Problems 10101 to 10200

Table 2.205: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

10101	$y^{'} x - \sqrt{a^{2} - x^{2}} = 0$	[_quadrature]	✓	0.619

10102	$y^{'} x + y - x \sin (x) = 0$	[_linear]	✓	1.315

10103	$y^{'} x - y - \frac{x}{\ln (x)} = 0$	[_linear]	✓	1.086

10104	$y^{'} x - y - x^{2} \sin (x) = 0$	[_linear]	✓	1.209

10105	$y^{'} x - y - \frac{x \cos (\ln (\ln (x)))}{\ln (x)} = 0$	[_linear]	✓	2.765

10106	$y^{'} x + a y + b x^{n} = 0$	[_linear]	✓	1.319

10107	$y^{'} x + x^{2} + y^{2} = 0$	[_rational, _Riccati]	✓	1.246

10108	$y^{'} x - y^{2} + 1 = 0$	[_separable]	✓	1.566

10109	$y^{'} x + a y^{2} - y + b x^{2} = 0$	[[_homogeneous, ‘class D‘], _rational, _Riccati]	✓	1.521

10110	$y^{'} x + a y^{2} - b y + c x^{2 b} = 0$	[_rational, _Riccati]	✓	3.192

10111	$y^{'} x + a y^{2} - b y - c x^{β} = 0$	[_rational, _Riccati]	✓	2.570

10112	$y^{'} x + a + x y^{2} = 0$	[_rational, [_Riccati, _special]]	✓	1.340

10113	$y^{'} x + x y^{2} - y = 0$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓	1.787

10114	$y^{'} x + x y^{2} - y - a x^{3} = 0$	[[_homogeneous, ‘class D‘], _rational, _Riccati]	✓	3.563

10115	$y^{'} x + x y^{2} - (2 x^{2} + 1) y - x^{3} = 0$	[[_homogeneous, ‘class D‘], _rational, _Riccati]	✓	3.235

10116	$y^{'} x + a x y^{2} + 2 y + b x = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]	✓	2.472

10117	$y^{'} x + a x y^{2} + b y + c x + d = 0$	[_rational, _Riccati]	✓	4.872

10118	$y^{'} x + x^{a} y^{2} + \frac{(a - b) y}{2} + x^{b} = 0$	[_rational, _Riccati]	✓	2.476

10119	$y^{'} x + a x^{α} y^{2} + b y - c x^{β} = 0$	[_rational, _Riccati]	✓	3.792

10120	$y^{'} x - y^{2} \ln (x) + y = 0$	[_Bernoulli]	✓	2.265

10121	$y^{'} x - y (2 y \ln (x) - 1) = 0$	[_Bernoulli]	✓	2.228

10122	$y^{'} x + f (x) (y^{2} - x^{2}) - y = 0$	[[_homogeneous, ‘class D‘], _Riccati]	✓	2.350

10123	$y^{'} x + y^{3} + 3 x y^{2} = 0$	[_rational, _Abel]	✗	1.025

10124	$y^{'} x - y - \sqrt{x^{2} + y^{2}} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	5.396

10125	$y^{'} x + a \sqrt{x^{2} + y^{2}} - y = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	82.015

10126	$y^{'} x - x \sqrt{x^{2} + y^{2}} - y = 0$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✗	3.614

10127	$y^{'} x - x (y - x) \sqrt{x^{2} + y^{2}} - y = 0$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✗	5.454

10128	$y^{'} x - e^{\frac{y}{x}} x - y - x = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	5.855

10129	$y^{'} x - y \ln (y) = 0$	[_separable]	✓	1.729

10130	$y^{'} x - y (\ln (x y) - 1) = 0$	[[_homogeneous, ‘class G‘]]	✓	2.054

10131	$y^{'} x - y (x \ln (\frac{x^{2}}{y}) + 2) = 0$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✗	2.968

10132	$y^{'} x - \sin (x - y) = 0$	[‘y=_G(x,y’)‘]	✗	3.447

10133	$y^{'} x + (\sin (y) - 3 x^{2} \cos (y)) \cos (y) = 0$	[‘y=_G(x,y’)‘]	✓	2.741

10134	$y^{'} x - y - x \sin (\frac{y}{x}) = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	3.758

10135	$y^{'} x + x - y + x \cos (\frac{y}{x}) = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	2.868

10136	$y^{'} x + x \tan (\frac{y}{x}) - y = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	3.456

