Problems 10301 to 10400

Table 2.209: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

10301	$x (y^{2} - 3 x) y^{'} + 2 y^{3} - 5 x y = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	3.567

10302	$x (y^{2} + x^{2} - a) y^{'} - (a + x^{2} + y^{2}) y = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	7.570

10303	$x (y^{2} + x y - x^{2}) y^{'} - y^{3} + x y^{2} + x^{2} y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	215.765

10304	$x (y^{2} + x^{2} y + x^{2}) y^{'} - 2 y^{3} - 2 x^{2} y^{2} + x^{4} = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	3.227

10305	$2 x (5 x^{2} + y^{2}) y^{'} + y^{3} - x^{2} y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	43.756

10306	$3 x y^{2} y^{'} + y^{3} - 2 x = 0$	[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli]	✓	2.324

10307	$(3 x y^{2} - x^{2}) y^{'} + y^{3} - 2 x y = 0$	[[_homogeneous, ‘class G‘], _exact, _rational]	✓	1.999

10308	$6 x y^{2} y^{'} + x + 2 y^{3} = 0$	[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli]	✓	2.701

10309	$(x^{2} + 6 x y^{2}) y^{'} - y (3 y^{2} - x) = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	2.719

10310	$(x^{2} y^{2} + x) y^{'} + y = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	7.684

10311	${(x y - 1)}^{2} x y^{'} + (1 + x^{2} y^{2}) y = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	1.963

10312	$(10 x^{3} y^{2} + x^{2} y + 2 x) y^{'} + 5 x^{2} y^{3} + x y^{2} = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	3.182

10313	$(y^{3} - 3 x) y^{'} - 3 y + x^{2} = 0$	[_exact, _rational]	✓	1.367

10314	$(y^{3} - x^{3}) y^{'} - x^{2} y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	143.296

10315	$(a + x^{2} + y^{2}) y y^{'} + (y^{2} + x^{2} - a) x = 0$	[_exact, _rational]	✓	2.489

10316	$2 y^{3} y^{'} + x y^{2} = 0$	[_separable]	✓	3.197

10317	$(2 y^{3} + y) y^{'} - 2 x^{3} - x = 0$	[_separable]	✓	2.755

10318	$(2 y^{3} + 5 x^{2} y) y^{'} + 5 x y^{2} + x^{3} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓	215.760

10319	$(3 x^{3} + 6 x^{2} y - 3 x y^{2} + 20 y^{3}) y^{'} + 4 x^{3} + 9 x^{2} y + 6 x y^{2} - y^{3} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓	252.637

10320	$(\frac{y^{2}}{b} + \frac{x^{2}}{a}) (y y^{'} + x) + \frac{(a - b) (y y^{'} - x)}{a + b} = 0$	[_rational]	✗	4.272

10321	$(2 a y^{3} + 3 a x y^{2} - b x^{3} + c x^{2}) y^{'} - a y^{3} + c y^{2} + 3 b x^{2} y + 2 b x^{3} = 0$	[_rational]	✗	3.668

10322	$x y^{3} y^{'} + y^{4} - x \sin (x) = 0$	[_Bernoulli]	✓	36.580

10323	$(2 x y^{3} - x^{4}) y^{'} + 2 x^{3} y - y^{4} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	8.503

10324	$(2 x y^{3} + y) y^{'} + 2 y^{2} = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	1.229

10325	$(2 x y^{3} + x y + x^{2}) y^{'} - x y + y^{2} = 0$	[_rational]	✓	1.720

10326	$(3 x y^{3} - 4 x y + y) y^{'} + y^{2} (y^{2} - 2) = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	1.745

10327	$(7 x y^{3} + y - 5 x) y^{'} + y^{4} - 5 y = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	1.862

10328	$(x^{2} y^{3} + x y) y^{'} - 1 = 0$	[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	1.658

10329	$(2 x^{2} y^{3} + x^{2} y^{2} - 2 x) y^{'} - 2 y - 1 = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	2.745

10330	$(10 x^{2} y^{3} - 3 y^{2} - 2) y^{'} + 5 x y^{4} + x = 0$	[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	1.619

10331	$(a x y^{3} + c) x y^{'} + (b x^{3} y + c) y = 0$	[_rational]	✓	1.960

10332	$(2 x^{3} y^{3} - x) y^{'} + 2 x^{3} y^{3} - y = 0$	[_rational]	✓	1.678

10333	$y (y^{3} - 2 x^{3}) y^{'} + (2 y^{3} - x^{3}) x = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	78.754

10334	$y ({(b x + a y)}^{3} + b x^{3}) y^{'} + x ({(b x + a y)}^{3} + a y^{3}) = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	14.214

10335	$(x + 2 y + 2 x^{2} y^{3} + x y^{4}) y^{'} + y^{5} + y = 0$	[_rational]	✓	3.659

10336	$a x^{2} y^{n} y^{'} - 2 y^{'} x + y = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	1.743

