ODE No. 479

3.479 ODE No. 479

$(b 2 y (x) + a 2 x + c 2) {(\frac{d}{d x} y (x))}^{2} + (a 1 x + b 1 y (x) + c 1) \frac{d}{d x} y (x) + a 0 x + b 0 y (x) + c 0 = 0$

Mathematica: cpu = 0 (sec), leaf count = 0 $Hanged$

Maple: cpu = 0.811 (sec), leaf count = 929 ${x - e^{\int^{\frac{1}{2 b 2 y (x) + 2 a 2 x + 2 c 2} (- a 1 x - b 1 y (x) - c 1 + \sqrt{- 4 a 0 a 2 x^{2} - 4 a 0 b 2 x y (x) + {a 1}^{2} x^{2} + 2 a 1 b 1 x y (x) - 4 a 2 b 0 x y (x) - 4 b 0 b 2 {(y (x))}^{2} + {b 1}^{2} {(y (x))}^{2} - 4 a 0 c 2 x + 2 a 1 c 1 x - 4 a 2 c 0 x - 4 b 0 c 2 y (x) + 2 b 1 c 1 y (x) - 4 b 2 c 0 y (x) - 4 c 0 c 2 + {c 1}^{2}})} \frac{{_a}^{2} a 1 b 2 - {_a}^{2} a 2 b 1 + 2_a a 0 b 2 - 2_a a 2 b 0 + a 0 b 1 - a 1 b 0}{({_a}^{3} b 2 + {_a}^{2} a 2 + {_a}^{2} b 1 +_a a 1 +_a b 0 + a 0) ({_a}^{2} b 2 +_a b 1 + b 0)} d_a} (\int^{\frac{1}{2 b 2 y (x) + 2 a 2 x + 2 c 2} (- a 1 x - b 1 y (x) - c 1 + \sqrt{- 4 a 0 a 2 x^{2} - 4 a 0 b 2 x y (x) + {a 1}^{2} x^{2} + 2 a 1 b 1 x y (x) - 4 a 2 b 0 x y (x) - 4 b 0 b 2 {(y (x))}^{2} + {b 1}^{2} {(y (x))}^{2} - 4 a 0 c 2 x + 2 a 1 c 1 x - 4 a 2 c 0 x - 4 b 0 c 2 y (x) + 2 b 1 c 1 y (x) - 4 b 2 c 0 y (x) - 4 c 0 c 2 + {c 1}^{2}})} - \frac{{_b}^{2} b 1 c 2 - {_b}^{2} b 2 c 1 + 2_b b 0 c 2 - 2_b b 2 c 0 + b 0 c 1 - b 1 c 0}{({_b}^{2} b 2 +_b b 1 + b 0) ({_b}^{3} b 2 + {_b}^{2} a 2 + {_b}^{2} b 1 +_b a 1 +_b b 0 + a 0)} e^{- \int \frac{{_b}^{2} a 1 b 2 - {_b}^{2} a 2 b 1 + 2_b a 0 b 2 - 2_b a 2 b 0 + a 0 b 1 - a 1 b 0}{({_b}^{2} b 2 +_b b 1 + b 0) ({_b}^{3} b 2 + {_b}^{2} a 2 + {_b}^{2} b 1 +_b a 1 +_b b 0 + a 0)} d_b} d_b +_C 1) = 0, x - e^{\int^{- \frac{1}{2 b 2 y (x) + 2 a 2 x + 2 c 2} (a 1 x + b 1 y (x) + \sqrt{- 4 a 0 a 2 x^{2} - 4 a 0 b 2 x y (x) + {a 1}^{2} x^{2} + 2 a 1 b 1 x y (x) - 4 a 2 b 0 x y (x) - 4 b 0 b 2 {(y (x))}^{2} + {b 1}^{2} {(y (x))}^{2} - 4 a 0 c 2 x + 2 a 1 c 1 x - 4 a 2 c 0 x - 4 b 0 c 2 y (x) + 2 b 1 c 1 y (x) - 4 b 2 c 0 y (x) - 4 c 0 c 2 + {c 1}^{2}} + c 1)} \frac{{_a}^{2} a 1 b 2 - {_a}^{2} a 2 b 1 + 2_a a 0 b 2 - 2_a a 2 b 0 + a 0 b 1 - a 1 b 0}{({_a}^{3} b 2 + {_a}^{2} a 2 + {_a}^{2} b 1 +_a a 1 +_a b 0 + a 0) ({_a}^{2} b 2 +_a b 1 + b 0)} d_a} (\int^{- \frac{1}{2 b 2 y (x) + 2 a 2 x + 2 c 2} (a 1 x + b 1 y (x) + \sqrt{- 4 a 0 a 2 x^{2} - 4 a 0 b 2 x y (x) + {a 1}^{2} x^{2} + 2 a 1 b 1 x y (x) - 4 a 2 b 0 x y (x) - 4 b 0 b 2 {(y (x))}^{2} + {b 1}^{2} {(y (x))}^{2} - 4 a 0 c 2 x + 2 a 1 c 1 x - 4 a 2 c 0 x - 4 b 0 c 2 y (x) + 2 b 1 c 1 y (x) - 4 b 2 c 0 y (x) - 4 c 0 c 2 + {c 1}^{2}} + c 1)} - \frac{{_b}^{2} b 1 c 2 - {_b}^{2} b 2 c 1 + 2_b b 0 c 2 - 2_b b 2 c 0 + b 0 c 1 - b 1 c 0}{({_b}^{2} b 2 +_b b 1 + b 0) ({_b}^{3} b 2 + {_b}^{2} a 2 + {_b}^{2} b 1 +_b a 1 +_b b 0 + a 0)} e^{- \int \frac{{_b}^{2} a 1 b 2 - {_b}^{2} a 2 b 1 + 2_b a 0 b 2 - 2_b a 2 b 0 + a 0 b 1 - a 1 b 0}{({_b}^{2} b 2 +_b b 1 + b 0) ({_b}^{3} b 2 + {_b}^{2} a 2 + {_b}^{2} b 1 +_b a 1 +_b b 0 + a 0)} d_b} d_b +_C 1) = 0}$

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