ODE No. 1427

2.1427 ODE No. 1427

Problem in Latex
Mathematica input
Maple input

$y^{″} (x) = y (x) (- \csc^{2} (x)) (- ((a^{2} b^{2} - (a + 1)^{2}) \sin^{2} (x)) - a (a + 1) b \sin (2 x) + (1 - a) a)$ ✓ Mathematica : cpu = 0.860577 (sec), leaf count = 129

${{y (x) \to c_{2} (e^{- a b x} \sin^{- a - 1} (x) + \frac{(2 a + 1) (- 1 + e^{2 i x}) e^{- a b x} \sin^{a - 2 (a + 1)} (x)_{2} F_{1} (1, i a (b + i); i b a + a + 2; e^{2 i x}) (b \sin (x) + \cos (x))}{2 (a (b - i) - i)}) + c_{1} e^{a b x} \sin^{a} (x) (b \sin (x) + \cos (x))}}$ ✓ Maple : cpu = 1.349 (sec), leaf count = 203

${y (x) = \frac{(c_{2} (\int - 2 e^{- 2 (\int \frac{- a b^{2} + (- 2 a - 1) b \sin (2 x) + (a b^{2} - a - 2) (\cos^{2} (2 x)) - a + (- 2 (a + 1) b \sin (2 x) - 2 a - 1) \cos (2 x) + 1}{(\cos (2 x) + 1) (b \cos (2 x) - b - \sin (2 x))} d x)} \sin (2 x) d x) + c_{1}) e^{\int \frac{- a b^{2} + (- 2 a - 1) b \sin (2 x) + (a b^{2} - a - 2) (\cos^{2} (2 x)) - a + (- 2 (a + 1) b \sin (2 x) - 2 a - 1) \cos (2 x) + 1}{(\cos (2 x) + 1) (b \cos (2 x) - b - \sin (2 x))} d x}}{\sqrt{\sin (2 x)}}}$

[next] [prev] [prev-tail] [front] [up]