10337	$y^{m} x^{n} (a x y^{'} + b y) + α x y^{'} + β y = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	2.691

10338	$(f (x + y) + 1) y^{'} + f (x + y) = 0$	[[_homogeneous, ‘class C‘], _exact, _dAlembert]	✓	1.762

10339	$(\sqrt{x y} - 1) x y^{'} - (\sqrt{x y} + 1) y = 0$	[[_homogeneous, ‘class G‘]]	✓	5.473

10340	$(2 x^{5 / 2} y^{3 / 2} + x^{2} y - x) y^{'} - x^{3 / 2} y^{5 / 2} + x y^{2} - y = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	101.311

10341	$(1 + \sqrt{x + y}) y^{'} + 1 = 0$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	1.768

10342	$\sqrt{- 1 + y^{2}} y^{'} - \sqrt{x^{2} - 1} = 0$	[_separable]	✓	2.440

10343	$(\sqrt{1 + y^{2}} + a x) y^{'} + \sqrt{x^{2} + 1} + a y = 0$	[_exact]	✓	36.473

10344	$(x + \sqrt{x^{2} + y^{2}}) y^{'} - y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	7.384

10345	$(y \sqrt{x^{2} + y^{2}} + (y^{2} - x^{2}) \sin (α) - 2 x y \cos (α)) y^{'} + x \sqrt{x^{2} + y^{2}} + 2 x y \sin (α) + (y^{2} - x^{2}) \cos (α) = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	185.713

10346	$(x \sqrt{x^{2} + y^{2} + 1} - y (x^{2} + y^{2})) y^{'} - y \sqrt{x^{2} + y^{2} + 1} - x (x^{2} + y^{2}) = 0$	[[_1st_order, _with_linear_symmetries]]	✓	2.610

10347	$(\frac{e 1 (x + a)}{{({(x + a)}^{2} + y^{2})}^{3 / 2}} + \frac{e 2 (x - a)}{{({(x - a)}^{2} + y^{2})}^{3 / 2}}) y^{'} - y (\frac{e 1}{{({(x + a)}^{2} + y^{2})}^{3 / 2}} + \frac{e 2}{{({(x - a)}^{2} + y^{2})}^{3 / 2}}) = 0$	unknown	✓	238.041

10348	$(e^{x} + x e^{y}) y^{'} + y e^{x} + e^{y} = 0$	[_exact]	✓	1.575

10349	$x (3 e^{x y} + 2 e^{- x y}) (y^{'} x + y) + 1 = 0$	[[_homogeneous, ‘class G‘]]	✓	31.299

10350	$(\ln (y) + x) y^{'} - 1 = 0$	[[_1st_order, _with_exponential_symmetries]]	✓	1.382

10351	$(\ln (y) + 2 x - 1) y^{'} - 2 y = 0$	[[_1st_order, _with_linear_symmetries]]	✓	1.815

10352	$x (2 x^{2} y \ln (y) + 1) y^{'} - 2 y = 0$	[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	1.751

10353	$x (y \ln (x y) + y - a x) y^{'} - y (a x \ln (x y) - y + a x) = 0$	[‘y=_G(x,y’)‘]	✓	2.132

10354	$y^{'} (1 + \sin (x)) \sin (y) + \cos (x) (\cos (y) - 1) = 0$	[_separable]	✓	5.546

10355	$\sin (y) + \cos (x) y + (x \cos (y) + \sin (x)) y^{'} = 0$	[_exact]	✓	9.001

10356	$x y^{'} \cot (\frac{y}{x}) + 2 x \sin (\frac{y}{x}) - y \cot (\frac{y}{x}) = 0$	[[_homogeneous, ‘class A‘]]	✓	4.227

10357	$y^{'} \cos (y) - \cos (x) \sin {(y)}^{2} - \sin (y) = 0$	[‘y=_G(x,y’)‘]	✗	49.634

10358	$y^{'} \cos (y) + x \sin (y) \cos {(y)}^{2} - \sin {(y)}^{3} = 0$	[‘y=_G(x,y’)‘]	✗	42.231

10359	$y^{'} (\cos (y) - \sin (α) \sin (x)) \cos (y) + (\cos (x) - \sin (α) \sin (y)) \cos (x) = 0$	unknown	✓	47.341

10360	$x \cos (y) y^{'} + \sin (y) = 0$	[_separable]	✓	4.540

10361	$(x \sin (y) - 1) y^{'} + \cos (y) = 0$	[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	5.320

10362	$(x \cos (y) + \cos (x)) y^{'} - y \sin (x) + \sin (y) = 0$	[_exact]	✓	30.127

10363	$(x^{2} \cos (y) + 2 y \sin (x)) y^{'} + 2 x \sin (y) + y^{2} \cos (x) = 0$	[_exact]	✓	40.236

10364	$x y^{'} \ln (x) \sin (y) + \cos (y) (1 - x \cos (y)) = 0$	[‘y=_G(x,y’)‘]	✗	59.908

