Problems 10201 to 10300

Table 2.207: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

10201	$\sqrt{x^{2} - 1} y^{'} - \sqrt{- 1 + y^{2}} = 0$	[_separable]	✓	5.903

10202	$y^{'} \sqrt{- x^{2} + 1} - y \sqrt{- 1 + y^{2}} = 0$	[_separable]	✓	15.987

10203	$y^{'} \sqrt{a^{2} + x^{2}} + y - \sqrt{a^{2} + x^{2}} + x = 0$	[_linear]	✓	1.799

10204	$x \ln (x) y^{'} + y - a x (1 + \ln (x)) = 0$	[_linear]	✓	1.789

10205	$x \ln (x) y^{'} - y^{2} \ln (x) - (2 \ln {(x)}^{2} + 1) y - \ln {(x)}^{3} = 0$	[_Riccati]	✓	2.338

10206	$y^{'} \sin (x) - y^{2} \sin {(x)}^{2} + (\cos (x) - 3 \sin (x)) y + 4 = 0$	[_Riccati]	✓	9.714

10207	$\cos (x) y^{'} + y + (1 + \sin (x)) \cos (x) = 0$	[_linear]	✓	2.940

10208	$\cos (x) y^{'} - y^{4} - y \sin (x) = 0$	[_Bernoulli]	✓	6.839

10209	$\cos (x) \sin (x) y^{'} - y - \sin {(x)}^{3} = 0$	[_linear]	✓	4.340

10210	$y^{'} \sin (2 x) + \sin (2 y) = 0$	[_separable]	✓	17.800

10211	$(a \sin {(x)}^{2} + b) y^{'} + a y \sin (2 x) + A x (a \sin {(x)}^{2} + c) = 0$	[_linear]	✓	14.600

10212	$2 f (x) y^{'} + 2 y^{2} f (x) - f^{'} (x) y - 2 f {(x)}^{2} = 0$	[_Riccati]	✓	1.228

10213	$y y^{'} + x^{3} + y = 0$	[_rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✗	0.803

10214	$y y^{'} + a y + x = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	13.392

10215	$y y^{'} + a y + \frac{(a^{2} - 1) x}{4} + b x^{n} = 0$	[_rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✗	2.254

10216	$y y^{'} + a y + b e^{x} - 2 a = 0$	[[_Abel, ‘2nd type‘, ‘class A‘]]	✗	1.857

10217	$y y^{'} + 4 x (x + 1) + y^{2} = 0$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓	2.363

10218	$y y^{'} + a y^{2} - b \cos (x + c) = 0$	[_Bernoulli]	✓	4.278

10219	$y y^{'} - \sqrt{a y^{2} + b} = 0$	[_quadrature]	✓	2.659

10220	$y y^{'} + x y^{2} - 4 x = 0$	[_separable]	✓	2.122

10221	$y y^{'} - x e^{\frac{x}{y}} = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	3.283

10222	$y y^{'} + x + f (x^{2} + y^{2}) g (x) = 0$	[NONE]	✗	3.013

10223	$(1 + y) y^{'} - y - x = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	6.469

10224	$(x + y - 1) y^{'} - y + 2 x + 3 = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	4.843

10225	$(y + 2 x - 2) y^{'} - y + x + 1 = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	4.178

10226	$(1 - 2 x + y) y^{'} + y + x = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	4.327

10227	$(y - x^{2}) y^{'} - x = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]]	✓	1.149

10228	$(y - x^{2}) y^{'} + 4 x y = 0$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	4.085

10229	$2 y y^{'} - x y^{2} - x^{3} = 0$	[_rational, _Bernoulli]	✓	1.547

10230	$(x + 2 y + 1) y^{'} + 1 - x - 2 y = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.067

10231	$(2 y + x + 7) y^{'} - y + 2 x + 4 = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.564

10232	$(- x + 2 y) y^{'} - y - 2 x = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.721

10233	$(2 y - 6 x) y^{'} - y + 3 x + 2 = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.977

10234	$(3 + 2 x + 4 y) y^{'} - 2 y - x - 1 = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.914

10235	$(4 y - 2 x - 3) y^{'} + 2 y - x - 1 = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.933

10236	$(4 y - 3 x - 5) y^{'} - 3 y + 7 x + 2 = 0$	[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.416

