ODE No. 659

2.659 ODE No. 659

Problem in Latex
Mathematica input
Maple input

$y^{'} (x) = x \sqrt{a^{2} x^{2} + 2 a b x + 4 a y (x) + b^{2} - 4 c} - \frac{a x}{2} - \frac{b}{2}$ ✓ Mathematica : cpu = 0.678838 (sec), leaf count = 164

$Solve [- \frac{\sqrt{a^{2} x^{2} + 2 a b x + 4 a y (x) + b^{2} - 4 c}}{2 a} - \frac{b \log (\sqrt{a^{2} x^{2} + 2 a b x + 4 a y (x) + b^{2} - 4 c} + a x + b)}{2 a} + \frac{b \tanh^{- 1} (\frac{2 a^{2} x + 2 a b}{2 a \sqrt{a^{2} x^{2} + 2 a b x + 4 a y (x) + b^{2} - 4 c}})}{2 a} + \frac{b \log (4 a y (x) - 4 c)}{4 a} + \frac{x^{2}}{2} = c_{1}, y (x)]$ ✓ Maple : cpu = 0.672 (sec), leaf count = 41

${_C 1 + a x^{2} + \frac{a}{2} - \sqrt{a^{2} x^{2} + 2 a b x + b^{2} + 4 a y (x) - 4 c} = 0}$

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