ﬁrst order ode parametric

Table 2.403: ﬁrst order ode parametric


#	ODE	CAS classiﬁcation	Solved	Maple	Mma	Sympy

70	${y^{'}}^{2} = 4 y$ i.c.	[_quadrature]	✓	✓	✓	✗

3286	$x y {y^{'}}^{2} + (x + y) y^{'} + 1 = 0$	[_quadrature]	✓	✓	✓	✓

3288	$x ({y^{'}}^{2} - 1) = 2 y y^{'}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

3295	$y = y^{'} x (y^{'} + 1)$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

3297	$y ({y^{'}}^{2} + 1) = 2$	[_quadrature]	✓	✓	✓	✓

3298	$y {y^{'}}^{2} - 2 y^{'} x + y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✗

3300	$x ({y^{'}}^{2} - 1) = 2 y y^{'}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

3301	$4 x - 2 y y^{'} + x {y^{'}}^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

3302	$2 x^{2} y + {y^{'}}^{2} = x^{3} y^{'}$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✓

3303	$y {y^{'}}^{2} = 3 y^{'} x + y$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

3304	$8 x + 1 = y {y^{'}}^{2}$	[[_homogeneous, ‘class C‘], _rational, _dAlembert]	✓	✓	✓	✓

3305	$y {y^{'}}^{2} + 2 y^{'} + 1 = 0$	[_quadrature]	✓	✓	✓	✗

3306	$({y^{'}}^{2} + 1) x = (x + y) y^{'}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

3307	$x^{2} - 3 y y^{'} + x {y^{'}}^{2} = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	✓	✓	✗

3308	$2 y^{'} x + y = x {y^{'}}^{2}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

3309	$x = {y^{'}}^{2} + y^{'}$	[_quadrature]	✓	✓	✓	✓

3310	$x = y - {y^{'}}^{3}$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	✓	✓

3311	$x + 2 y y^{'} = x {y^{'}}^{2}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

3312	$4 x - 2 y y^{'} + x {y^{'}}^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

3314	$y ({y^{'}}^{2} + 1) = 2 y^{'} x$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✗

3315	$2 x + x {y^{'}}^{2} = 2 y y^{'}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

3316	$x = y y^{'} + {y^{'}}^{2}$	[_dAlembert]	✓	✓	✓	✗

3317	$4 x {y^{'}}^{2} + 2 y^{'} x = y$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

3318	$y = y^{'} x (y^{'} + 1)$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

3319	$2 x {y^{'}}^{3} + 1 = y {y^{'}}^{2}$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✗

3320	${y^{'}}^{3} + x y^{'} y = 2 y^{2}$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✗

3323	$\frac{1}{{y^{'}}^{2}} + y^{'} x = 2 y$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✗

4087	$y = y^{'} + \frac{{y^{'}}^{2}}{2}$	[_quadrature]	✓	✓	✓	✓

4089	$y - x = {y^{'}}^{2} (1 - \frac{2 y^{'}}{3})$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	✓	✗

4385	$x ({y^{'}}^{2} - 1) = 2 y^{'}$	[_quadrature]	✓	✓	✓	✓

4386	$x y^{'} (y^{'} + 2) = y$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

4389	$y = 2 y^{'} x + y^{2} {y^{'}}^{3}$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✗

4390	${y^{'}}^{3} + y^{2} = x y^{'} y$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✗	✗

4392	$y = y^{'} x - x^{2} {y^{'}}^{3}$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✗	✗

4397	$5 y + {y^{'}}^{2} = x (x + y^{'})$	[[_homogeneous, ‘class G‘]]	✓	✓	✗	✓

4413	$4 x - 2 y y^{'} + x {y^{'}}^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

4434	$2 {y^{'}}^{3} - 3 {y^{'}}^{2} + x = y$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	✗	✗

5334	${y^{'}}^{2} = y$	[_quadrature]	✓	✓	✓	✓

5335	${y^{'}}^{2} = x - y$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	✓	✓

5336	${y^{'}}^{2} = y + x^{2}$	[[_homogeneous, ‘class G‘]]	✓	✓	✓	✗

5337	${y^{'}}^{2} + x^{2} = 4 y$	[[_homogeneous, ‘class G‘]]	✓	✓	✓	✗

5338	${y^{'}}^{2} + 3 x^{2} = 8 y$	[[_homogeneous, ‘class G‘]]	✓	✓	✓	✗

5339	${y^{'}}^{2} + a x^{2} + b y = 0$	[[_homogeneous, ‘class G‘]]	✓	✗	✓	✗

5348	${y^{'}}^{2} = a^{2} y^{n}$	[_quadrature]	✓	✓	✓	✓

5356	${y^{'}}^{2} + 2 y^{'} + x = 0$	[_quadrature]	✓	✓	✓	✓

5357	${y^{'}}^{2} - 2 y^{'} + a (x - y) = 0$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	✓	✓

5362	${y^{'}}^{2} + a y^{'} + b x = 0$	[_quadrature]	✓	✓	✓	✓

5363	${y^{'}}^{2} + a y^{'} + b y = 0$	[_quadrature]	✓	✓	✓	✓

5364	${y^{'}}^{2} + y^{'} x + 1 = 0$	[_quadrature]	✓	✓	✓	✓

5367	${y^{'}}^{2} - y^{'} x - y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✗

5368	${y^{'}}^{2} + y^{'} x + x - y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✓

5373	${y^{'}}^{2} - 2 y^{'} x + 1 = 0$	[_quadrature]	✓	✓	✓	✓

5374	${y^{'}}^{2} + 2 y^{'} x - 3 x^{2} = 0$	[_quadrature]	✓	✓	✓	✓

5375	${y^{'}}^{2} + 2 y^{'} x - y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✗

5376	${y^{'}}^{2} + 2 y^{'} x - y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✗

5379	${y^{'}}^{2} + 2 (1 - x) y^{'} - 2 x + 2 y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✓

5380	${y^{'}}^{2} + 3 y^{'} x - y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✗

5382	${y^{'}}^{2} + a x y^{'} = b c x^{2}$	[_quadrature]	✓	✓	✓	✓

5387	${y^{'}}^{2} + a x^{3} y^{'} - 2 a x^{2} y = 0$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✓

5388	${y^{'}}^{2} - 2 a x^{3} y^{'} + 4 a x^{2} y = 0$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✓

5389	${y^{'}}^{2} + 4 x^{5} y^{'} - 12 y x^{4} = 0$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✓

5391	$y y^{'} + {y^{'}}^{2} = (x + y) x$	[_quadrature]	✓	✓	✓	✓

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

5393	${y^{'}}^{2} + (x + y) y^{'} + x y = 0$	[_quadrature]	✓	✓	✓	✓

5394	${y^{'}}^{2} - 2 y y^{'} - 2 x = 0$	[_dAlembert]	✓	✓	✓	✗

5396	${y^{'}}^{2} - 2 (x - y) y^{'} - 4 x y = 0$	[_quadrature]	✓	✓	✓	✓

5400	${y^{'}}^{2} + a y y^{'} - a x = 0$	[_dAlembert]	✓	✓	✓	✗

5401	${y^{'}}^{2} - a y y^{'} - a x = 0$	[_dAlembert]	✓	✓	✓	✗

5402	${y^{'}}^{2} + (a x + b y) y^{'} + a b x y = 0$	[_quadrature]	✓	✓	✓	✓

5403	${y^{'}}^{2} - x y^{'} y + y^{2} \ln (a y) = 0$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓	✓	✗

5404	${y^{'}}^{2} - (1 + 2 x y) y^{'} + 2 x y = 0$	[_quadrature]	✓	✓	✓	✓

5406	${y^{'}}^{2} - (x - y) y y^{'} - x y^{3} = 0$	[_separable]	✓	✓	✓	✓

5407	${y^{'}}^{2} + x y^{2} y^{'} + y^{3} = 0$	[[_homogeneous, ‘class G‘]]	✓	✓	✓	✗

5410	${y^{'}}^{2} + 2 x y^{3} y^{'} + y^{4} = 0$	[[_homogeneous, ‘class G‘]]	✓	✓	✓	✓

5411	${y^{'}}^{2} + 2 y y^{'} \cot (x) - y^{2} = 0$	[_separable]	✓	✓	✓	✓

5413	${y^{'}}^{2} = e^{4 x - 2 y} (y^{'} - 1)$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	✓	✗

5414	$2 {y^{'}}^{2} + y^{'} x - 2 y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✗

5416	$2 {y^{'}}^{2} - 2 x^{2} y^{'} + 3 x y = 0$	[[_homogeneous, ‘class G‘]]	✓	✓	✓	✗

