ﬁrst order ode abel

Table 2.423: ﬁrst order ode abel


#	ODE	CAS classiﬁcation	Solved?

1183	$y^{'} = y (- 2 + y) (- 1 + y)$	[_quadrature]	✓

1590	$y^{'} + \frac{(y + 1) (y - 1) (y - 2)}{x + 1} = 0$ i.c.	[_separable]	✓

1594	$y^{'} = - 2 x (y^{3} - 3 y + 2)$ i.c.	[_separable]	✓

1598	$y^{'} + x^{2} (y + 1) {(y - 2)}^{2} = 0$	[_separable]	✓

2868	$x^{2} + 3 x y^{'} = y^{3} + 2 y$ i.c.	[_rational, _Abel]	✓

4692	$y^{'} = (a + b x y) y^{2}$	[[_homogeneous, ‘class G‘], _Abel]	✓

6019	$- a y^{3} - \frac{b}{x^{3 / 2}} + y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational, _Abel]	✓

6020	$a x y^{3} + b y^{2} + y^{'} = 0$	[[_homogeneous, ‘class G‘], _Abel]	✓

6021	$y^{'} - x^{a} y^{3} + 3 y^{2} - x^{- a} y - x^{- 2 a} + a x^{- a - 1} = 0$	[_Abel]	✓

6664	$y^{'} + (x + y) x = x^{3} {(x + y)}^{3} - 1$	[_Abel]	✓

7057	$y^{'} = y (2 - y) (4 - y)$	[_quadrature]	✓

10052	$- a y^{3} - \frac{b}{x^{3 / 2}} + y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational, _Abel]	✓

10055	$a x y^{3} + b y^{2} + y^{'} = 0$	[[_homogeneous, ‘class G‘], _Abel]	✓

10060	$y^{'} - x^{a} y^{3} + 3 y^{2} - x^{- a} y - x^{- 2 a} + a x^{- a - 1} = 0$	[_Abel]	✓

10199	$x^{2 n + 1} y^{'} - a y^{3} - b x^{3 n} = 0$	[[_homogeneous, ‘class G‘], _Abel]	✓

10691	$y^{'} = (1 + y^{2} e^{- 2 b x} + y^{3} e^{- 3 b x}) e^{b x}$	[[_1st_order, _with_linear_symmetries], _Abel]	✓

10695	$y^{'} = (1 + y^{2} e^{- \frac{4 x}{3}} + y^{3} e^{- 2 x}) e^{\frac{2 x}{3}}$	[[_1st_order, _with_linear_symmetries], _Abel]	✓

10696	$y^{'} = (1 + y^{2} e^{- 2 x} + y^{3} e^{- 3 x}) e^{x}$	[[_1st_order, _with_linear_symmetries], _Abel]	✓

10716	$y^{'} = (1 + y^{2} e^{2 x^{2}} + y^{3} e^{3 x^{2}}) e^{- x^{2}} x$	[_Abel]	✓

10870	$y^{'} = \frac{(- 256 a x^{2} + 512 + 512 y^{2} + 128 y a x^{4} + 8 a^{2} x^{8} + 512 y^{3} + 192 x^{4} a y^{2} + 24 y a^{2} x^{8} + a^{3} x^{12}) x}{512}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel]	✓

10878	$y^{'} = - \frac{(- 108 x^{3 / 2} - 216 - 216 y^{2} + 72 x^{3} y - 6 x^{6} - 216 y^{3} + 108 x^{3} y^{2} - 18 y x^{6} + x^{9}) \sqrt{x}}{216}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel]	✓

10895	$y^{'} = \frac{32 x^{5} + 64 x^{6} + 64 y^{2} x^{6} + 32 x^{4} y + 4 x^{2} + 64 x^{6} y^{3} + 48 x^{4} y^{2} + 12 x^{2} y + 1}{64 x^{8}}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel]	✓

10923	$y^{'} = - \frac{(- 8 e^{- x^{2}} + 8 x^{2} e^{- x^{2}} - 8 - 8 y^{2} + 8 x^{2} e^{- x^{2}} y - 2 x^{4} e^{- 2 x^{2}} - 8 y^{3} + 12 x^{2} e^{- x^{2}} y^{2} - 6 y x^{4} e^{- 2 x^{2}} + x^{6} e^{- 3 x^{2}}) x}{8}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel]	✓

10934	$y^{'} = \frac{- x^{2} + x + 1 + y^{2} + 5 x^{2} y - 2 x y + 4 x^{4} - 3 x^{3} + y^{3} + 3 y^{2} x^{2} - 3 x y^{2} + 3 x^{4} y - 6 x^{3} y + x^{6} - 3 x^{5}}{x}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel]	✓

