ODE No. 1717

2.1717 ODE No. 1717

$a y^{'} (x)^{2} + b y (x)^{3} + y (x) y^{″} (x) = 0$ ✓ Mathematica : cpu = 1.56299 (sec), leaf count = 290

${{y (x) \to InverseFunction [- \frac{\sqrt{2 a + 3} {# 1}^{a + 1} \sqrt{\frac{- 2 b {# 1}^{2 a + 3} + 2 a c_{1} + 3 c_{1}}{(2 a + 3) c_{1}}}_{2} F_{1} (\frac{1}{2}, \frac{a + 1}{2 a + 3}; \frac{a + 1}{2 a + 3} + 1; \frac{2 b {# 1}^{2 a + 3}}{2 a c_{1} + 3 c_{1}})}{(a + 1) \sqrt{- 2 b {# 1}^{2 a + 3} + 2 a c_{1} + 3 c_{1}}} &] [c_{2} + x]}, {y (x) \to InverseFunction [\frac{\sqrt{2 a + 3} {# 1}^{a + 1} \sqrt{\frac{- 2 b {# 1}^{2 a + 3} + 2 a c_{1} + 3 c_{1}}{(2 a + 3) c_{1}}}_{2} F_{1} (\frac{1}{2}, \frac{a + 1}{2 a + 3}; \frac{a + 1}{2 a + 3} + 1; \frac{2 b {# 1}^{2 a + 3}}{2 a c_{1} + 3 c_{1}})}{(a + 1) \sqrt{- 2 b {# 1}^{2 a + 3} + 2 a c_{1} + 3 c_{1}}} &] [c_{2} + x]}}$

✓ Maple : cpu = 0.468 (sec), leaf count = 108

${\int^{y (x)} (2 a + 3) {_a}^{2 a} \frac{1}{\sqrt{- (2 a + 3) {_a}^{2 a} (2 {_a}^{2 a + 3} b -_C 1)}} d_a - x -_C 2 = 0, \int^{y (x)} - (2 a + 3) {_a}^{2 a} \frac{1}{\sqrt{- (2 a + 3) {_a}^{2 a} (2 {_a}^{2 a + 3} b -_C 1)}} d_a - x -_C 2 = 0}$

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