10137	$y^{'} x - y f (x y) = 0$	[[_homogeneous, ‘class G‘]]	✓	1.153

10138	$y^{'} x - y f (x^{a} y^{b}) = 0$	[[_homogeneous, ‘class G‘]]	✓	1.567

10139	$y^{'} x + a y - f (x) g (x^{a} y) = 0$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✗	3.192

10140	$(x + 1) y^{'} + y (y - x) = 0$	[_rational, _Bernoulli]	✓	1.376

10141	$2 y^{'} x - y - 2 x^{3} = 0$	[_linear]	✓	1.781

10142	$(2 x + 1) y^{'} - 4 e^{- y} + 2 = 0$	[_separable]	✓	2.041

10143	$3 y^{'} x - 3 x y^{4} \ln (x) - y = 0$	[_Bernoulli]	✓	3.481

10144	$x^{2} y^{'} + y - x = 0$	[_linear]	✓	1.118

10145	$x^{2} y^{'} - y + x^{2} e^{x - \frac{1}{x}} = 0$	[_linear]	✓	1.559

10146	$x^{2} y^{'} - (x - 1) y = 0$	[_separable]	✓	1.417

10147	$x^{2} y^{'} + x^{2} + x y + y^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓	1.710

10148	$x^{2} y^{'} - y^{2} - x y = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	1.710

10149	$x^{2} y^{'} - y^{2} - x y - x^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓	1.948

10150	$x^{2} (y^{'} + y^{2}) + a x^{k} - b (b - 1) = 0$	[_rational, _Riccati]	✓	3.648

10151	$x^{2} (y^{'} + y^{2}) + 4 x y + 2 = 0$	[[_homogeneous, ‘class G‘], _rational, _Riccati]	✓	1.611

10152	$x^{2} (y^{'} + y^{2}) + y a x + b = 0$	[[_homogeneous, ‘class G‘], _rational, _Riccati]	✓	2.016

10153	$x^{2} (y^{'} - y^{2}) - a x^{2} y + a x + 2 = 0$	[_rational, _Riccati]	✓	2.297

10154	$x^{2} (y^{'} + a y^{2}) - b = 0$	[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]]	✓	2.026

10155	$x^{2} (y^{'} + a y^{2}) + b x^{α} + c = 0$	[_rational, _Riccati]	✓	2.838

10156	$x^{2} y^{'} + a y^{3} - a x^{2} y^{2} = 0$	[_rational, _Abel]	✗	1.198

10157	$x^{2} y^{'} + x y^{3} + a y^{2} = 0$	[_rational, _Abel]	✗	1.228

10158	$x^{2} y^{'} + a x^{2} y^{3} + b y^{2} = 0$	[_rational, _Abel]	✗	1.612

10159	$(x^{2} + 1) y^{'} + x y - 1 = 0$	[_linear]	✓	1.136

10160	$(x^{2} + 1) y^{'} + x y - x (x^{2} + 1) = 0$	[_linear]	✓	3.757

10161	$(x^{2} + 1) y^{'} + 2 x y - 2 x^{2} = 0$	[_linear]	✓	1.235

10162	$(x^{2} + 1) y^{'} + (1 + y^{2}) (2 x y - 1) = 0$	[_rational, _Abel]	✗	1.407

10163	$(x^{2} + 1) y^{'} + x \sin (y) \cos (y) - x (x^{2} + 1) \cos {(y)}^{2} = 0$	[‘y=_G(x,y’)‘]	✗	15.054

10164	$(x^{2} - 1) y^{'} - x y + a = 0$	[_linear]	✓	2.458

10165	$(x^{2} - 1) y^{'} + 2 x y - \cos (x) = 0$	[_linear]	✓	2.458

10166	$(x^{2} - 1) y^{'} + y^{2} - 2 x y + 1 = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]	✓	1.779

10167	$(x^{2} - 1) y^{'} - y (y - x) = 0$	[_rational, _Bernoulli]	✓	2.933

10168	$(x^{2} - 1) y^{'} + a (1 - 2 x y + y^{2}) = 0$	[_rational, _Riccati]	✗	4.140

10169	$(x^{2} - 1) y^{'} + a x y^{2} + x y = 0$	[_separable]	✓	3.058

10170	$(x^{2} - 1) y^{'} - 2 x y \ln (y) = 0$	[_separable]	✓	2.650

10171	$(x^{2} - 4) y^{'} + (x + 2) y^{2} - 4 y = 0$	[_rational, _Bernoulli]	✓	1.621