10950	$y^{'} = \frac{150 x^{3} + 125 \sqrt{x} + 125 + 125 y^{2} - 100 x^{3} y - 500 y \sqrt{x} + 20 x^{6} + 200 x^{7 / 2} + 500 x + 125 y^{3} - 150 x^{3} y^{2} - 750 y^{2} \sqrt{x} + 60 y x^{6} + 600 y x^{7 / 2} + 1500 x y - 8 x^{9} - 120 x^{13 / 2} - 600 x^{4} - 1000 x^{3 / 2}}{125 x}$	[_rational, _Abel]	✓

10959	$y^{'} = \frac{- 4 \cos (x) x + 4 \sin (x) x^{2} + 4 x + 4 + 4 y^{2} + 8 y \cos (x) x - 8 x y + 2 x^{2} \cos (2 x) + 6 x^{2} - 8 x^{2} \cos (x) + 4 y^{3} + 12 y^{2} \cos (x) x - 12 x y^{2} + 6 y x^{2} \cos (2 x) + 18 x^{2} y - 24 y \cos (x) x^{2} + x^{3} \cos (3 x) + 15 x^{3} \cos (x) - 6 x^{3} \cos (2 x) - 10 x^{3}}{4 x}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel]	✓

10963	$y^{'} = - \frac{x (- 513 - 756 x^{3} - 432 x - 864 x^{4} - 378 y - 1134 x^{2} - 576 x^{5} - 216 y^{3} - 540 y^{2} - 972 x^{4} y^{2} - 216 x^{4} y - 1296 y^{2} x^{2} + 720 x^{3} y - 456 x^{6} - 594 x^{2} y - 144 x^{7} - 96 x^{8} + 64 x^{9} - 216 x^{6} y^{3} - 288 y x^{6} - 216 y^{2} x^{6} + 432 x^{3} y^{2} - 288 y x^{8} - 648 x^{4} y^{3} + 288 y x^{7} + 864 y^{2} x^{5} + 432 y^{2} x^{7} + 1008 x^{5} y - 648 y^{3} x^{2})}{216 {(x^{2} + 1)}^{4}}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel]	✓

10969	$y^{'} = y (y^{2} + y e^{b x} + e^{2 b x}) e^{- 2 b x}$	[[_1st_order, _with_linear_symmetries], _Abel]	✓

10970	$y^{'} = y^{3} - 3 y^{2} x^{2} + 3 x^{4} y - x^{6} + 2 x$	[[_1st_order, _with_linear_symmetries], _Abel]	✓

10971	$y^{'} = y^{3} + y^{2} x^{2} + \frac{x^{4} y}{3} + \frac{x^{6}}{27} - \frac{2 x}{3}$	[[_1st_order, _with_linear_symmetries], _Abel]	✓

10973	$y^{'} = y (y^{2} + e^{- x^{2}} y + e^{- 2 x^{2}}) e^{2 x^{2}} x$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], _Abel]	✓

10975	$y^{'} = \frac{y^{3} - 3 x y^{2} + 3 x^{2} y - x^{3} + x}{x}$	[[_1st_order, _with_linear_symmetries], _rational, _Abel]	✓

10976	$y^{'} = \frac{x^{3} y^{3} + 6 y^{2} x^{2} + 12 x y + 8 + 2 x}{x^{3}}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel]	✓

10977	$y^{'} = \frac{y^{3} a^{3} x^{3} + 3 y^{2} a^{2} x^{2} + 3 y a x + 1 + a^{2} x}{x^{3} a^{3}}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel]	✓

10981	$y^{'} = \frac{(1 + x y) (y^{2} x^{2} + x^{2} y + 2 x y + 1 + x + x^{2})}{x^{5}}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel]	✓

10982	$y^{'} = \frac{y^{3} - 3 x y^{2} \ln (x) + 3 x^{2} \ln {(x)}^{2} y - x^{3} \ln {(x)}^{3} + x^{2} + x y}{x^{2}}$	[_Abel]	✓

13638	$x^{'} = - x (- x + 1) (2 - x)$	[_quadrature]	✓

14947	$y^{'} - y^{3} = 8$	[_quadrature]	✓

15849	$y^{'} = y^{3} + 1$	[_quadrature]	✓

15850	$y^{'} = y^{3} - 1$	[_quadrature]	✓

2.3.15 ﬁrst order ode abel