5418	$3 {y^{'}}^{2} - 2 y^{'} x + y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✗

5419	$3 {y^{'}}^{2} + 4 y^{'} x + x^{2} - y = 0$	[[_homogeneous, ‘class G‘]]	✓	✓	✓	✓

5420	$4 {y^{'}}^{2} = 9 x$	[_quadrature]	✓	✓	✓	✓

5421	$4 {y^{'}}^{2} + 2 x e^{- 2 y} y^{'} - e^{- 2 y} = 0$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✗

5422	$4 {y^{'}}^{2} + 2 e^{2 x - 2 y} y^{'} - e^{2 x - 2 y} = 0$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	✓	✗

5423	$5 {y^{'}}^{2} + 3 y^{'} x - y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✗

5424	$5 {y^{'}}^{2} + 6 y^{'} x - 2 y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✗

5425	$9 {y^{'}}^{2} + 3 x y^{4} y^{'} + y^{5} = 0$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✗

5426	$x {y^{'}}^{2} = a$	[_quadrature]	✓	✓	✓	✓

5427	$x {y^{'}}^{2} = - x^{2} + a$	[_quadrature]	✓	✓	✓	✓

5428	$x {y^{'}}^{2} = y$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

5429	$x {y^{'}}^{2} + x - 2 y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

5430	$x {y^{'}}^{2} + y^{'} = y$	[_rational, _dAlembert]	✓	✓	✓	✗

5431	$x {y^{'}}^{2} + 2 y^{'} - y = 0$	[_rational, _dAlembert]	✓	✓	✓	✗

5432	$x {y^{'}}^{2} - 2 y^{'} - y = 0$	[_rational, _dAlembert]	✓	✓	✓	✗

5433	$x {y^{'}}^{2} + 4 y^{'} - 2 y = 0$	[_rational, _dAlembert]	✓	✓	✓	✗

5434	$x {y^{'}}^{2} + y^{'} x - y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

5435	$x {y^{'}}^{2} - (x^{2} + 1) y^{'} + x = 0$	[_quadrature]	✓	✓	✓	✓

5438	$x {y^{'}}^{2} - y y^{'} + a x = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

5439	$x {y^{'}}^{2} + y y^{'} + x^{3} = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	✓	✓	✗

5440	$x {y^{'}}^{2} - y y^{'} + a y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✗

5441	$x {y^{'}}^{2} + y y^{'} - y^{4} = 0$	[[_homogeneous, ‘class G‘]]	✓	✓	✓	✓

5445	$x {y^{'}}^{2} - (3 x - y) y^{'} + y = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	✓	✓	✓

5446	$x {y^{'}}^{2} + a + b x - y - b y = 0$	[[_homogeneous, ‘class C‘], _rational, _dAlembert]	✓	✓	✓	✗

5447	$x {y^{'}}^{2} - 2 y y^{'} + a = 0$	[[_homogeneous, ‘class G‘], _rational, _dAlembert]	✓	✓	✓	✗

5448	$x {y^{'}}^{2} - 2 y y^{'} + a x = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

5449	$x {y^{'}}^{2} - 2 y y^{'} + x + 2 y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

5450	$x {y^{'}}^{2} - 3 y y^{'} + 9 x^{2} = 0$	[[_homogeneous, ‘class G‘]]	✓	✓	✓	✗

5451	$x {y^{'}}^{2} - (2 x + 3 y) y^{'} + 6 y = 0$	[_quadrature]	✓	✓	✓	✓

5453	$x {y^{'}}^{2} + a y y^{'} + b x = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

5454	$x {y^{'}}^{2} - (x y + 1) y^{'} + y = 0$	[_quadrature]	✓	✓	✓	✓

5455	$x {y^{'}}^{2} + y (1 - x) y^{'} - y^{2} = 0$	[_quadrature]	✓	✓	✓	✓

5456	$x {y^{'}}^{2} + (1 - x^{2} y) y^{'} - x y = 0$	[_quadrature]	✓	✓	✓	✓

5457	$(x + 1) {y^{'}}^{2} = y$	[[_homogeneous, ‘class C‘], _rational, _dAlembert]	✓	✓	✓	✓

5460	$2 x {y^{'}}^{2} + (2 x - y) y^{'} + 1 - y = 0$	[_rational, _dAlembert]	✓	✓	✓	✗

5461	$3 x {y^{'}}^{2} - 6 y y^{'} + x + 2 y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

5463	$(3 x + 5) {y^{'}}^{2} - (3 + 3 y) y^{'} + y = 0$	[_rational, _dAlembert]	✓	✓	✓	✗

5465	$4 x {y^{'}}^{2} + 2 y^{'} x - y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

5466	$4 x {y^{'}}^{2} - 3 y y^{'} + 3 = 0$	[[_homogeneous, ‘class G‘], _rational, _dAlembert]	✓	✓	✓	✗

5467	$4 x {y^{'}}^{2} + 4 y y^{'} = 1$	[[_homogeneous, ‘class G‘], _rational, _dAlembert]	✓	✓	✓	✗

5468	$4 x {y^{'}}^{2} + 4 y y^{'} - y^{4} = 0$	[[_homogeneous, ‘class G‘]]	✓	✓	✓	✓

5469	$4 (2 - x) {y^{'}}^{2} + 1 = 0$	[_quadrature]	✓	✓	✓	✓

5470	$16 x {y^{'}}^{2} + 8 y y^{'} + y^{6} = 0$	[[_homogeneous, ‘class G‘]]	✓	✓	✓	✓

5471	$x^{2} {y^{'}}^{2} = a^{2}$	[_quadrature]	✓	✓	✓	✓

5477	$x^{2} {y^{'}}^{2} + 2 a x y^{'} + a^{2} + x^{2} - 2 a y = 0$	[_rational]	✓	✓	✓	✗

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

5496	$(a^{2} + x^{2}) {y^{'}}^{2} = b^{2}$	[_quadrature]	✓	✓	✓	✓

5497	$(a^{2} - x^{2}) {y^{'}}^{2} + b^{2} = 0$	[_quadrature]	✓	✓	✓	✓

5498	$(a^{2} - x^{2}) {y^{'}}^{2} = b^{2}$	[_quadrature]	✓	✓	✓	✓

5499	$(a^{2} - x^{2}) {y^{'}}^{2} = x^{2}$	[_quadrature]	✓	✓	✓	✓

5500	$(a^{2} - x^{2}) {y^{'}}^{2} + 2 x y^{'} y + x^{2} = 0$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓	✓	✗

5506	$x^{3} {y^{'}}^{2} = a$	[_quadrature]	✓	✓	✓	✓

5507	$x^{3} {y^{'}}^{2} + y^{'} x - y = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	✓	✓	✗

5508	$x^{3} {y^{'}}^{2} + x^{2} y y^{'} + a = 0$	[[_homogeneous, ‘class G‘]]	✓	✓	✓	✗

5511	$x^{4} {y^{'}}^{2} - y^{'} x - y = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	✓	✓	✓

5512	$x^{4} {y^{'}}^{2} + 2 x^{3} y y^{'} - 4 = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	✓	✓	✓

5515	$3 x^{4} {y^{'}}^{2} - x y - y = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓	✓	✗

5516	$4 x^{5} {y^{'}}^{2} + 12 x^{4} y y^{'} + 9 = 0$	[[_homogeneous, ‘class G‘]]	✓	✓	✓	✗

5517	$x^{6} {y^{'}}^{2} - 2 y^{'} x - 4 y = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	✓	✓	✓

5518	$x^{8} {y^{'}}^{2} + 3 y^{'} x + 9 y = 0$	[[_homogeneous, ‘class G‘]]	✓	✓	✓	✓

5519	$y {y^{'}}^{2} = a$	[_quadrature]	✓	✓	✓	✓

5520	$y {y^{'}}^{2} = a^{2} x$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	✓	✓	✓

5521	$y {y^{'}}^{2} = e^{2 x}$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✓

5522	$y {y^{'}}^{2} + 2 a x y^{'} - a y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✗

5523	$y {y^{'}}^{2} - 4 a^{2} x y^{'} + a^{2} y = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	✓	✓	✓

5524	$y {y^{'}}^{2} + a x y^{'} + b y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

5525	$y {y^{'}}^{2} - (- 2 b x + a) y^{'} - b y = 0$	[[_homogeneous, ‘class C‘], _rational, _dAlembert]	✓	✓	✓	✗

5526	$y {y^{'}}^{2} + x^{3} y^{'} - x^{2} y = 0$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✗

5527	$y {y^{'}}^{2} + (x - y) y^{'} - x = 0$	[_quadrature]	✓	✓	✓	✓

5528	$y {y^{'}}^{2} - (x + y) y^{'} + y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

