ODE No. 528

2.528 ODE No. 528

Problem in Latex
Mathematica input
Maple input

$a b x + a y^{'} (x)^{2} + b y (x) + y^{'} (x)^{3} = 0$ ✓ Mathematica : cpu = 0.615321 (sec), leaf count = 398

$Solve [{x = - \frac{- a (\frac{\sqrt[3]{2} a^{2}}{3 \sqrt[3]{\sqrt{{(- 2 a^{3} - 27 a b x - 27 b y (x))}^{2} - 4 a^{6}} - 2 a^{3} - 27 a b x - 27 b y (x)}} + \frac{\sqrt[3]{\sqrt{{(- 2 a^{3} - 27 a b x - 27 b y (x))}^{2} - 4 a^{6}} - 2 a^{3} - 27 a b x - 27 b y (x)}}{3 \sqrt[3]{2}} - \frac{a}{3}) + \frac{3}{2} {(\frac{\sqrt[3]{2} a^{2}}{3 \sqrt[3]{\sqrt{{(- 2 a^{3} - 27 a b x - 27 b y (x))}^{2} - 4 a^{6}} - 2 a^{3} - 27 a b x - 27 b y (x)}} + \frac{\sqrt[3]{\sqrt{{(- 2 a^{3} - 27 a b x - 27 b y (x))}^{2} - 4 a^{6}} - 2 a^{3} - 27 a b x - 27 b y (x)}}{3 \sqrt[3]{2}} - \frac{a}{3})}^{2} + a^{2} \log (\frac{\sqrt[3]{2} a^{2}}{3 \sqrt[3]{\sqrt{{(- 2 a^{3} - 27 a b x - 27 b y (x))}^{2} - 4 a^{6}} - 2 a^{3} - 27 a b x - 27 b y (x)}} + \frac{\sqrt[3]{\sqrt{{(- 2 a^{3} - 27 a b x - 27 b y (x))}^{2} - 4 a^{6}} - 2 a^{3} - 27 a b x - 27 b y (x)}}{3 \sqrt[3]{2}} + \frac{2 a}{3})}{b} + c_{1}}, y (x)]$ ✓ Maple : cpu = 0.334 (sec), leaf count = 86

${y (x) = - a x - \frac{{(e^{R o o t O f (- 2 a^{2}_Z - 3 e^{2_Z} + 8 a e^{_Z} + 2_C 1 b - 5 a^{2} - 2 b x)} - a)}^{2} e^{R o o t O f (- 2 a^{2}_Z - 3 e^{2_Z} + 8 a e^{_Z} + 2_C 1 b - 5 a^{2} - 2 b x)}}{b}}$

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