10237	$(4 y + 11 x - 11) y^{'} - 25 y - 8 x + 62 = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	9.163

10238	$(12 y - 5 x - 8) y^{'} - 5 y + 2 x + 3 = 0$	[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.243

10239	$a y y^{'} + b y^{2} + f (x) = 0$	[_Bernoulli]	✓	2.430

10240	$(a y + b x + c) y^{'} + α y + β x + γ = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	7.863

10241	$x y^{'} y + x^{2} + y^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	3.874

10242	$x y^{'} y - y^{2} + a x^{3} \cos (x) = 0$	[[_homogeneous, ‘class D‘], _Bernoulli]	✓	3.413

10243	$x y^{'} y - y^{2} + x y + x^{3} - 2 x^{2} = 0$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✗	1.273

10244	$(x y + a) y^{'} + b y = 0$	[[_1st_order, _with_exponential_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	1.188

10245	$x (4 + y) y^{'} - y^{2} - 2 y - 2 x = 0$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	6.056

10246	$x (a + y) y^{'} + b y + c x = 0$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✗	1.062

10247	$(a + (x + y) x) y^{'} - y (x + y) - b = 0$	[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	1.526

10248	$y^{2} - 3 x y - 2 x^{2} + (x y - x^{2}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	4.765

10249	$2 x y^{'} y - y^{2} + a x = 0$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	2.042

10250	$2 x y^{'} y - y^{2} + a x^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	5.033

10251	$2 x y^{'} y + 2 y^{2} + 1 = 0$	[_separable]	✓	2.437

10252	$x (x + 2 y - 1) y^{'} - (2 x + y + 1) y = 0$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	1.609

10253	$y (2 x - y - 1) + x (2 y - x - 1) y^{'} = 0$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	1.598

10254	$(2 x y + 4 x^{3}) y^{'} + y^{2} + 112 x^{2} y = 0$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	1.758

10255	$x (2 x + 3 y) y^{'} + 3 {(x + y)}^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	5.998

10256	$(3 x + 2) (y - 2 x - 1) y^{'} - y^{2} + x y - 7 x^{2} - 9 x - 3 = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	2.357

10257	$(3 + 6 x y + x^{2}) y^{'} + 2 x + 2 x y + 3 y^{2} = 0$	[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	1.625

10258	$(y a x + b x^{n}) y^{'} + α y^{3} + β y^{2} = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]]	✓	5.717

10259	$(B x y + A x^{2} + a x + b y + c) y^{'} - B g {(x)}^{2} + A x y + α x + β y + γ = 0$	[[_Abel, ‘2nd type‘, ‘class B‘]]	✗	7.880

10260	$(x^{2} y - 1) y^{'} + x y^{2} - 1 = 0$	[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	1.423

10261	$(x^{2} y - 1) y^{'} - x y^{2} + 1 = 0$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✗	1.855

10262	$(x^{2} y - 1) y^{'} + 8 x y^{2} - 8 = 0$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✗	1.174

10263	$x (x y - 2) y^{'} + x^{2} y^{3} + x y^{2} - 2 y = 0$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]]	✓	2.403

10264	$x (x y - 3) y^{'} + x y^{2} - y = 0$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	2.774

10265	$x^{2} (- 1 + y) y^{'} + (x - 1) y = 0$	[_separable]	✓	1.765

10266	$x (x y + x^{4} - 1) y^{'} - y (x y - x^{4} - 1) = 0$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✗	1.359

10267	$2 x^{2} y y^{'} + y^{2} - 2 x^{3} - x^{2} = 0$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓	2.625

10268	$2 x^{2} y y^{'} - y^{2} - x^{2} e^{x - \frac{1}{x}} = 0$	[_Bernoulli]	✓	2.516

10269	$(x + 2 x^{2} y) y^{'} - x^{2} y^{3} + 2 x y^{2} + y = 0$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]]	✓	2.752

10270	$(2 x^{2} y - x) y^{'} - 2 x y^{2} - y = 0$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	2.094

10271	$(2 x^{2} y - x^{3}) y^{'} + y^{3} - 4 x y^{2} + 2 x^{3} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]	✓	42.106