5529	$y {y^{'}}^{2} - (x y + 1) y^{'} + x = 0$	[_quadrature]	✓	✓	✓	✓

5530	$y {y^{'}}^{2} + (x - y^{2}) y^{'} - x y = 0$	[_quadrature]	✓	✓	✓	✓

5531	$y {y^{'}}^{2} + y = a$	[_quadrature]	✓	✓	✓	✓

5532	$(x + y) {y^{'}}^{2} + 2 y^{'} x - y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

5533	$(2 x - y) {y^{'}}^{2} - 2 (1 - x) y^{'} + 2 - y = 0$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	✓	✗

5534	$2 y {y^{'}}^{2} + (5 - 4 x) y^{'} + 2 y = 0$	[[_homogeneous, ‘class C‘], _rational, _dAlembert]	✓	✓	✓	✗

5535	$9 y {y^{'}}^{2} + 4 x^{3} y^{'} - 4 x^{2} y = 0$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✗

5536	$(1 - a y) {y^{'}}^{2} = a y$	[_quadrature]	✓	✓	✓	✓

5537	$(x^{2} - a y) {y^{'}}^{2} - 2 x y^{'} y = 0$	[_quadrature]	✓	✓	✓	✓

5538	$x y {y^{'}}^{2} + (x + y) y^{'} + 1 = 0$	[_quadrature]	✓	✓	✓	✓

5549	$y^{2} {y^{'}}^{2} - 3 y^{'} x + y = 0$	[[_1st_order, _with_linear_symmetries], _rational]	✓	✓	✓	✗

5551	$y^{2} {y^{'}}^{2} - 4 a y y^{'} + 4 a^{2} - 4 a x + y^{2} = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓	✓	✗

5552	$y^{2} {y^{'}}^{2} - (x + 1) y y^{'} + x = 0$	[_quadrature]	✓	✓	✓	✓

5554	$y^{2} {y^{'}}^{2} + 2 x y^{'} y + a - y^{2} = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓	✓	✗

5571	$9 y^{2} {y^{'}}^{2} - 3 y^{'} x + y = 0$	[[_1st_order, _with_linear_symmetries], _rational]	✓	✓	✓	✗

5576	$x y^{2} {y^{'}}^{2} - y^{3} y^{'} + a^{2} x = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	✓	✓	✗

5578	$2 x y^{2} {y^{'}}^{2} - y^{3} y^{'} - a = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	✓	✓	✗

5580	$4 y^{3} {y^{'}}^{2} - 4 y^{'} x + y = 0$	[[_1st_order, _with_linear_symmetries], _rational]	✓	✓	✓	✗

5581	$3 x y^{4} {y^{'}}^{2} - y^{5} y^{'} + 1 = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	✓	✓	✗

5582	$9 x y^{4} {y^{'}}^{2} - 3 y^{5} y^{'} - a = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	✓	✓	✗

5584	${y^{'}}^{3} = b x + a$	[_quadrature]	✓	✓	✓	✓

5586	${y^{'}}^{3} + x - y = 0$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	✓	✓

5591	${y^{'}}^{3} + y^{'} + a - b x = 0$	[_quadrature]	✓	✓	✓	✓

5592	${y^{'}}^{3} + y^{'} - y = 0$	[_quadrature]	✓	✓	✓	✗

5593	${y^{'}}^{3} + y^{'} = e^{y}$	[_quadrature]	✓	✓	✓	✗

5596	${y^{'}}^{3} + 2 y^{'} x - y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✗	✗

5597	${y^{'}}^{3} - 2 y^{'} x - y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✗	✗

5602	${y^{'}}^{3} - a x y y^{'} + 2 a y^{2} = 0$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✗

5603	${y^{'}}^{3} - x y^{4} y^{'} - y^{5} = 0$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✗

5604	${y^{'}}^{3} + e^{3 x - 2 y} (y^{'} - 1) = 0$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	✗	✗

5605	${y^{'}}^{3} + e^{- 2 y} (e^{2 x} + e^{3 x}) y^{'} - e^{3 x - 2 y} = 0$	[‘y=_G(x,y’)‘]	✓	✓	✗	✗

5606	${y^{'}}^{3} + {y^{'}}^{2} - y = 0$	[_quadrature]	✓	✓	✓	✓

5613	${y^{'}}^{3} + (\cos (x) \cot (x) - y) {y^{'}}^{2} - (1 + y \cos (x) \cot (x)) y^{'} + y = 0$	[_quadrature]	✓	✓	✓	✓

5614	${y^{'}}^{3} + (2 x - y^{2}) {y^{'}}^{2} - 2 x y^{2} y^{'} = 0$	[_quadrature]	✓	✓	✓	✓

5618	$2 {y^{'}}^{3} + y^{'} x - 2 y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✗	✗

5619	$2 {y^{'}}^{3} + {y^{'}}^{2} - y = 0$	[_quadrature]	✓	✓	✗	✓

5620	$3 {y^{'}}^{3} - x^{4} y^{'} + 2 x^{3} y = 0$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✗

5621	$4 {y^{'}}^{3} + 4 y^{'} = x$	[_quadrature]	✓	✓	✓	✓

5622	$8 {y^{'}}^{3} + 12 {y^{'}}^{2} = 27 x + 27 y$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	✗	✗

5625	$x {y^{'}}^{3} - 2 y {y^{'}}^{2} + 4 x^{2} = 0$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✗

5626	$2 x {y^{'}}^{3} - 3 y {y^{'}}^{2} - x = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✗

5627	$4 x {y^{'}}^{3} - 6 y {y^{'}}^{2} - x + 3 y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✗

5628	$8 x {y^{'}}^{3} - 12 y {y^{'}}^{2} + 9 y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✗

5630	$(a^{2} - x^{2}) {y^{'}}^{3} + b x (a^{2} - x^{2}) {y^{'}}^{2} - y^{'} - b x = 0$	[_quadrature]	✓	✓	✓	✓

5634	$x^{6} {y^{'}}^{3} - y^{'} x - y = 0$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✗	✗

5635	$y {y^{'}}^{3} - 3 y^{'} x + 3 y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✓

5636	$2 y {y^{'}}^{3} - 3 y^{'} x + 2 y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✗

5637	$(x + 2 y) {y^{'}}^{3} + 3 (x + y) {y^{'}}^{2} + (2 x + y) y^{'} = 0$	[_quadrature]	✓	✓	✓	✓

5638	$y^{2} {y^{'}}^{3} - y^{'} x + y = 0$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✗	✗

5639	$y^{2} {y^{'}}^{3} + 2 y^{'} x - y = 0$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✗

5640	$4 y^{2} {y^{'}}^{3} - 2 y^{'} x + y = 0$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✗


5641	$16 y^{2} {y^{'}}^{3} + 2 y^{'} x - y = 0$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✗

5644	$y^{4} {y^{'}}^{3} - 6 y^{'} x + 2 y = 0$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✗

5664	$\sqrt{{y^{'}}^{2} + 1} + a y^{'} = y$	[_quadrature]	✓	✓	✓	✓

5665	$\sqrt{{y^{'}}^{2} + 1} = y^{'} x$	[_quadrature]	✓	✓	✓	✓

5698	$y = x {y^{'}}^{2} + {y^{'}}^{2}$	[[_homogeneous, ‘class C‘], _rational, _dAlembert]	✓	✓	✓	✓

5751	${y^{'}}^{2} - \frac{a^{2}}{x^{2}} = 0$	[_quadrature]	✓	✓	✓	✓

5752	${y^{'}}^{2} = \frac{1 - x}{x}$	[_quadrature]	✓	✓	✓	✓

5753	${y^{'}}^{2} + \frac{2 x y^{'}}{y} - 1 = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✗

5754	$y = a y^{'} + b {y^{'}}^{2}$	[_quadrature]	✓	✓	✓	✓

5755	$x = a y^{'} + b {y^{'}}^{2}$	[_quadrature]	✓	✓	✓	✓

5756	$y = \sqrt{{y^{'}}^{2} + 1} + a y^{'}$	[_quadrature]	✓	✓	✓	✓

5758	$y^{'} - \frac{\sqrt{{y^{'}}^{2} + 1}}{x} = 0$	[_quadrature]	✓	✓	✓	✓

5759	$x^{2} {({y^{'}}^{2} + 1)}^{3} - a^{2} = 0$	[_quadrature]	✓	✓	✓	✓

5760	${y^{'}}^{2} + 1 = \frac{{(x + a)}^{2}}{2 a x + x^{2}}$	[_quadrature]	✓	✓	✓	✓

