ODE No. 376

3.376 ODE No. 376

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

Mathematica: cpu = 0.313040 (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 = 0.796 (sec), leaf count = 215 ${y (x) = - \frac{1}{4 b} e^{- \frac{1}{2 a} (a \ln (- \frac{1}{4 b}) + 2 a l a m b e r t W (2 \frac{e^{- 1}}{a} e^{\frac{_C 1 b}{a}} \frac{1}{\sqrt{- b^{- 1}}} {(e^{\frac{b x}{a}})}^{- 1}) - 2_C 1 b + 2 b x + 2 a)} (e^{- \frac{1}{2 a} (a \ln (- \frac{1}{4 b}) + 2 a l a m b e r t W (2 \frac{e^{- 1}}{a} e^{\frac{_C 1 b}{a}} \frac{1}{\sqrt{- b^{- 1}}} {(e^{\frac{b x}{a}})}^{- 1}) - 2_C 1 b + 2 b x + 2 a)} + 2 a), y (x) = - \frac{1}{4 b} e^{R o o t O f (- a \ln (- \frac{{(e^{_Z} + 2 a)}^{2}}{4 b}) + 2_C 1 b - 2 b x + 2 e^{_Z} + 2 a)} (e^{R o o t O f (- a \ln (- \frac{{(e^{_Z} + 2 a)}^{2}}{4 b}) + 2_C 1 b - 2 b x + 2 e^{_Z} + 2 a)} + 2 a)}$

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