10272	$2 x^{3} + y y^{'} + 3 x^{2} y^{2} + 7 = 0$	[_rational, _Bernoulli]	✓	2.921

10273	$2 x (x^{3} y + 1) y^{'} + (3 x^{3} y - 1) y = 0$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	2.051

10274	$(x^{n (n + 1)} y - 1) y^{'} + 2 {(n + 1)}^{2} x^{n - 1} (x^{n^{2}} y^{2} - 1) = 0$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✗	5.830

10275	$(y - x) \sqrt{x^{2} + 1} y^{'} - a \sqrt{{(1 + y^{2})}^{3}} = 0$	[‘x=_G(y,y’)‘]	✗	341.698

10276	$y y^{'} \sin {(x)}^{2} + y^{2} \cos (x) \sin (x) - 1 = 0$	[_exact, _Bernoulli]	✓	6.493

10277	$f (x) y y^{'} + g (x) y^{2} + h (x) = 0$	[_Bernoulli]	✓	2.135

10278	$(- x + y^{2}) y^{'} - y + x^{2} = 0$	[_exact, _rational]	✓	1.272

10279	$(x^{2} + y^{2}) y^{'} + 2 x (2 x + y) = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓	4.328

10280	$(x^{2} + y^{2}) y^{'} - y^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	5.453

10281	$2 x y + (a + x^{2} + y^{2}) y^{'} = 0$	[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	1.235

10282	$2 x y + x^{2} + b + (a + x^{2} + y^{2}) y^{'} = 0$	[_exact, _rational]	✓	1.430

10283	$(x^{2} + y^{2} + x) y^{'} - y = 0$	[_rational]	✓	1.310

10284	$(y^{2} - x^{2}) y^{'} + 2 x y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	5.032

10285	$(x^{4} + y^{2}) y^{'} - 4 x^{3} y = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	3.065

10286	$(y^{2} + 4 \sin (x)) y^{'} - \cos (x) = 0$	[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	2.406

10287	$(x + 2 y + y^{2}) y^{'} + y (1 + y) + {(x + y)}^{2} y^{2} = 0$	[_rational]	✗	4.135

10288	${(x + y)}^{2} y^{'} - a^{2} = 0$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	14.902

10289	$x^{2} + 2 x y - y^{2} + (y^{2} + 2 x y - x^{2}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	13.408

10290	${(y + 3 x - 1)}^{2} y^{'} - (2 y - 1) (4 y + 6 x - 3) = 0$	[[_homogeneous, ‘class C‘], _rational]	✓	3.353

10291	$3 (y^{2} - x^{2}) y^{'} + 2 y^{3} - 6 x y (x + 1) - 3 e^{x} = 0$	[‘y=_G(x,y’)‘]	✓	2.358

10292	$(x^{2} + 4 y^{2}) y^{'} - x y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	3.986

10293	$(3 x^{2} + 2 x y + 4 y^{2}) y^{'} + 2 x^{2} + 6 x y + y^{2} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓	7.867

10294	${(1 - 3 x + 2 y)}^{2} y^{'} - {(3 y - 2 x - 4)}^{2} = 0$	[[_homogeneous, ‘class C‘], _rational]	✓	37.352

10295	${(2 y - 4 x + 1)}^{2} y^{'} - {(y - 2 x)}^{2} = 0$	[[_homogeneous, ‘class C‘], _rational, _dAlembert]	✓	2.434

10296	$(1 - 3 x^{2} y + 6 y^{2}) y^{'} - 3 x y^{2} + x = 0$	[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	1.479

10297	${(6 y - x)}^{2} y^{'} - 6 y^{2} + 2 x y + a = 0$	[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✓	1.650

10298	$(a y^{2} + 2 b x y + c x^{2}) y^{'} + b y^{2} + 2 c x y + d x^{2} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓	529.819

10299	$(b {(β y + α x)}^{2} - β (a x + b y)) y^{'} + a {(β y + α x)}^{2} - α (a x + b y) = 0$	[[_1st_order, _with_linear_symmetries], _rational]	✓	2.212

10300	${(a y + b x + c)}^{2} y^{'} + {(α y + β x + γ)}^{2} = 0$	[[_homogeneous, ‘class C‘], _rational]	✓	4.307

2.2.103 Problems 10201 to 10300