ODE No. 403

3.403 ODE No. 403

$a {(\frac{d}{d x} y (x))}^{2} + b \frac{d}{d x} y (x) - y (x) = 0$

Mathematica: cpu = 0.302538 (sec), leaf count = 116 ${{y (x) \to InverseFunction [\frac{\sqrt{4 # 1 a + b^{2}} + b \log (\sqrt{4 # 1 a + b^{2}} - b)}{2 a} &] [\frac{x}{2 a} + c_{1}]}, {y (x) \to InverseFunction [\frac{\sqrt{4 # 1 a + b^{2}} - b \log (\sqrt{4 # 1 a + b^{2}} + b)}{2 a} &] [c_{1} - \frac{x}{2 a}]}}$

Maple: cpu = 0.858 (sec), leaf count = 197 ${y (x) = \frac{1}{4 a} e^{- \frac{1}{2 b} (b \ln (\frac{1}{4 a}) + 2 b l a m b e r t W (2 \frac{e^{- 1}}{b \sqrt{a^{- 1}}} e^{\frac{x}{b}} {(e^{\frac{_C 1}{b}})}^{- 1}) + 2_C 1 + 2 b - 2 x)} (e^{- \frac{1}{2 b} (b \ln (\frac{1}{4 a}) + 2 b l a m b e r t W (2 \frac{e^{- 1}}{b \sqrt{a^{- 1}}} e^{\frac{x}{b}} {(e^{\frac{_C 1}{b}})}^{- 1}) + 2_C 1 + 2 b - 2 x)} + 2 b), y (x) = \frac{1}{4 a} e^{R o o t O f (b \ln (\frac{{(e^{_Z} + 2 b)}^{2}}{4 a}) - 2 e^{_Z} + 2_C 1 - 2 b - 2 x)} (e^{R o o t O f (b \ln (\frac{{(e^{_Z} + 2 b)}^{2}}{4 a}) - 2 e^{_Z} + 2_C 1 - 2 b - 2 x)} + 2 b)}$

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