ODE No. 1792

8.202 ODE No. 1792

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

Mathematica: cpu = 25.014176 (sec), leaf count = 222 ${{y (x) \to InverseFunction [\int_{1}^{# 1} - \frac{K [2]^{- \frac{c}{a}} (1 - K [2])^{\frac{1}{2} (\frac{2 b}{a} + \frac{2 c}{a})}}{\sqrt{2 \int_{1}^{K [2]} - \frac{h (K [1]) \exp (- \frac{2 (c \log (K [1]) - (b + c) \log (1 - K [1]))}{a})}{a (K [1] - 1) K [1]} d K [1] + c_{1}}} d K [2] &] [c_{2} + x]}, {y (x) \to InverseFunction [\int_{1}^{# 1} \frac{K [3]^{- \frac{c}{a}} (1 - K [3])^{\frac{1}{2} (\frac{2 b}{a} + \frac{2 c}{a})}}{\sqrt{2 \int_{1}^{K [3]} - \frac{h (K [1]) \exp (- \frac{2 (c \log (K [1]) - (b + c) \log (1 - K [1]))}{a})}{a (K [1] - 1) K [1]} d K [1] + c_{1}}} d K [3] &] [c_{2} + x]}}$

Maple: cpu = 0.562 (sec), leaf count = 192 ${\int^{y (x)} a \frac{1}{\sqrt{- a (-_C 1 a + 2 \int \frac{h (_b)}{_b (_b - 1)} {({(_b - 1)}^{\frac{b}{a}})}^{2} {({(_b - 1)}^{\frac{c}{a}})}^{2} {({_b}^{\frac{c}{a}})}^{- 2} d_b)}} {({_b}^{\frac{c}{a}})}^{- 1} {({(_b - 1)}^{- \frac{c + b}{a}})}^{- 1} d_b - x -_C 2 = 0, \int^{y (x)} - a \frac{1}{\sqrt{- a (-_C 1 a + 2 \int \frac{h (_b)}{_b (_b - 1)} {({(_b - 1)}^{\frac{b}{a}})}^{2} {({(_b - 1)}^{\frac{c}{a}})}^{2} {({_b}^{\frac{c}{a}})}^{- 2} d_b)}} {({_b}^{\frac{c}{a}})}^{- 1} {({(_b - 1)}^{- \frac{c + b}{a}})}^{- 1} d_b - x -_C 2 = 0}$

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