5767	$y y^{'} = x + y^{2} - y^{2} {y^{'}}^{2}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓	✓	✓

5768	$y - \frac{1}{\sqrt{{y^{'}}^{2} + 1}} = x + \frac{y^{'}}{\sqrt{{y^{'}}^{2} + 1}}$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	✓	✓

5769	$y - 2 y^{'} x = x {y^{'}}^{2}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

6027	$y {y^{'}}^{2} + 2 y^{'} x - y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✗

6028	$(- x^{2} + 1) {y^{'}}^{2} + 1 = 0$	[_quadrature]	✓	✓	✓	✓

6667	$x {y^{'}}^{2} + (y - 1 - x^{2}) y^{'} - x (- 1 + y) = 0$	[_quadrature]	✓	✓	✓	✓

6668	$4 x - 2 y y^{'} + x {y^{'}}^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

6669	$3 x^{4} {y^{'}}^{2} - y^{'} x - y = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	✓	✓	✓

6670	$8 y {y^{'}}^{2} - 2 y^{'} x + y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✗

6671	$y^{2} {y^{'}}^{2} + 3 y^{'} x - y = 0$	[[_1st_order, _with_linear_symmetries], _rational]	✓	✓	✓	✗

6673	$16 y^{3} {y^{'}}^{2} - 4 y^{'} x + y = 0$	[[_1st_order, _with_linear_symmetries], _rational]	✓	✓	✓	✗

6675	$x {y^{'}}^{2} - y y^{'} - y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✗

6676	$y = 2 y^{'} x + y^{2} {y^{'}}^{3}$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✗

6677	${y^{'}}^{2} - y^{'} x - y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✗

6678	$y = x (y^{'} + 1) + {y^{'}}^{2}$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✓

6680	$y {y^{'}}^{2} - y^{'} x + 3 y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

6682	$y^{2} {y^{'}}^{2} + 3 y^{'} x - y = 0$	[[_1st_order, _with_linear_symmetries], _rational]	✓	✓	✓	✗

6683	$4 x - 2 y y^{'} + x {y^{'}}^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

6684	$x {y^{'}}^{2} - 2 y y^{'} + x + 2 y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

6686	$y = - y^{'} x + x^{4} {y^{'}}^{2}$	[[_homogeneous, ‘class G‘], _rational]	✓	✓	✓	✓

6687	$2 y = {y^{'}}^{2} + 4 y^{'} x$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✗

6689	${y^{'}}^{3} - 4 x^{4} y^{'} + 8 x^{3} y = 0$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✗	✗

6917	${y^{'}}^{2} = 4 y$	[_quadrature]	✓	✓	✓	✓

6920	${y^{'}}^{2} - 2 y^{'} + 4 y = 4 x - 1$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	✓	✗

6993	${y^{'}}^{2} = 4 x^{2}$	[_quadrature]	✓	✓	✓	✓

7136	$1 + {x^{'}}^{2} = \frac{a}{y}$	[_quadrature]	✓	✓	✓	✓

7438	$y^{'} (y^{'} + y) = (x + y) x$ i.c.	[_quadrature]	✓	✓	✓	✓

7442	$y {y^{'}}^{2} + 2 y^{'} x - y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✗

7515	${y^{'}}^{2} = 4 x^{2}$	[_quadrature]	✓	✓	✓	✓

7782	$y^{'} x + y = x^{4} {y^{'}}^{2}$	[[_homogeneous, ‘class G‘], _rational]	✓	✓	✓	✓

8435	$x {y^{'}}^{2} - (2 x + 3 y) y^{'} + 6 y = 0$	[_quadrature]	✓	✓	✓	✓

8438	$x {y^{'}}^{2} + (1 - x^{2} y) y^{'} - x y = 0$	[_quadrature]	✓	✓	✓	✓

8439	${y^{'}}^{2} - (x^{2} y + 3) y^{'} + 3 x^{2} y = 0$	[_quadrature]	✓	✓	✓	✓

8440	$x {y^{'}}^{2} - (x y + 1) y^{'} + y = 0$	[_quadrature]	✓	✓	✓	✓

8443	$y {y^{'}}^{2} + (x - y^{2}) y^{'} - x y = 0$	[_quadrature]	✓	✓	✓	✓

8445	$(4 x - y) {y^{'}}^{2} + 6 (x - y) y^{'} + 2 x - 5 y = 0$	[_quadrature]	✓	✓	✓	✓

8447	$x y {y^{'}}^{2} + (x y^{2} - 1) y^{'} - y = 0$	[_quadrature]	✓	✓	✓	✓

8452	$x y {y^{'}}^{2} + (x + y) y^{'} + 1 = 0$	[_quadrature]	✓	✓	✓	✓

8453	$4 x - 2 y y^{'} + x {y^{'}}^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

8454	$3 x^{4} {y^{'}}^{2} - y^{'} x - y = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	✓	✓	✓

8455	${y^{'}}^{2} - y^{'} x - y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✗

8457	${y^{'}}^{2} + 4 x^{5} y^{'} - 12 y x^{4} = 0$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✓

8458	$4 y^{3} {y^{'}}^{2} - 4 y^{'} x + y = 0$	[[_1st_order, _with_linear_symmetries], _rational]	✓	✓	✓	✗

8459	$4 y^{3} {y^{'}}^{2} + 4 y^{'} x + y = 0$	[[_1st_order, _with_linear_symmetries], _rational]	✓	✓	✓	✗

8460	${y^{'}}^{3} + x {y^{'}}^{2} - y = 0$	[_dAlembert]	✓	✓	✓	✗

8461	$y^{4} {y^{'}}^{3} - 6 y^{'} x + 2 y = 0$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✗

8462	${y^{'}}^{2} + x^{3} y^{'} - 2 x^{2} y = 0$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✓

8463	${y^{'}}^{2} + 4 x^{5} y^{'} - 12 y x^{4} = 0$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✓

8464	$2 x {y^{'}}^{3} - 6 y {y^{'}}^{2} + x^{4} = 0$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✗

8467	$x^{8} {y^{'}}^{2} + 3 y^{'} x + 9 y = 0$	[[_homogeneous, ‘class G‘]]	✓	✓	✓	✓

8468	$x^{4} {y^{'}}^{2} + 2 x^{3} y y^{'} - 4 = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	✓	✓	✓

8469	$4 x - 2 y y^{'} + x {y^{'}}^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

8470	$3 x^{4} {y^{'}}^{2} - y^{'} x - y = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	✓	✓	✓

8473	$x^{6} {y^{'}}^{3} - 3 y^{'} x - 3 y = 0$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✗

8474	$y = x^{6} {y^{'}}^{3} - y^{'} x$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✗	✗

8477	${y^{'}}^{2} - y^{'} x - y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✗

8478	$2 {y^{'}}^{3} + y^{'} x - 2 y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✗	✗

8479	$2 {y^{'}}^{2} + y^{'} x - 2 y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✗

8480	${y^{'}}^{3} + 2 y^{'} x - y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✗	✗

8481	$4 x {y^{'}}^{2} - 3 y y^{'} + 3 = 0$	[[_homogeneous, ‘class G‘], _rational, _dAlembert]	✓	✓	✓	✗

8482	${y^{'}}^{3} - y^{'} x + 2 y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✗

8483	$5 {y^{'}}^{2} + 6 y^{'} x - 2 y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✗

8484	$2 x {y^{'}}^{2} + (2 x - y) y^{'} + 1 - y = 0$	[_rational, _dAlembert]	✓	✓	✓	✗

8485	$5 {y^{'}}^{2} + 3 y^{'} x - y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✗

8486	${y^{'}}^{2} + 3 y^{'} x - y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✗

8487	$y = y^{'} x + x^{3} {y^{'}}^{2}$	[[_homogeneous, ‘class G‘], _rational]	✓	✓	✓	✗

8532	$x^{3} {y^{'}}^{2} + x^{2} y y^{'} + 4 = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	✓	✓	✗

8533	$6 x {y^{'}}^{2} - (3 x + 2 y) y^{'} + y = 0$	[_quadrature]	✓	✓	✓	✓

8534	$9 {y^{'}}^{2} + 3 x y^{4} y^{'} + y^{5} = 0$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✗

8535	$4 y^{3} {y^{'}}^{2} - 4 y^{'} x + y = 0$	[[_1st_order, _with_linear_symmetries], _rational]	✓	✓	✓	✗

8536	$x^{6} {y^{'}}^{2} - 2 y^{'} x - 4 y = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	✓	✓	✓

8537	$5 {y^{'}}^{2} + 6 y^{'} x - 2 y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✗

