ODE No. 184

2.184 ODE No. 184

Problem in Latex
Mathematica input
Maple input

$(y^{'} (x) + y (x)^{2}) {(a x^{2} + b x + c)}^{2} + A = 0$ ✓ Mathematica : cpu = 1.09594 (sec), leaf count = 704

${{y (x) \to - \frac{- \frac{2 a \sqrt{a x^{2} + b x + c} \exp (- \frac{\sqrt{4 a c - b^{2}} \sqrt{1 - \frac{4 A}{b^{2} - 4 a c}} \tan^{- 1} (\frac{2 a x + b}{\sqrt{4 a c - b^{2}}})}{\sqrt{b^{2} - 4 a c}})}{(b^{2} - 4 a c) (\frac{(2 a x + b)^{2}}{4 a c - b^{2}} + 1)} + \frac{(2 a x + b) \exp (- \frac{\sqrt{4 a c - b^{2}} \sqrt{1 - \frac{4 A}{b^{2} - 4 a c}} \tan^{- 1} (\frac{2 a x + b}{\sqrt{4 a c - b^{2}}})}{\sqrt{b^{2} - 4 a c}})}{2 \sqrt{b^{2} - 4 a c} \sqrt{1 - \frac{4 A}{b^{2} - 4 a c}} \sqrt{a x^{2} + b x + c}} + c_{1} (\frac{2 a \sqrt{1 - \frac{4 A}{b^{2} - 4 a c}} \sqrt{x (a x + b) + c} \exp (\frac{\sqrt{4 a c - b^{2}} \sqrt{1 - \frac{4 A}{b^{2} - 4 a c}} \tan^{- 1} (\frac{2 a x + b}{\sqrt{4 a c - b^{2}}})}{\sqrt{b^{2} - 4 a c}})}{\sqrt{b^{2} - 4 a c} (\frac{(2 a x + b)^{2}}{4 a c - b^{2}} + 1)} + \frac{(2 a x + b) \exp (\frac{\sqrt{4 a c - b^{2}} \sqrt{1 - \frac{4 A}{b^{2} - 4 a c}} \tan^{- 1} (\frac{2 a x + b}{\sqrt{4 a c - b^{2}}})}{\sqrt{b^{2} - 4 a c}})}{2 \sqrt{x (a x + b) + c}})}{- \frac{\sqrt{a x^{2} + b x + c} \exp (- \frac{\sqrt{4 a c - b^{2}} \sqrt{1 - \frac{4 A}{b^{2} - 4 a c}} \tan^{- 1} (\frac{2 a x + b}{\sqrt{4 a c - b^{2}}})}{\sqrt{b^{2} - 4 a c}})}{\sqrt{b^{2} - 4 a c} \sqrt{1 - \frac{4 A}{b^{2} - 4 a c}}} + c_{1} \sqrt{x (a x + b) + c} (- \exp (\frac{\sqrt{4 a c - b^{2}} \sqrt{1 - \frac{4 A}{b^{2} - 4 a c}} \tan^{- 1} (\frac{2 a x + b}{\sqrt{4 a c - b^{2}}})}{\sqrt{b^{2} - 4 a c}}))}}}$ ✓ Maple : cpu = 0.328 (sec), leaf count = 493

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

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