ODE No. 41

2.41 ODE No. 41

Problem in Latex
Mathematica input
Maple input

$a x y (x)^{3} + b y (x)^{2} + y^{'} (x) = 0$ ✓ Mathematica : cpu = 0.160415 (sec), leaf count = 98

$Solve [\frac{b^{2} \log (x)}{a} = \frac{b^{2} (\frac{2 \tan^{- 1} (\frac{- 2 a x y (x) - b}{b \sqrt{- \frac{4 a}{b^{2}} - 1}})}{\sqrt{- \frac{4 a}{b^{2}} - 1}} - \log (\frac{a x^{2} y (x)^{2} + b x y (x) - 1}{a x^{2} y (x)^{2}}))}{2 a} + c_{1}, y (x)]$

✓ Maple : cpu = 0.309 (sec), leaf count = 103

${y (x) = \frac{1}{x} e^{R o o t O f (2 \sqrt{b^{2} + 4 a} b A r t a n h (\frac{2 a e^{_Z} + b}{\sqrt{b^{2} + 4 a}}) - \ln (x^{2} (a e^{2_Z} + b e^{_Z} - 1)) b^{2} + 2_C 1 b^{2} + 2_Z b^{2} - 4 \ln (x^{2} (a e^{2_Z} + b e^{_Z} - 1)) a + 8 a_C 1 + 8_Z a)}}$

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