8538	$y^{2} {y^{'}}^{2} - (x + 1) y y^{'} + x = 0$	[_quadrature]	✓	✓	✓	✓

8539	$4 x^{5} {y^{'}}^{2} + 12 x^{4} y y^{'} + 9 = 0$	[[_homogeneous, ‘class G‘]]	✓	✓	✓	✗

8540	$4 y^{2} {y^{'}}^{3} - 2 y^{'} x + y = 0$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✗

8543	$16 x {y^{'}}^{2} + 8 y y^{'} + y^{6} = 0$	[[_homogeneous, ‘class G‘]]	✓	✓	✓	✓

8544	$x {y^{'}}^{2} - (x^{2} + 1) y^{'} + x = 0$	[_quadrature]	✓	✓	✓	✓

8546	$9 x y^{4} {y^{'}}^{2} - 3 y^{5} y^{'} - 1 = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	✓	✓	✗

8548	$x^{6} {y^{'}}^{2} = 8 y^{'} x + 16 y$	[[_homogeneous, ‘class G‘]]	✓	✓	✓	✓

8552	$x {y^{'}}^{2} + y (1 - x) y^{'} - y^{2} = 0$	[_quadrature]	✓	✓	✓	✓

8553	$y {y^{'}}^{2} - (x + y) y^{'} + y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

8555	$x {y^{'}}^{3} - 2 y {y^{'}}^{2} + 4 x^{2} = 0$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✗

8734	$y = y^{'} x + x^{2} {y^{'}}^{2}$	[_separable]	✓	✓	✓	✓

8740	$y = x {y^{'}}^{2} + {y^{'}}^{2}$	[[_homogeneous, ‘class C‘], _rational, _dAlembert]	✓	✓	✓	✓

8755	$y = x {y^{'}}^{2}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

9029	$y {y^{'}}^{2} = 0$	[_quadrature]	✓	✓	✓	✓

9032	${y^{'}}^{2} = x$	[_quadrature]	✓	✓	✓	✓

9033	${y^{'}}^{2} = x + y$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	✓	✓

9034	${y^{'}}^{2} = \frac{y}{x}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

9035	${y^{'}}^{2} = \frac{y^{2}}{x}$	[_separable]	✓	✓	✓	✓

9036	${y^{'}}^{2} = \frac{y^{3}}{x}$	[[_homogeneous, ‘class G‘]]	✓	✓	✓	✓

9037	${y^{'}}^{3} = \frac{y^{2}}{x}$	[[_homogeneous, ‘class G‘], _rational]	✓	✓	✓	✓

9038	${y^{'}}^{2} = \frac{1}{x y}$	[[_homogeneous, ‘class G‘]]	✓	✓	✓	✓

9039	${y^{'}}^{2} = \frac{1}{x y^{3}}$	[[_homogeneous, ‘class G‘]]	✓	✓	✓	✗

10373	${y^{'}}^{2} + a y + b x^{2} = 0$	[[_homogeneous, ‘class G‘]]	✓	✗	✓	✗

10379	${y^{'}}^{2} + a y^{'} + b x = 0$	[_quadrature]	✓	✓	✓	✓

10380	${y^{'}}^{2} + a y^{'} + b y = 0$	[_quadrature]	✓	✓	✓	✓

10384	${y^{'}}^{2} + 2 y^{'} x - y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✗

10385	${y^{'}}^{2} - 2 y^{'} x + y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✗

10389	${y^{'}}^{2} - 2 x^{2} y^{'} + 2 x y = 0$	[[_homogeneous, ‘class G‘]]	✓	✓	✓	✗

10390	${y^{'}}^{2} + a x^{3} y^{'} - 2 a x^{2} y = 0$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✓

10391	${y^{'}}^{2} + (y^{'} - y) e^{x} = 0$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✗

10392	${y^{'}}^{2} - 2 y y^{'} - 2 x = 0$	[_dAlembert]	✓	✓	✓	✗

10394	${y^{'}}^{2} + a y y^{'} - b x - c = 0$	[_dAlembert]	✓	✓	✓	✗

10395	${y^{'}}^{2} + (b x + a y) y^{'} + a b x y = 0$	[_quadrature]	✓	✓	✓	✓

10396	${y^{'}}^{2} - x y^{'} y + y^{2} \ln (a y) = 0$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓	✓	✗

10397	${y^{'}}^{2} + 2 y y^{'} \cot (x) - y^{2} = 0$	[_separable]	✓	✓	✓	✓

10398	${y^{'}}^{2} + y (y - x) y^{'} - x y^{3} = 0$	[_separable]	✓	✓	✓	✓

10402	$2 {y^{'}}^{2} - 2 x^{2} y^{'} + 3 x y = 0$	[[_homogeneous, ‘class G‘]]	✓	✓	✓	✗

10403	$3 {y^{'}}^{2} - 2 y^{'} x + y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✗

10404	$3 {y^{'}}^{2} + 4 y^{'} x + x^{2} - y = 0$	[[_homogeneous, ‘class G‘]]	✓	✓	✓	✓

10405	$a {y^{'}}^{2} + b y^{'} - y = 0$	[_quadrature]	✓	✓	✓	✓

10406	$a {y^{'}}^{2} + b x^{2} y^{'} + c x y = 0$	[[_homogeneous, ‘class G‘]]	✓	✓	✓	✗

10409	$x {y^{'}}^{2} - y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

10410	$x {y^{'}}^{2} + x - 2 y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

10411	$x {y^{'}}^{2} - 2 y^{'} - y = 0$	[_rational, _dAlembert]	✓	✓	✓	✗

10412	$x {y^{'}}^{2} + 4 y^{'} - 2 y = 0$	[_rational, _dAlembert]	✓	✓	✓	✗

10413	$x {y^{'}}^{2} + y^{'} x - y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

10415	$x {y^{'}}^{2} + y y^{'} - x^{2} = 0$	[[_homogeneous, ‘class G‘]]	✓	✓	✓	✗

10416	$x {y^{'}}^{2} + y y^{'} + x^{3} = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	✓	✓	✗

10417	$x {y^{'}}^{2} + y y^{'} - y^{4} = 0$	[[_homogeneous, ‘class G‘]]	✓	✓	✓	✓

10418	$x {y^{'}}^{2} + (y - 3 x) y^{'} + y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

10420	$x {y^{'}}^{2} - y y^{'} + a y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✗

10422	$x {y^{'}}^{2} - 2 y y^{'} + a = 0$	[[_homogeneous, ‘class G‘], _rational, _dAlembert]	✓	✓	✓	✗

10423	$x {y^{'}}^{2} - 2 y y^{'} - x = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

10424	$4 x - 2 y y^{'} + x {y^{'}}^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

10425	$x {y^{'}}^{2} - 2 y y^{'} + x + 2 y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

10426	$x {y^{'}}^{2} + a y y^{'} + b x = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

10434	${(y^{'} x + a)}^{2} - 2 a y + x^{2} = 0$	[_rational]	✓	✓	✓	✗

10448	${y^{'}}^{2} (x^{2} - 1) - 1 = 0$	[_quadrature]	✓	✓	✓	✓

10451	$(- a^{2} + x^{2}) {y^{'}}^{2} - 2 x y^{'} y - x^{2} = 0$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓	✓	✗

10456	$x^{3} {y^{'}}^{2} + x^{2} y y^{'} + a = 0$	[[_homogeneous, ‘class G‘]]	✓	✓	✓	✗

10458	$x^{4} {y^{'}}^{2} - y^{'} x - y = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	✓	✓	✓

10460	$e^{- 2 x} {y^{'}}^{2} - {(y^{'} - 1)}^{2} + e^{- 2 y} = 0$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓	✓	✗

10462	$y {y^{'}}^{2} - 1 = 0$	[_quadrature]	✓	✓	✓	✓

10463	$y {y^{'}}^{2} - e^{2 x} = 0$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✓

10464	$y {y^{'}}^{2} + 2 y^{'} x - y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✗

10465	$y {y^{'}}^{2} + 2 y^{'} x - 9 y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

10466	$y {y^{'}}^{2} - 2 y^{'} x + y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✗

10467	$y {y^{'}}^{2} - 4 y^{'} x + y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

10468	$y {y^{'}}^{2} - 4 a^{2} x y^{'} + a^{2} y = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	✓	✓	✓

10469	$y {y^{'}}^{2} + a x y^{'} + b y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

10470	$y {y^{'}}^{2} + x^{3} y^{'} - x^{2} y = 0$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✗

10471	$y {y^{'}}^{2} - (y - x) y^{'} - x = 0$	[_quadrature]	✓	✓	✓	✓

10472	$(x + y) {y^{'}}^{2} + 2 y^{'} x - y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

