Problems 5801 to 5900

Table 2.119: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

5801	$2 x y + (x^{2} + y^{2}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓	0.223

5802	$e^{x} \sin (y) + e^{- y} - (x e^{- y} - e^{x} \cos (y)) y^{'} = 0$	[_exact]	✓	0.346

5803	$\cos (y) - (x \sin (y) - y^{2}) y^{'} = 0$	[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	0.283

5804	$x - 2 x y + e^{y} + (y - x^{2} + x e^{y}) y^{'} = 0$	[_exact]	✓	1.878

5805	$x^{2} - x + y^{2} - (e^{y} - 2 x y) y^{'} = 0$	[_exact]	✓	1.604

5806	$2 x + \cos (x) y + (2 y + \sin (x) - \sin (y)) y^{'} = 0$	[_exact]	✓	0.312

5807	$x \sqrt{x^{2} + y^{2}} - \frac{x^{2} y y^{'}}{y - \sqrt{x^{2} + y^{2}}} = 0$	[[_homogeneous, ‘class A‘], _exact, _dAlembert]	✓	0.427

5808	$4 x^{3} - \sin (x) + y^{3} - (y^{2} + 1 - 3 x y^{2}) y^{'} = 0$	[_exact]	✓	0.444

5809	$e^{x} (y^{3} + x y^{3} + 1) + 3 y^{2} (x e^{x} - 6) y^{'} = 0$ i.c.	[_exact, _Bernoulli]	✓	0.685

5810	$\sin (x) \cos (y) + \cos (x) \sin (y) y^{'} = 0$ i.c.	[_separable]	✓	0.943

5811	$y^{2} e^{x y^{2}} + 4 x^{3} + (2 x y e^{x y^{2}} - 3 y^{2}) y^{'} = 0$ i.c.	[_exact]	✓	0.415

5812	$y^{2} + y - y^{'} x = 0$	[_separable]	✓	0.269

5813	$y \sec (x) + y^{'} \sin (x) = 0$	[_separable]	✓	0.290

5814	$e^{x} - \sin (y) + y^{'} \cos (y) = 0$	[‘y=_G(x,y’)‘]	✓	0.338

5815	$(x^{2} + 1) y^{'} + x y = 0$	[_separable]	✓	0.263

5816	$y^{3} + x y^{2} + y + (x^{3} + x^{2} y + x) y^{'} = 0$	[_rational, [_Abel, ‘2nd type‘, ‘class C‘]]	✓	0.826

5817	$3 y - y^{'} x = 0$	[_separable]	✓	0.219

5818	$y - 3 y^{'} x = 0$	[_separable]	✓	0.240

5819	$y (2 x^{2} y^{3} + 3) + x (x^{2} y^{3} - 1) y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	2.688

5820	$2 x y + x^{2} + (x^{2} + y^{2}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓	0.236

5821	$x^{2} + \cos (x) y + (y^{3} + \sin (x)) y^{'} = 0$	[_exact]	✓	0.254

5822	$x^{2} + y^{2} + x + x y^{'} y = 0$	[_rational, _Bernoulli]	✓	0.435

5823	$x - 2 x y + e^{y} + (y - x^{2} + x e^{y}) y^{'} = 0$	[_exact]	✓	0.303

5824	$e^{x} \sin (y) + e^{- y} - (x e^{- y} - e^{x} \cos (y)) y^{'} = 0$	[_exact]	✓	0.332

5825	$x^{2} - y^{2} - y - (x^{2} - y^{2} - x) y^{'} = 0$	[[_1st_order, _with_linear_symmetries], _rational]	✓	1.617

5826	$x^{4} y^{2} - y + (x^{2} y^{4} - x) y^{'} = 0$	[_rational]	✓	0.316

5827	$y (2 x + y^{3}) - x (2 x - y^{3}) y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	0.308

5828	$\arctan (x y) + \frac{x y - 2 x y^{2}}{1 + x^{2} y^{2}} + \frac{(x^{2} - 2 x^{2} y) y^{'}}{1 + x^{2} y^{2}} = 0$	[_exact]	✓	0.578

5829	$e^{x} (x + 1) + (e^{y} y - x e^{x}) y^{'} = 0$	[‘y=_G(x,y’)‘]	✓	0.420

5830	$\frac{x y + 1}{y} + \frac{(- x + 2 y) y^{'}}{y^{2}} = 0$	[[_homogeneous, ‘class D‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	0.420