10365	$\sin (x) \cos (y) + \cos (x) \sin (y) y^{'} = 0$	[_separable]	✓	2.683

10366	$3 \sin (x) \sin (y) y^{'} + 5 \cos {(x)}^{4} y = 0$	[_separable]	✓	5.348

10367	$y^{'} \cos (a y) - b (1 - c \cos (a y)) \sqrt{\cos {(a y)}^{2} - 1 + c \cos (a y)} = 0$	[_quadrature]	✓	21.756

10368	$(x \sin (x y) + \cos (x + y) - \sin (y)) y^{'} + y \sin (x y) + \cos (x + y) + \cos (x) = 0$	[_exact]	✓	41.912

10369	$(x^{2} y \sin (x y) - 4 x) y^{'} + x y^{2} \sin (x y) - y = 0$	[[_homogeneous, ‘class G‘]]	✓	39.114

10370	$(y^{'} x - y) \cos {(\frac{y}{x})}^{2} + x = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	10.625

10371	$(y \sin (\frac{y}{x}) - x \cos (\frac{y}{x})) x y^{'} - (x \cos (\frac{y}{x}) + y \sin (\frac{y}{x})) y = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	7.345

10372	$(y f (x^{2} + y^{2}) - x) y^{'} + y + x f (x^{2} + y^{2}) = 0$	[[_1st_order, _with_linear_symmetries]]	✓	2.573

10373	$f (x^{2} + a y^{2}) (a y y^{'} + x) - y - y^{'} x = 0$	[_exact]	✗	3.407

10374	${y^{'}}^{2} + a y + b x^{2} = 0$	[[_homogeneous, ‘class G‘]]	✓	2.117

10375	${y^{'}}^{2} + y^{2} - a^{2} = 0$	[_quadrature]	✓	1.171

10376	${y^{'}}^{2} - y^{3} + y^{2} = 0$	[_quadrature]	✓	20.208

10377	${y^{'}}^{2} - 4 y^{3} + a y + b = 0$	[_quadrature]	✓	141.202

10378	${y^{'}}^{2} + a^{2} y^{2} (\ln {(y)}^{2} - 1) = 0$	[_quadrature]	✓	0.916

10379	${y^{'}}^{2} - 2 y^{'} - y^{2} = 0$	[_quadrature]	✓	39.059

10380	${y^{'}}^{2} + a y^{'} + b x = 0$	[_quadrature]	✓	0.341

10381	${y^{'}}^{2} + a y^{'} + b y = 0$	[_quadrature]	✓	0.702

10382	${y^{'}}^{2} + (x - 2) y^{'} - y + 1 = 0$	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	0.567

10383	${y^{'}}^{2} + (x + a) y^{'} - y = 0$	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	0.591

10384	${y^{'}}^{2} - (x + 1) y^{'} + y = 0$	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	0.552

10385	${y^{'}}^{2} + 2 y^{'} x - y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	0.543

10386	${y^{'}}^{2} - 2 y^{'} x + y = 0$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	0.554

10387	${y^{'}}^{2} + a x y^{'} - b x^{2} - c = 0$	[_quadrature]	✓	0.664

10388	${y^{'}}^{2} + a x y^{'} + b y + c x^{2} = 0$	[[_homogeneous, ‘class G‘]]	✓	3.016

10389	${y^{'}}^{2} + (a x + b) y^{'} - a y + c = 0$	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	0.665

10390	${y^{'}}^{2} - 2 x^{2} y^{'} + 2 x y = 0$	[[_homogeneous, ‘class G‘]]	✓	2.070

10391	${y^{'}}^{2} + a x^{3} y^{'} - 2 a x^{2} y = 0$	[[_1st_order, _with_linear_symmetries]]	✓	2.502

10392	${y^{'}}^{2} + (y^{'} - y) e^{x} = 0$	[[_1st_order, _with_linear_symmetries]]	✓	3.828

10393	${y^{'}}^{2} - 2 y y^{'} - 2 x = 0$	[_dAlembert]	✓	82.163

10394	${y^{'}}^{2} - (4 y + 1) y^{'} + (4 y + 1) y = 0$	[_quadrature]	✓	1.924

10395	${y^{'}}^{2} + a y y^{'} - b x - c = 0$	[_dAlembert]	✓	35.596

10396	${y^{'}}^{2} + (b x + a y) y^{'} + a b x y = 0$	[_quadrature]	✓	0.470

10397	${y^{'}}^{2} - x y^{'} y + y^{2} \ln (a y) = 0$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	5.361

10398	${y^{'}}^{2} + 2 y y^{'} \cot (x) - y^{2} = 0$	[_separable]	✓	1.421

10399	${y^{'}}^{2} + y (y - x) y^{'} - x y^{3} = 0$	[_separable]	✓	0.501

10400	${y^{'}}^{2} - 2 x^{3} y^{2} y^{'} - 4 x^{2} y^{3} = 0$	[[_1st_order, _with_linear_symmetries]]	✓	2.451

2.2.104 Problems 10301 to 10400