10473	$(y - 2 x) {y^{'}}^{2} - 2 (x - 1) y^{'} + y - 2 = 0$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	✓	✗

10474	$2 y {y^{'}}^{2} - (4 x - 5) y^{'} + 2 y = 0$	[[_homogeneous, ‘class C‘], _rational, _dAlembert]	✓	✓	✓	✗

10475	$4 y {y^{'}}^{2} + 2 y^{'} x - y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✗

10476	$9 y {y^{'}}^{2} + 4 x^{3} y^{'} - 4 x^{2} y = 0$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✗

10477	$a y {y^{'}}^{2} + (2 x - b) y^{'} - y = 0$	[[_homogeneous, ‘class C‘], _rational, _dAlembert]	✓	✓	✓	✗

10478	$(b + a y) ({y^{'}}^{2} + 1) - c = 0$	[_quadrature]	✓	✓	✓	✓

10479	$(b_{2} y + a_{2} x + c_{2}) {y^{'}}^{2} + (a_{1} x + b_{1} y + c_{1}) y^{'} + a_{0} x + b_{0} y + c_{0} = 0$	[_rational, _dAlembert]	✓	✓	✓	✗

10488	$y^{2} {y^{'}}^{2} - 4 a y y^{'} + 4 a^{2} - 4 a x + y^{2} = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓	✓	✗

10493	$(y^{2} - 2 a x + a^{2}) {y^{'}}^{2} + 2 a y y^{'} + y^{2} = 0$	[‘y=_G(x,y’)‘]	✓	✓	✓	✗

10498	$(3 y - 2) {y^{'}}^{2} - 4 + 4 y = 0$	[_quadrature]	✓	✓	✓	✓

10513	$\sin (y) {y^{'}}^{2} + 2 x y^{'} \cos {(y)}^{3} - \sin (y) \cos {(y)}^{4} = 0$	[‘y=_G(x,y’)‘]	✓	✗	✓	✗

10514	${y^{'}}^{2} (a \cos (y) + b) - c \cos (y) + d = 0$	[_quadrature]	✓	✓	✓	✓

10520	${y^{'}}^{3} + y^{'} - y = 0$	[_quadrature]	✓	✓	✓	✗

10525	${y^{'}}^{2} - a x y y^{'} + 2 a y^{2} = 0$	[_separable]	✓	✓	✓	✓

10527	${y^{'}}^{3} - x y^{4} y^{'} - y^{5} = 0$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✗

10529	${y^{'}}^{3} + x {y^{'}}^{2} - y = 0$	[_dAlembert]	✓	✓	✓	✗

10534	$4 x {y^{'}}^{3} - 6 y {y^{'}}^{2} - x + 3 y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✗

10535	$8 x {y^{'}}^{3} - 12 y {y^{'}}^{2} + 9 y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✗

10536	$(- a^{2} + x^{2}) {y^{'}}^{3} + b x (- a^{2} + x^{2}) {y^{'}}^{2} + y^{'} + b x = 0$	[_quadrature]	✓	✓	✓	✓

10539	${y^{'}}^{3} \sin (x) - (y \sin (x) - \cos {(x)}^{2}) {y^{'}}^{2} - (\cos {(x)}^{2} y + \sin (x)) y^{'} + y \sin (x) = 0$	[_quadrature]	✓	✓	✓	✗

10540	$2 y {y^{'}}^{3} - y {y^{'}}^{2} + 2 y^{'} x - x = 0$	[_quadrature]	✓	✓	✓	✓

10541	$y^{2} {y^{'}}^{3} + 2 y^{'} x - y = 0$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✗

10542	$16 y^{2} {y^{'}}^{3} + 2 y^{'} x - y = 0$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✗

10549	$x^{2} {({y^{'}}^{2} + 1)}^{3} - a^{2} = 0$	[_quadrature]	✓	✓	✓	✓

12799	${y^{'}}^{2} + (x + y) y^{'} + x y = 0$	[_quadrature]	✓	✓	✓	✓

12800	$x {y^{'}}^{2} - 2 y y^{'} - x = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

12803	$(x^{2} + 1) {y^{'}}^{2} = 1$	[_quadrature]	✓	✓	✓	✓

12806	$4 x {y^{'}}^{2} + 2 y^{'} x - y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

12807	$x {y^{'}}^{2} - 2 y y^{'} - x = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

12809	$y = - y^{'} x + x^{4} {y^{'}}^{2}$	[[_homogeneous, ‘class G‘], _rational]	✓	✓	✓	✓

12810	${y^{'}}^{2} + 2 y^{'} x - y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✗

12811	$x + y^{'} y (2 {y^{'}}^{2} + 3) = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	✓	✗	✗

12812	$a^{2} y {y^{'}}^{2} - 2 y^{'} x + y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✗

12813	$x {y^{'}}^{2} - 2 y y^{'} - x = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

12814	${y^{'}}^{3} - 4 x y^{'} y + 8 y^{2} = 0$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✗	✗

12816	$4 e^{2 y} {y^{'}}^{2} + 2 y^{'} x - 1 = 0$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓	✓	✗

12817	$4 e^{2 y} {y^{'}}^{2} + 2 e^{2 x} y^{'} - e^{2 x} = 0$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	✓	✗

12818	$e^{2 y} {y^{'}}^{3} + (e^{2 x} + e^{3 x}) y^{'} - e^{3 x} = 0$	[‘y=_G(x,y’)‘]	✓	✓	✗	✗

12819	$x y^{2} {y^{'}}^{2} - y^{3} y^{'} + x = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	✓	✓	✗

12821	$y = 2 y^{'} x + y^{2} {y^{'}}^{3}$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✗

12822	$a^{2} y {y^{'}}^{2} - 2 y^{'} x + y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✗

12826	$x^{3} {y^{'}}^{2} + x^{2} y y^{'} + 1 = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	✓	✓	✗

12827	$3 x {y^{'}}^{2} - 6 y y^{'} + x + 2 y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

12828	$y = (x + 1) {y^{'}}^{2}$	[[_homogeneous, ‘class C‘], _rational, _dAlembert]	✓	✓	✓	✓

12830	${y^{'}}^{2} + 2 y y^{'} \cot (x) = y^{2}$	[_separable]	✓	✓	✓	✓

12833	$y = y^{'} x + \frac{y {y^{'}}^{2}}{x^{2}}$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✗

12836	$x {y^{'}}^{2} - 2 y y^{'} - x = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

12838	$x^{2} {y^{'}}^{2} - {(x - 1)}^{2} = 0$	[_quadrature]	✓	✓	✓	✓

12839	$8 {(y^{'} + 1)}^{3} = 27 (x + y) {(1 - y^{'})}^{3}$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	✓	✗

12840	$4 {y^{'}}^{2} = 9 x$	[_quadrature]	✓	✓	✓	✓

13183	${y^{'}}^{2} - 4 y = 0$	[_quadrature]	✓	✓	✓	✓

13784	${y^{'}}^{2} + x^{2} = 1$	[_quadrature]	✓	✓	✓	✓

13786	$x = {y^{'}}^{3} - y^{'} + 2$	[_quadrature]	✓	✓	✗	✓

13796	${y^{'}}^{3} - e^{2 x} y^{'} = 0$	[_quadrature]	✓	✓	✓	✓

13797	$y = 5 y^{'} x - {y^{'}}^{2}$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✗

13807	$y = x^{2} + 2 y^{'} x + \frac{{y^{'}}^{2}}{2}$	[[_homogeneous, ‘class G‘]]	✓	✓	✗	✓

13809	$y ({y^{'}}^{2} + 1) = a$	[_quadrature]	✓	✓	✓	✓

13821	${y^{'}}^{2} - 2 y^{'} x + y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✗

13822	${y^{'}}^{2} + 2 y y^{'} \cot (x) - y^{2} = 0$	[_separable]	✓	✓	✓	✓

13890	$\sinh (x) {y^{'}}^{2} + 3 y = 0$	[‘y=_G(x,y’)‘]	✓	✓	✓	✗

14079	$y {y^{'}}^{2} + 2 y^{'} x - y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✗

14138	$y = 2 y^{'} x + {y^{'}}^{2}$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✗

14139	$y = x {y^{'}}^{2} + {y^{'}}^{2}$	[[_homogeneous, ‘class C‘], _rational, _dAlembert]	✓	✓	✓	✓

14140	$y = x (y^{'} + 1) + {y^{'}}^{2}$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✓

14141	$y = y {y^{'}}^{2} + 2 y^{'} x$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✗

