} - 3 x^{2} + 6 x - 6 \log (x + 1))^{6}})}{6 c_{1} + 2 x^{3} - 3 x^{2} + 6 x - 6 \log (x + 1)}}, {y (x) \to \frac{6 W (- \frac{1}{6} \sqrt[3]{- 1} \sqrt[6]{e^{- 12 x} (6 c_{1} + 2 x^{3} - 3 x^{2} + 6 x - 6 \log (x + 1))^{6}})}{6 c_{1} + 2 x^{3} - 3 x^{2} + 6 x - 6 \log (x + 1)}}, {y (x) \to \frac{6 W (\frac{1}{6} \sqrt[3]{- 1} \sqrt[6]{e^{- 12 x} (6 c_{1} + 2 x^{3} - 3 x^{2} + 6 x - 6 \log (x + 1))^{6}})}{6 c_{1} + 2 x^{3} - 3 x^{2} + 6 x - 6 \log (x + 1)}}, {y (x) \to \frac{6 W (- \frac{1}{6} (- 1)^{2 / 3} \sqrt[6]{e^{- 12 x} (6 c_{1} + 2 x^{3} - 3 x^{2} + 6 x - 6 \log (x + 1))^{6}})}{6 c_{1} + 2 x^{3} - 3 x^{2} + 6 x - 6 \log (x + 1)}}, {y (x) \to \frac{6 W (\frac{1}{6} (- 1)^{2 / 3} \sqrt[6]{e^{- 12 x} (6 c_{1} + 2 x^{3} - 3 x^{2} + 6 x - 6 \log (x + 1))^{6}})}{6 c_{1} + 2 x^{3} - 3 x^{2} + 6 x - 6 \log (x + 1)}}}$

✓ Maple : cpu = 0.244 (sec), leaf count = 41

${y (x) = e^{- l a m b e r t W (- \frac{(- 2 x^{3} + 3 x^{2} + 6 \ln (1 + x) + 6_C 1 - 6 x) e^{- 2 x}}{6}) - 2 x}}$

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