ﬁrst order ode ﬂip role

Table 2.445: ﬁrst order ode ﬂip role


#	ODE	ODE classiﬁcation	Solved?

3002	$1 + x y (x y^{2} + 1) y^{'} = 0$ i.c.	[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓

4391	$2 y^{'} x - y = y^{'} \ln (y y^{'})$	[[_1st_order, _with_linear_symmetries]]	✓

4409	$y^{'} = \frac{1}{x y + x^{3} y^{3}}$	[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓

5248	$x (x^{3} - 3 x^{3} y + 4 y^{2}) y^{'} = 6 y^{3}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓

5302	$(x + 2 y + 2 x^{2} y^{3} + x y^{4}) y^{'} + (1 + y^{4}) y = 0$	[_rational]	✓

5392	${y^{'}}^{2} - y y^{'} + e^{x} = 0$	[[_1st_order, _with_linear_symmetries]]	✓

5495	$(- x^{2} + 1) {y^{'}}^{2} + 2 x y^{'} y + 4 x^{2} = 0$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓

5542	$x y {y^{'}}^{2} + (a + x^{2} - y^{2}) y^{'} - x y = 0$	[_rational]	✓

7779	$y^{'} x + y = y^{'} \sqrt{1 - x^{2} y^{2}}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓

10328	$(x^{2} y^{3} + x y) y^{'} - 1 = 0$	[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓

10335	$(x + 2 y + 2 x^{2} y^{3} + x y^{4}) y^{'} + y^{5} + y = 0$	[_rational]	✓

10486	$a x y {y^{'}}^{2} - (a y^{2} + b x^{2} + c) y^{'} + b x y = 0$	[_rational]	✓

10698	$y^{'} = \frac{1}{x (x y^{2} + 1 + x) y}$	[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓

10768	$y^{'} = \frac{2 y^{6}}{y^{3} + 2 + 16 x y^{2} + 32 x^{2} y^{4}}$	[_rational]	✓

10834	$y^{'} = \frac{y (x - y) (1 + y)}{x (x y + x - y)}$	[_rational, [_Abel, ‘2nd type‘, ‘class C‘]]	✓

10841	$y^{'} = \frac{y (x + y) (1 + y)}{x (x y + x + y)}$	[_rational, [_Abel, ‘2nd type‘, ‘class C‘]]	✓

10907	$y^{'} = - (- \frac{\ln (y)}{x} + \frac{\cos (x) \ln (y)}{\sin (x)} -_F1 (x)) y$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓

10914	$y^{'} = \frac{2 y^{8}}{y^{5} + 2 y^{6} + 2 y^{2} + 16 x y^{4} + 32 y^{6} x^{2} + 2 + 24 x y^{2} + 96 x^{2} y^{4} + 128 x^{3} y^{6}}$	[_rational]	✓

10917	$y^{'} = - (- \frac{\ln (y)}{x} + \frac{\ln (y)}{x \ln (x)} -_F1 (x)) y$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓

10920	$y^{'} = - \frac{(- \frac{\ln {(y)}^{2}}{2 x} -_F1 (x)) y}{\ln (y)}$	[NONE]	✓

10944	$y^{'} = - \frac{216 y}{- 216 y^{4} - 252 y^{3} - 396 y^{2} - 216 y + 36 x^{2} - 72 x y + 60 y^{5} - 36 x y^{3} - 72 x y^{2} - 24 x y^{4} + 4 y^{8} + 12 y^{7} + 33 y^{6}}$	[_rational]	✓

10962	$y^{'} = - \frac{1296 y}{216 - 216 x^{2} y^{4} + 216 x y^{2} - 648 x^{2} y - 1728 y^{3} - 324 x^{2} y^{3} - 432 x y - 570 y^{8} - 846 y^{7} - 126 y^{10} - 315 y^{9} - 8 y^{12} - 36 y^{11} - 2376 y^{2} + 72 y^{8} x - 1944 y^{4} - 612 y^{5} + 1080 x y^{3} - 648 x^{2} y^{2} + 216 y^{7} x + 1080 y^{5} x + 594 x y^{6} + 1152 x y^{4} - 882 y^{6} + 216 x^{2} + 216 x^{3} - 1296 y}$	[_rational]	✓

14132	$(x^{2} y^{3} + x y) y^{'} = 1$	[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓

16753	${y^{'}}^{2} - y y^{'} + e^{x} = 0$	[[_1st_order, _with_linear_symmetries]]	✓

16793	${y^{'}}^{2} - y y^{'} + e^{x} = 0$	[[_1st_order, _with_linear_symmetries]]	✓

17842	$(x^{2} y^{3} + x y) y^{'} = 1$	[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓

17898	${y^{'}}^{2} - y y^{'} + e^{x} = 0$	[[_1st_order, _with_linear_symmetries]]	✓

17991	$y^{'} x + y = y^{'} \sqrt{1 - x^{2} y^{2}}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓

18717	$(x^{2} y^{3} + x y) y^{'} = 1$	[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓

19236	$x y {y^{'}}^{2} - (x^{2} + y^{2} - 1) y^{'} + x y = 0$	[_rational]	✓

2.3.26 ﬁrst order ode ﬂip role