ODE No. 406

2.406 ODE No. 406

Problem in Latex
Mathematica input
Maple input

$a y^{'} (x)^{2} - y (x) y^{'} (x) - x = 0$ ✓ Mathematica : cpu = 0.622743 (sec), leaf count = 49

$Solve [{x = \frac{a K $ 348736 \sinh^{- 1} (K $ 348736)}{\sqrt{{K $ 348736}^{2} + 1}} + \frac{c_{1} K $ 348736}{\sqrt{{K $ 348736}^{2} + 1}}, y (x) = a K $ 348736 - \frac{x}{K $ 348736}}, {y (x), K $ 348736}]$ ✓ Maple : cpu = 0.21 (sec), leaf count = 262

${(- \frac{\sqrt{2}}{2} (y (x) + \sqrt{4 a x + {(y (x))}^{2}}) A r c s i n h (\frac{1}{2 a} (y (x) + \sqrt{4 a x + {(y (x))}^{2}})) + x \sqrt{\frac{1}{a^{2}} (y (x) \sqrt{4 a x + {(y (x))}^{2}} + 2 a^{2} + 2 a x + {(y (x))}^{2})} +_C 1 y (x) +_C 1 \sqrt{4 a x + {(y (x))}^{2}}) \frac{1}{\sqrt{\frac{1}{a^{2}} (y (x) \sqrt{4 a x + {(y (x))}^{2}} + {(y (x))}^{2} + 2 a (x + a))}} = 0, ((y (x) - \sqrt{4 a x + {(y (x))}^{2}}) A r c s i n h (\frac{1}{2 a} (- y (x) + \sqrt{4 a x + {(y (x))}^{2}})) + x \sqrt{- 2 \frac{y (x) \sqrt{4 a x + {(y (x))}^{2}} - 2 a^{2} - 2 a x - {(y (x))}^{2}}{a^{2}}} -_C 1 y (x) +_C 1 \sqrt{4 a x + {(y (x))}^{2}}) \frac{1}{\sqrt{\frac{1}{a^{2}} (- 2 y (x) \sqrt{4 a x + {(y (x))}^{2}} + 2 {(y (x))}^{2} + 4 a (x + a))}} = 0}$

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