ODE No. 1638

2.1638 ODE No. 1638

Problem in Latex
Mathematica input
Maple input

$a y^{'} (x)^{2} + b \sin (y (x)) + y^{″} (x) = 0$ ✓ Mathematica : cpu = 4.59654 (sec), leaf count = 146

${{y (x) \to InverseFunction [\int_{1}^{# 1} - \frac{\sqrt{4 a^{2} + 1}}{\sqrt{4 e^{- 2 a K [1]} c_{1} a^{2} - 4 b \sin (K [1]) a + e^{- 2 a K [1]} c_{1} + 2 b \cos (K [1])}} d K [1] &] [c_{2} + x]}, {y (x) \to InverseFunction [\int_{1}^{# 1} \frac{\sqrt{4 a^{2} + 1}}{\sqrt{4 e^{- 2 a K [2]} c_{1} a^{2} - 4 b \sin (K [2]) a + e^{- 2 a K [2]} c_{1} + 2 b \cos (K [2])}} d K [2] &] [c_{2} + x]}}$ ✓ Maple : cpu = 0.161 (sec), leaf count = 115

${\int^{y (x)} (- 4 a^{2} - 1) \frac{1}{\sqrt{16_C 1 {(a^{2} + 1 / 4)}^{2} e^{- 2 a_a} - 16 (a^{2} + 1 / 4) (a \sin (_a) - 1 / 2 \cos (_a)) b}} d_a - x -_C 2 = 0, \int^{y (x)} (4 a^{2} + 1) \frac{1}{\sqrt{16_C 1 {(a^{2} + 1 / 4)}^{2} e^{- 2 a_a} - 16 (a^{2} + 1 / 4) (a \sin (_a) - 1 / 2 \cos (_a)) b}} d_a - x -_C 2 = 0}$

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