ODE No. 231

3.231 ODE No. 231

$(a y (x) + b x + c) \frac{d}{d x} y (x) + α y (x) + β x + γ = 0$

Mathematica: cpu = 2.446311 (sec), leaf count = 252 $Solve [\frac{(α - b)^{2} (- \log (\frac{(a y (x) + b x + c)^{2} (- \frac{(α (b x + c) - a (β x + γ)) (a (α - b) y (x) + a (β x + γ) + b^{2} (- x) - b c)}{(a y (x) + b x + c)^{2}} + a β - α b)}{(α (b x + c) - a (β x + γ))^{2}}) - \frac{2 \tan^{- 1} (\frac{\frac{2 (a (β x + γ) - α (b x + c))}{a y (x) + b x + c} + α - b}{(α - b) \sqrt{\frac{4 (a β - α b)}{(α - b)^{2}} - 1}})}{\sqrt{\frac{4 (a β - α b)}{(α - b)^{2}} - 1}})}{2 (a β - α b)} = \frac{(α - b)^{2} \log (a (β x + γ) - α (b x + c))}{a β - α b} + c_{1}, y (x)]$

Maple: cpu = 0.156 (sec), leaf count = 206 ${y (x) = \frac{1}{- a β + b α} (- b γ + β c + \frac{x (a β - b α) + a γ - α c}{2 a} (\sqrt{4 a β - α^{2} - 2 b α - b^{2}} \tan (R o o t O f (\sqrt{4 a β - α^{2} - 2 b α - b^{2}} \ln (\frac{{(a β x - α b x + a γ - α c)}^{2} (4 a β {(\tan (_Z))}^{2} - α^{2} {(\tan (_Z))}^{2} - 2 α b {(\tan (_Z))}^{2} - b^{2} {(\tan (_Z))}^{2} + 4 a β - α^{2} - 2 b α - b^{2})}{4 a}) + 2_C 1 \sqrt{4 a β - α^{2} - 2 b α - b^{2}} + 2_Z α - 2_Z b)) + α + b))}$

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