14142	$y = y y^{'} + y^{'} - {y^{'}}^{2}$	[_quadrature]	✓	✓	✓	✓

14200	$y = x {y^{'}}^{2} + {y^{'}}^{2}$	[[_homogeneous, ‘class C‘], _rational, _dAlembert]	✓	✓	✓	✓

14253	${y^{'}}^{2} - 4 y = 0$	[_quadrature]	✓	✓	✓	✓

14254	${y^{'}}^{2} - 9 x y = 0$	[[_homogeneous, ‘class G‘]]	✓	✓	✓	✓

14255	${y^{'}}^{2} = x^{6}$	[_quadrature]	✓	✓	✓	✓

15707	${y^{'}}^{2} + y = 0$	[_quadrature]	✓	✓	✓	✓

16054	$y = t {y^{'}}^{2} + 3 {y^{'}}^{2} - 2 {y^{'}}^{3}$	[_dAlembert]	✓	✓	✓	✗

16056	$y = t (2 - y^{'}) + 2 {y^{'}}^{2} + 1$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✗

16740	$4 {y^{'}}^{2} - 9 x = 0$	[_quadrature]	✓	✓	✓	✓

16741	${y^{'}}^{2} - 2 y y^{'} = y^{2} (- 1 + e^{2 x})$	[_separable]	✓	✓	✓	✓

16742	${y^{'}}^{2} - 2 y^{'} x - 8 x^{2} = 0$	[_quadrature]	✓	✓	✓	✓

16744	${y^{'}}^{2} - (2 x + y) y^{'} + x^{2} + x y = 0$	[_quadrature]	✓	✓	✓	✓

16745	${y^{'}}^{3} + (x + 2) e^{y} = 0$	[[_1st_order, _with_exponential_symmetries]]	✓	✓	✓	✗

16746	${y^{'}}^{3} = y {y^{'}}^{2} - x^{2} y^{'} + x^{2} y$	[_quadrature]	✓	✓	✓	✓

16747	${y^{'}}^{2} - y y^{'} + e^{x} = 0$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✗

16748	${y^{'}}^{2} - 4 y^{'} x + 2 y + 2 x^{2} = 0$	[[_homogeneous, ‘class G‘]]	✓	✓	✓	✓

16749	$y = {y^{'}}^{2} e^{y^{'}}$	[_quadrature]	✓	✓	✓	✓

16752	$x = {y^{'}}^{2} - 2 y^{'} + 2$	[_quadrature]	✓	✓	✓	✓

16755	$x {y^{'}}^{2} = e^{\frac{1}{y^{'}}}$	[_quadrature]	✓	✓	✓	✗

16756	$x {({y^{'}}^{2} + 1)}^{3 / 2} = a$	[_quadrature]	✓	✓	✓	✓

16762	$y = x (y^{'} + 1) + {y^{'}}^{2}$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✓

16764	$y = x {y^{'}}^{2} - \frac{1}{y^{'}}$	[_dAlembert]	✓	✓	✓	✗

16775	$y^{2} ({y^{'}}^{2} + 1) - 4 y y^{'} - 4 x = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓	✓	✗

16776	${y^{'}}^{2} - 4 y = 0$	[_quadrature]	✓	✓	✓	✓

16777	${y^{'}}^{3} - 4 x y^{'} y + 8 y^{2} = 0$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✗	✗

16782	$8 {y^{'}}^{3} - 12 {y^{'}}^{2} = 27 y - 27 x$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	✗	✗

16784	$y = {y^{'}}^{2} - y^{'} x + x$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✗

16787	${y^{'}}^{2} - y y^{'} + e^{x} = 0$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✗

16788	$3 x {y^{'}}^{2} - 6 y y^{'} + x + 2 y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

16828	$y^{'} + x {y^{'}}^{2} - y = 0$	[_rational, _dAlembert]	✓	✓	✓	✗

17859	$y {y^{'}}^{2} + (x - y) y^{'} - x = 0$	[_quadrature]	✓	✓	✓	✓

17862	$x {y^{'}}^{2} + 2 y^{'} x - y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

17863	$x {y^{'}}^{3} = y^{'} + 1$	[_quadrature]	✓	✓	✓	✓

17866	$y = {y^{'}}^{2} e^{y^{'}}$	[_quadrature]	✓	✓	✓	✓

17868	$y ({y^{'}}^{2} + 1) = 2 α$	[_quadrature]	✓	✓	✓	✓

17870	$y = 2 y^{'} x + \frac{x^{2}}{2} + {y^{'}}^{2}$	[[_homogeneous, ‘class G‘]]	✓	✓	✗	✓

17872	$x = y y^{'} + a {y^{'}}^{2}$	[_dAlembert]	✓	✓	✓	✗

17873	$y = x {y^{'}}^{2} + {y^{'}}^{3}$	[_dAlembert]	✓	✓	✓	✗

17875	$y = 2 y^{'} x + y^{2} {y^{'}}^{3}$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✗

17877	${y^{'}}^{2} + 2 y^{'} x + 2 y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✗

17885	$4 x - 2 y y^{'} + x {y^{'}}^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

17886	$x {y^{'}}^{2} + 2 y^{'} x - y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

17889	$x^{2} {y^{'}}^{2} - 2 x y^{'} y + 2 x y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

17891	$y = 2 y^{'} x + \frac{x^{2}}{2} + {y^{'}}^{2}$	[[_homogeneous, ‘class G‘]]	✓	✓	✗	✓

17892	${y^{'}}^{2} - y y^{'} + e^{x} = 0$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✗

17989	$y^{'} x + y = x^{4} {y^{'}}^{2}$	[[_homogeneous, ‘class G‘], _rational]	✓	✓	✓	✓

18482	$x {y^{'}}^{2} + 2 y^{'} - y = 0$	[_rational, _dAlembert]	✓	✓	✓	✗

18483	$2 {y^{'}}^{3} + {y^{'}}^{2} - y = 0$	[_quadrature]	✓	✓	✗	✓

18486	${y^{'}}^{2} (x^{2} - 1) = 1$	[_quadrature]	✓	✓	✓	✓

18526	$y - 2 y^{'} x - y {y^{'}}^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✗

18629	$x = {y^{'}}^{2} + y$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	✓	✓

18723	${y^{'}}^{3} + 2 x {y^{'}}^{2} - y^{2} {y^{'}}^{2} - 2 x y^{2} y^{'} = 0$	[_quadrature]	✓	✓	✓	✓

18724	${y^{'}}^{2} - a x^{3} = 0$	[_quadrature]	✓	✓	✓	✓

18725	$(x + 2 y) {y^{'}}^{3} + 3 (x + y) {y^{'}}^{2} + (2 x + y) y^{'} = 0$	[_quadrature]	✓	✓	✓	✓

18726	${y^{'}}^{3} = a x^{4}$	[_quadrature]	✓	✓	✓	✓

18729	$x - y y^{'} = a {y^{'}}^{2}$	[_dAlembert]	✓	✓	✓	✗

18731	$4 y = {y^{'}}^{2} + x^{2}$	[[_homogeneous, ‘class G‘]]	✓	✓	✓	✗

18732	$x {y^{'}}^{2} - 2 y y^{'} + a x = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

18733	$y = 2 y^{'} + 3 {y^{'}}^{2}$	[_quadrature]	✓	✓	✓	✓

18734	$({y^{'}}^{2} + 1) x = 1$	[_quadrature]	✓	✓	✓	✓

18735	$x^{2} = a^{2} ({y^{'}}^{2} + 1)$	[_quadrature]	✓	✓	✓	✓

18738	$y = y {y^{'}}^{2} + 2 y^{'} x$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✗

18739	$y = x (y^{'} + 1) + {y^{'}}^{2}$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✓

18740	$x^{2} (y - y^{'} x) = y {y^{'}}^{2}$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✗

18742	$e^{4 x} (y^{'} - 1) + e^{2 y} {y^{'}}^{2} = 0$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	✓	✗

18748	$y = - y^{'} x + x^{4} {y^{'}}^{2}$	[[_homogeneous, ‘class G‘], _rational]	✓	✓	✓	✓

18750	$a y {y^{'}}^{2} + (2 x - b) y^{'} - y = 0$	[[_homogeneous, ‘class C‘], _rational, _dAlembert]	✓	✓	✓	✗

18758	${y^{'}}^{2} + 2 y y^{'} \cot (x) = y^{2}$	[_separable]	✓	✓	✓	✓

18759	$({y^{'}}^{2} - \frac{1}{a^{2} - x^{2}}) (y^{'} - \sqrt{\frac{y}{x}}) = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	✓	✓	✓

18762	${y^{'}}^{3} - 4 x y^{'} y + 8 y^{2} = 0$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✗	✗

