ODE No. 390

2.390 ODE No. 390

Problem in Latex
Mathematica input
Maple input

$a y (x) y^{'} (x) - b x - c + y^{'} (x)^{2} = 0$ ✓ Mathematica : cpu = 1.5136 (sec), leaf count = 142

$Solve [{x = e^{b (\frac{\log (K $ 318599)}{b} - \frac{\log (b - a {K $ 318599}^{2})}{2 b})} (\frac{\tan^{- 1} (\frac{\sqrt{a} K $ 318599}{\sqrt{b - a {K $ 318599}^{2}}})}{\sqrt{a}} - \frac{c \sqrt{b - a {K $ 318599}^{2}}}{b K $ 318599}) + c_{1} e^{b (\frac{\log (K $ 318599)}{b} - \frac{\log (b - a {K $ 318599}^{2})}{2 b})}, y (x) = \frac{b x}{a K $ 318599} + \frac{c - {K $ 318599}^{2}}{a K $ 318599}}, {y (x), K $ 318599}]$ ✓ Maple : cpu = 1.137 (sec), leaf count = 281

${y (x) = 2 \frac{e^{R o o t O f (\sqrt{a}_C 1 b e^{2_Z} - a e^{2_Z} b x + \sqrt{a}_C 1 b^{2} - e^{2_Z}_Z b - a e^{2_Z} c + a b^{2} x -_Z b^{2} + a b c)} (- 1 / 4 {(e^{2 R o o t O f (\sqrt{a}_C 1 b e^{2_Z} - a e^{2_Z} b x + \sqrt{a}_C 1 b^{2} - e^{2_Z}_Z b - a e^{2_Z} c + a b^{2} x -_Z b^{2} + a b c)} + b)}^{2} e^{- 2 R o o t O f (\sqrt{a}_C 1 b e^{2_Z} - a e^{2_Z} b x + \sqrt{a}_C 1 b^{2} - e^{2_Z}_Z b - a e^{2_Z} c + a b^{2} x -_Z b^{2} + a b c)} + a (b x + c))}{a^{3 / 2} (e^{2 R o o t O f (\sqrt{a}_C 1 b e^{2_Z} - a e^{2_Z} b x + \sqrt{a}_C 1 b^{2} - e^{2_Z}_Z b - a e^{2_Z} c + a b^{2} x -_Z b^{2} + a b c)} + b)}}$

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