ODE No. 384

3.384 ODE No. 384

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

Problem in Latex
Mathematica input
Maple input

Mathematica: cpu = 2.056261 (sec), leaf count = 183 ${{y (x) \to \frac{- 2 \sqrt{- a^{4} e^{2 c_{1}} x^{2} - 2 a^{4} e^{2 c_{1}} x + a^{4} (- e^{2 c_{1}})} + 2 a^{3} x + a^{3} - 2 a^{2} b x - a b^{2} - a e^{2 c_{1}} + 4 a c}{4 a^{2}}}, {y (x) \to \frac{2 \sqrt{- a^{4} e^{2 c_{1}} x^{2} - 2 a^{4} e^{2 c_{1}} x + a^{4} (- e^{2 c_{1}})} + 2 a^{3} x + a^{3} - 2 a^{2} b x - a b^{2} - a e^{2 c_{1}} + 4 a c}{4 a^{2}}}}$

Maple: cpu = 0.468 (sec), leaf count = 50 ${y (x) = \frac{- a^{2} x^{2} - 2 a b x - b^{2} + 4 c}{4 a}, y (x) =_C 1 x + \frac{{_C 1}^{2} +_C 1 b + c}{a}}$

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