ODE No. 249

2.249 ODE No. 249

Problem in Latex
Mathematica input
Maple input

$y^{'} (x) (a x y (x) + b x^{n}) + α y (x)^{3} + β y (x)^{2} = 0$ ✓ Mathematica : cpu = 3.36538 (sec), leaf count = 115

$Solve [\frac{(a (- n) + a + α y (x)) y (x)^{\frac{a - a n}{β} - 1} (α y (x) + β)^{\frac{a (n - 1)}{β}}}{a^{2} (n - 1)^{2} (a (n - 1) + β)} + \frac{x^{1 - n} \exp (- \frac{a (n - 1) (\log (y (x)) - \log (α y (x) + β))}{β})}{a b (1 - n) (n - 1)} = c_{1}, y (x)]$ ✓ Maple : cpu = 0.182 (sec), leaf count = 202

${y (x) = β {(R o o t O f (- x^{1 - n} {_Z}^{\frac{a (n - 1)}{β}} a^{2} β n +_C 1 a^{2} b n^{2} + x^{1 - n} {_Z}^{\frac{a (n - 1)}{β}} a^{2} β - x^{1 - n} {_Z}^{\frac{a (n - 1)}{β}} a β^{2} - {_Z}^{\frac{a n - a + β}{β}} β a b n + {_Z}^{\frac{a (n - 1)}{β}} a α b n - 2_C 1 a^{2} b n +_C 1 a b β n + {_Z}^{\frac{a n - a + β}{β}} β a b - {_Z}^{\frac{a (n - 1)}{β}} a α b + {_Z}^{\frac{a (n - 1)}{β}} α b β +_C 1 a^{2} b -_C 1 a b β) β - α)}^{- 1}}$

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