10172	$(x^{2} - 5 x + 6) y^{'} + 3 x y - 8 y + x^{2} = 0$	[_linear]	✓	1.531

10173	$(x - a) (x - b) y^{'} + k (x + y - a) (x + y - b) + y^{2} = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]	✓	3.578

10174	$2 x^{2} y^{'} - 2 y^{2} - x y + 2 a^{2} x = 0$	[_rational, _Riccati]	✓	1.798

10175	$2 x^{2} y^{'} - 2 y^{2} - 3 x y + 2 a^{2} x = 0$	[_rational, _Riccati]	✓	2.096

10176	$x (2 x - 1) y^{'} + y^{2} - (1 + 4 x) y + 4 x = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]	✓	2.509

10177	$2 x (x - 1) y^{'} + (x - 1) y^{2} - x = 0$	[_rational, _Riccati]	✓	2.761

10178	$3 x^{2} y^{'} - 7 y^{2} - 3 x y - x^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓	2.246

10179	$3 (x^{2} - 4) y^{'} + y^{2} - x y - 3 = 0$	[_rational, _Riccati]	✓	142.954

10180	${(a x + b)}^{2} y^{'} + (a x + b) y^{3} + c y^{2} = 0$	[_rational, _Abel]	✗	2.503

10181	$x^{3} y^{'} - y^{2} - x^{4} = 0$	[[_homogeneous, ‘class G‘], _rational, _Riccati]	✓	1.288

10182	$x^{3} y^{'} - y^{2} - x^{2} y = 0$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓	1.774

10183	$x^{3} y^{'} - x^{4} y^{2} + x^{2} y + 20 = 0$	[[_homogeneous, ‘class G‘], _rational, _Riccati]	✓	1.904

10184	$x^{3} y^{'} - y^{2} x^{6} - (2 x - 3) x^{2} y + 3 = 0$	[_rational, _Riccati]	✓	1.955

10185	$x (x^{2} + 1) y^{'} + x^{2} y = 0$	[_separable]	✓	1.224

10186	$x (x^{2} - 1) y^{'} - (2 x^{2} - 1) y + a x^{3} = 0$	[_linear]	✓	1.344

10187	$x (x^{2} - 1) y^{'} + (x^{2} - 1) y^{2} - x^{2} = 0$	[_rational, _Riccati]	✓	146.027

10188	$x^{2} (x - 1) y^{'} - y^{2} - x (x - 2) y = 0$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓	2.118

10189	$2 x (x^{2} - 1) y^{'} + 2 (x^{2} - 1) y^{2} - (3 x^{2} - 5) y + x^{2} - 3 = 0$	[_rational, _Riccati]	✓	2.495

10190	$3 x (x^{2} - 1) y^{'} + x y^{2} - (x^{2} + 1) y - 3 x = 0$	[_rational, _Riccati]	✓	68.002

10191	$(a x^{2} + b x + c) (y^{'} x - y) - y^{2} + x^{2} = 0$	[[_homogeneous, ‘class D‘], _rational, _Riccati]	✓	3.193

10192	$x^{4} (y^{'} + y^{2}) + a = 0$	[_rational, [_Riccati, _special]]	✓	1.521

10193	$x (x^{3} - 1) y^{'} - 2 x y^{2} + y + x^{2} = 0$	[_rational, _Riccati]	✓	2.009

10194	$(2 x^{4} - x) y^{'} - 2 (x^{3} - 1) y = 0$	[_separable]	✓	1.487

10195	${(a x^{2} + b x + c)}^{2} (y^{'} + y^{2}) + A = 0$	[_rational, _Riccati]	✓	3.575

10196	$x^{7} y^{'} + 5 x^{3} y^{2} + 2 (x^{2} + 1) y^{3} = 0$	[_rational, _Abel]	✗	1.427

10197	$x^{n} y^{'} + y^{2} - (n - 1) x^{n - 1} y + x^{2 n - 2} = 0$	[[_homogeneous, ‘class G‘], _Riccati]	✓	2.762

10198	$x^{n} y^{'} - a y^{2} - b x^{2 n - 2} = 0$	[[_homogeneous, ‘class G‘], _Riccati]	✓	4.433

10199	$x^{2 n + 1} y^{'} - a y^{3} - b x^{3 n} = 0$	[[_homogeneous, ‘class G‘], _Abel]	✓	4.123

10200	$x^{m (n - 1) + n} y^{'} - a y^{n} - b x^{n (m + 1)} = 0$	[[_homogeneous, ‘class G‘]]	✓	73.423

2.2.102 Problems 10101 to 10200