18765	$e^{3 x} (y^{'} - 1) + e^{2 y} {y^{'}}^{3} = 0$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], _dAlembert]	✓	✓	✗	✗

18769	$y = 2 y^{'} x + y^{2} {y^{'}}^{3}$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✗

18774	${(y^{'} + 1)}^{3} = \frac{7 (x + y) {(1 - y^{'})}^{3}}{4 a}$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	✓	✓	✗

18777	${y^{'}}^{2} + 2 y^{'} x - y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✗

18778	$a {y^{'}}^{3} = 27 y$	[_quadrature]	✓	✓	✓	✓

18779	$x {y^{'}}^{2} - 2 y y^{'} + a x = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

18780	$x^{3} {y^{'}}^{2} + x^{2} y y^{'} + a^{3} = 0$	[[_homogeneous, ‘class G‘]]	✓	✓	✓	✗

18784	$4 {y^{'}}^{2} = 9 x$	[_quadrature]	✓	✓	✓	✓

18786	$(8 {y^{'}}^{3} - 27) x = 12 y {y^{'}}^{2}$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✗

19062	${x^{'}}^{2} = k^{2} (1 - e^{- \frac{2 g x}{k^{2}}})$ i.c.	[_quadrature]	✓	✓	✗	✗

19136	${y^{'}}^{2} + 2 y^{'} x - 3 x^{2} = 0$	[_quadrature]	✓	✓	✓	✓

19137	${y^{'}}^{2} + 2 y y^{'} \cot (x) = y^{2}$	[_separable]	✓	✓	✓	✓

19139	$y^{'} (y^{'} - y) = (x + y) x$	[_quadrature]	✓	✓	✓	✓

19140	$y {y^{'}}^{2} + (x - y) y^{'} - x = 0$	[_quadrature]	✓	✓	✓	✓

19141	$x + y {y^{'}}^{2} = (x y + 1) y^{'}$	[_quadrature]	✓	✓	✓	✓

19142	$x {y^{'}}^{2} + (y - x) y^{'} - y = 0$	[_quadrature]	✓	✓	✓	✓

19143	${y^{'}}^{3} - a x^{4} = 0$	[_quadrature]	✓	✓	✓	✓

19144	${y^{'}}^{2} + y^{'} x + y y^{'} + x y = 0$	[_quadrature]	✓	✓	✓	✓

19149	${y^{'}}^{3} + 2 x {y^{'}}^{2} - y^{2} {y^{'}}^{2} - 2 x y^{2} y^{'} = 0$	[_quadrature]	✓	✓	✓	✓

19152	${y^{'}}^{2} - y y^{'} + x = 0$	[_dAlembert]	✓	✓	✓	✗

19155	$y = x {y^{'}}^{2} + y^{'}$	[_rational, _dAlembert]	✓	✓	✓	✗

19156	$x {y^{'}}^{2} + a x = 2 y y^{'}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

19157	${y^{'}}^{3} + y^{'} = e^{y}$	[_quadrature]	✓	✓	✓	✗

19160	$y = \ln (\cos (y^{'})) + y^{'} \tan (y^{'})$	[_dAlembert]	✓	✓	✓	✗

19161	$x = y y^{'} - {y^{'}}^{2}$	[_dAlembert]	✓	✓	✓	✗

19162	$(2 x - b) y^{'} = y - a y {y^{'}}^{2}$	[[_homogeneous, ‘class C‘], _rational, _dAlembert]	✓	✓	✓	✗

19164	$y {y^{'}}^{2} + 2 y^{'} x = y$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✗

19165	$({y^{'}}^{2} + 1) x = 1$	[_quadrature]	✓	✓	✓	✓

19166	$x^{2} = a^{2} ({y^{'}}^{2} + 1)$	[_quadrature]	✓	✓	✓	✓

19176	$4 y {y^{'}}^{2} + 2 y^{'} x - y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✗

19177	$y {y^{'}}^{2} + 2 y^{'} x - y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✗

19181	$x + y^{'} y (2 {y^{'}}^{2} + 3) = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	✓	✗	✗

19182	$y = \frac{2 a {y^{'}}^{2}}{{({y^{'}}^{2} + 1)}^{2}}$	[_quadrature]	✓	✓	✓	✓

19184	$4 x {y^{'}}^{2} + 4 y y^{'} = y^{4}$	[[_homogeneous, ‘class G‘]]	✓	✓	✓	✓

19188	$a^{2} y {y^{'}}^{2} - 4 y^{'} x + y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

19189	$x^{2} (y - y^{'} x) = y {y^{'}}^{2}$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✗

19190	$({y^{'}}^{2} - \frac{1}{a^{2} - x^{2}}) (y^{'} - \sqrt{\frac{y}{x}}) = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	✓	✓	✓

19192	$y y^{'} + x = a {y^{'}}^{2}$	[_dAlembert]	✓	✓	✓	✗

19194	$2 y = y^{'} x + \frac{a}{y^{'}}$	[[_homogeneous, ‘class G‘], _rational, _dAlembert]	✓	✓	✓	✗

19195	$y = \sqrt{{y^{'}}^{2} + 1} + a y^{'}$	[_quadrature]	✓	✓	✓	✓

19197	$y = a y^{'} + b {y^{'}}^{2}$	[_quadrature]	✓	✓	✓	✓

19205	$x {y^{'}}^{2} - 2 y y^{'} + a x = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

19208	$4 {y^{'}}^{2} = 9 x$	[_quadrature]	✓	✓	✓	✓

19211	$3 y = 2 y^{'} x - \frac{2 {y^{'}}^{2}}{x}$	[[_homogeneous, ‘class G‘]]	✓	✓	✓	✗

19216	$y {y^{'}}^{2} - 2 y^{'} x + y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✗

19217	$3 x {y^{'}}^{2} - 6 y y^{'} + x + 2 y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

19218	${y^{'}}^{2} + 2 x^{3} y^{'} - 4 x^{2} y = 0$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✓

19220	$(- a^{2} + x^{2}) {y^{'}}^{2} - 2 x y^{'} y - x^{2} = 0$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓	✓	✗

19223	$y + x^{2} = {y^{'}}^{2}$	[[_homogeneous, ‘class G‘]]	✓	✓	✓	✗

19224	${y^{'}}^{3} = y^{4} (y^{'} x + y)$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✗

19225	${(1 - y^{'})}^{2} - e^{- 2 y} = e^{- 2 x} {y^{'}}^{2}$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓	✓	✗

19231	$8 x {y^{'}}^{3} = y (12 {y^{'}}^{2} - 9)$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✗

19467	$(a^{2} - x^{2}) {y^{'}}^{3} + b x (a^{2} - x^{2}) {y^{'}}^{2} - y^{'} - b x = 0$	[_quadrature]	✓	✓	✓	✓

19468	$(x + 2 y) {y^{'}}^{3} + 3 (x + y) {y^{'}}^{2} + (2 x + y) y^{'} = 0$	[_quadrature]	✓	✓	✓	✓

19470	$y = \frac{x}{y^{'}} - a y^{'}$	[_dAlembert]	✓	✓	✓	✗

19472	$x {y^{'}}^{3} = a + b y^{'}$	[_quadrature]	✓	✓	✓	✓

19474	$a y {y^{'}}^{2} + (2 x - b) y^{'} - y = 0$	[[_homogeneous, ‘class C‘], _rational, _dAlembert]	✓	✓	✓	✗

19475	$y = x (y^{'} + 1) + {y^{'}}^{2}$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✓

19476	$e^{3 x} (y^{'} - 1) + e^{2 y} {y^{'}}^{3} = 0$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], _dAlembert]	✓	✓	✗	✗

19477	$y = 2 y^{'} x + y^{2} {y^{'}}^{3}$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✗

19478	$y = - y^{'} x + x^{4} {y^{'}}^{2}$	[[_homogeneous, ‘class G‘], _rational]	✓	✓	✓	✓

19479	$y - 2 y^{'} x + a y {y^{'}}^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✗

19480	$x^{2} (y - y^{'} x) = y {y^{'}}^{2}$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✓	✗

19492	${y^{'}}^{3} - 4 x y^{'} y + 8 y^{2} = 0$	[[_1st_order, _with_linear_symmetries]]	✓	✓	✗	✗

19493	${y^{'}}^{2} + 2 y^{'} x - y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	✓	✓	✗

19494	$x^{3} {y^{'}}^{2} + x^{2} y y^{'} + a^{3} = 0$	[[_homogeneous, ‘class G‘]]	✓	✓	✓	✗

19496	$x {y^{'}}^{2} - 2 y y^{'} + x + 2 y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	✓	✓	✓

2.3.5 ﬁrst order ode parametric