ODE No. 376

2.376 ODE No. 376

$a y^{'} (x) + b y (x) + y^{'} (x)^{2} = 0$ ✓ Mathematica : cpu = 0.311751 (sec), leaf count = 110

${{y (x) \to InverseFunction [- \frac{\sqrt{a^{2} - 4 # 1 b} + a \log (\sqrt{a^{2} - 4 # 1 b} - a)}{2 b} &] [c_{1} + \frac{x}{2}]}, {y (x) \to InverseFunction [- \frac{\sqrt{a^{2} - 4 # 1 b} - a \log (\sqrt{a^{2} - 4 # 1 b} + a)}{2 b} &] [c_{1} - \frac{x}{2}]}}$

✓ Maple : cpu = 1.165 (sec), leaf count = 215

${y (x) = - \frac{1}{4 b} e^{- \frac{1}{2 a} (2 a l a m b e r t W (2 \frac{e^{- 1}}{a} e^{\frac{_C 1 b}{a}} \frac{1}{\sqrt{- b^{- 1}}} {(e^{\frac{b x}{a}})}^{- 1}) + a \ln (- \frac{1}{4 b}) - 2_C 1 b + 2 b x + 2 a)} (e^{- \frac{1}{2 a} (2 a l a m b e r t W (2 \frac{e^{- 1}}{a} e^{\frac{_C 1 b}{a}} \frac{1}{\sqrt{- b^{- 1}}} {(e^{\frac{b x}{a}})}^{- 1}) + a \ln (- \frac{1}{4 b}) - 2_C 1 b + 2 b x + 2 a)} + 2 a), y (x) = - \frac{1}{4 b} e^{R o o t O f (- a \ln (- \frac{{(e^{_Z} + 2 a)}^{2}}{4 b}) + 2_C 1 b - 2 b x + 2 e^{_Z} + 2 a)} (e^{R o o t O f (- a \ln (- \frac{{(e^{_Z} + 2 a)}^{2}}{4 b}) + 2_C 1 b - 2 b x + 2 e^{_Z} + 2 a)} + 2 a)}$

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