ODE No. 558

2.558 ODE No. 558

Problem in Latex
Mathematica input
Maple input

$a x \sqrt{y^{'} (x)^{2} + 1} + x y^{'} (x) - y (x) = 0$ ✓ Mathematica : cpu = 0.590884 (sec), leaf count = 327

${Solve [\frac{2 i \tan^{- 1} (\frac{y (x)}{x \sqrt{a^{2} - \frac{y (x)^{2}}{x^{2}} - 1}}) + a \tanh^{- 1} (\frac{- a^{2} - \frac{i y (x)}{x} + 1}{a \sqrt{a^{2} - \frac{y (x)^{2}}{x^{2}} - 1}}) - a \tanh^{- 1} (\frac{- a^{2} + \frac{i y (x)}{x} + 1}{a \sqrt{a^{2} - \frac{y (x)^{2}}{x^{2}} - 1}}) + a \log (\frac{y (x)^{2}}{x^{2}} + 1)}{2 a^{2} - 2} = \frac{a \log (x - a^{2} x)}{1 - a^{2}} + c_{1}, y (x)], Solve [\frac{- 2 i \tan^{- 1} (\frac{y (x)}{x \sqrt{a^{2} - \frac{y (x)^{2}}{x^{2}} - 1}}) - a \tanh^{- 1} (\frac{- a^{2} - \frac{i y (x)}{x} + 1}{a \sqrt{a^{2} - \frac{y (x)^{2}}{x^{2}} - 1}}) + a \tanh^{- 1} (\frac{- a^{2} + \frac{i y (x)}{x} + 1}{a \sqrt{a^{2} - \frac{y (x)^{2}}{x^{2}} - 1}}) + a \log (\frac{y (x)^{2}}{x^{2}} + 1)}{2 a^{2} - 2} = \frac{a \log (x - a^{2} x)}{1 - a^{2}} + c_{1}, y (x)]}$ ✓ Maple : cpu = 0.275 (sec), leaf count = 223

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

[next] [prev] [prev-tail] [front] [up]