ODE No. 791

2.791 ODE No. 791

Problem in Latex
Mathematica input
Maple input

$y^{'} (x) = \frac{sech (\frac{1}{x - 1}) (- 2 x^{3} y (x) - 2 x^{2} y (x) + x^{5} + x^{4} + 2 x^{2} \cosh (\frac{1}{x - 1}) + x y (x)^{2} + y (x)^{2} - x - 2 x \cosh (\frac{1}{x - 1}) - 1)}{x - 1}$ ✓ Mathematica : cpu = 7.09919 (sec), leaf count = 110

${{y (x) \to \frac{\exp (\int_{1}^{x} \frac{2 (K [5] + 1) sech (\frac{1}{K [5] - 1})}{K [5] - 1} d K [5])}{- \int_{1}^{x} \frac{\exp (\int_{1}^{K [6]} \frac{2 (K [5] + 1) sech (\frac{1}{K [5] - 1})}{K [5] - 1} d K [5]) (K [6] + 1) sech (\frac{1}{K [6] - 1})}{K [6] - 1} d K [6] + c_{1}} + \frac{x^{3} + x^{2}}{x + 1} + 1}}$ ✓ Maple : cpu = 8.148 (sec), leaf count = 306

${y (x) = ((- x^{2} + 1) {(e^{\frac{1}{{(e^{{(x - 1)}^{- 1}})}^{2} + 1} \int \frac{e^{{(x - 1)}^{- 1}} (1 + x)}{({(e^{{(x - 1)}^{- 1}})}^{2} + 1) (x - 1)} d x})}^{4} {(e^{\frac{1}{{(e^{{(x - 1)}^{- 1}})}^{2} + 1} \int \frac{e^{{(x - 1)}^{- 1}} (1 + x)}{({(e^{{(x - 1)}^{- 1}})}^{2} + 1) (x - 1)} d x e^{2 {(x - 1)}^{- 1}}})}^{4} + {(e^{\frac{_C 1}{{(e^{{(x - 1)}^{- 1}})}^{2} + 1} e^{2 {(x - 1)}^{- 1}}})}^{4} {(e^{\frac{_C 1}{{(e^{{(x - 1)}^{- 1}})}^{2} + 1}})}^{4} (x^{2} + 1)) {({(e^{\frac{_C 1}{{(e^{{(x - 1)}^{- 1}})}^{2} + 1} e^{2 {(x - 1)}^{- 1}}})}^{4} {(e^{\frac{_C 1}{{(e^{{(x - 1)}^{- 1}})}^{2} + 1}})}^{4} - {(e^{\frac{1}{{(e^{{(x - 1)}^{- 1}})}^{2} + 1} \int \frac{e^{{(x - 1)}^{- 1}} (1 + x)}{({(e^{{(x - 1)}^{- 1}})}^{2} + 1) (x - 1)} d x e^{2 {(x - 1)}^{- 1}}})}^{4} {(e^{\frac{1}{{(e^{{(x - 1)}^{- 1}})}^{2} + 1} \int \frac{e^{{(x - 1)}^{- 1}} (1 + x)}{({(e^{{(x - 1)}^{- 1}})}^{2} + 1) (x - 1)} d x})}^{4})}^{- 1}}$

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