5831	$y^{2} - 3 x y - 2 x^{2} + (x y - x^{2}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	0.637

5832	$(2 x + y + 1) y - x (x + 2 y - 1) y^{'} = 0$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	0.386

5833	$y (2 x - y - 1) + x (2 y - x - 1) y^{'} = 0$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	0.404

5834	$y^{2} + 12 x^{2} y + (2 x y + 4 x^{3}) y^{'} = 0$	[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	0.691

5835	$x (2 x + 3 y) y^{'} + 3 {(x + y)}^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	0.601

5836	$y - (x^{2} + y^{2} + x) y^{'} = 0$	[_rational]	✓	1.249

5837	$2 x y + (a + x^{2} + y^{2}) y^{'} = 0$	[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	0.224

5838	$2 x y + x^{2} + b + (a + x^{2} + y^{2}) y^{'} = 0$	[_exact, _rational]	✓	0.219

5839	$y^{'} x + y = x^{3}$	[_linear]	✓	1.107

5840	$y^{'} + a y = b$	[_quadrature]	✓	0.680

5841	$y^{'} x + y = y^{2} \ln (x)$	[_Bernoulli]	✓	2.227

5842	$x^{'} + 2 x y = e^{- y^{2}}$	[_linear]	✓	1.415

5843	$r^{'} = (r + e^{- θ}) \tan (θ)$	[_linear]	✓	1.970

5844	$y^{'} - \frac{2 x y}{x^{2} + 1} = 1$	[_linear]	✓	1.466

5845	$y^{'} + y = x y^{3}$	[_Bernoulli]	✓	0.555

5846	$(- x^{3} + 1) y^{'} - 2 (x + 1) y = y^{5 / 2}$	[_rational, _Bernoulli]	✓	2.778

5847	$\tan (θ) r^{'} - r = \tan {(θ)}^{2}$	[_linear]	✓	1.713

5848	$2 y + y^{'} = 3 e^{- 2 x}$	[[_linear, ‘class A‘]]	✓	1.040

5849	$2 y + y^{'} = \frac{3 e^{- 2 x}}{4}$	[[_linear, ‘class A‘]]	✓	1.090

5850	$2 y + y^{'} = \sin (x)$	[[_linear, ‘class A‘]]	✓	1.387

5851	$y^{'} + \cos (x) y = e^{2 x}$	[_linear]	✓	1.990

5852	$y^{'} + \cos (x) y = \frac{\sin (2 x)}{2}$	[_linear]	✓	2.355

5853	$y^{'} x + y = x \sin (x)$	[_linear]	✓	1.328

5854	$y^{'} x - y = x^{2} \sin (x)$	[_linear]	✓	1.231

5855	$y^{'} x + x y^{2} - y = 0$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓	1.755

5856	$y^{'} x - y (2 y \ln (x) - 1) = 0$	[_Bernoulli]	✓	2.225

5857	$x^{2} (x - 1) y^{'} - y^{2} - x (x - 2) y = 0$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓	2.147

5858	$y^{'} - y = e^{x}$ i.c.	[[_linear, ‘class A‘]]	✓	1.181

5859	$y^{'} + \frac{y}{x} = \frac{y^{2}}{x}$ i.c.	[_separable]	✓	2.835

5860	$2 \cos (x) y^{'} = y \sin (x) - y^{3}$ i.c.	[_Bernoulli]	✓	7.019

5861	$(x - \cos (y)) y^{'} + \tan (y) = 0$ i.c.	[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	5.871

5862	$y^{'} = x^{3} + \frac{2 y}{x} - \frac{y^{2}}{x}$	[_rational, _Riccati]	✓	1.860

5863	$y^{'} = 2 \sec (x) \tan (x) - \sin (x) y^{2}$	[_Riccati]	✓	3.871

5864	$y^{'} = \frac{1}{x^{2}} - \frac{y}{x} - y^{2}$	[[_homogeneous, ‘class G‘], _rational, _Riccati]	✓	1.805

5865	$y^{'} = 1 + \frac{y}{x} - \frac{y^{2}}{x^{2}}$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓	2.445

5866	$2 x y^{'} y + (x + 1) y^{2} = e^{x}$	[_Bernoulli]	✓	1.967

5867	$y^{'} \cos (y) + \sin (y) = x^{2}$	[‘y=_G(x,y’)‘]	✓	2.173

5868	$(x + 1) y^{'} - 1 - y = (x + 1) \sqrt{1 + y}$	[[_1st_order, _with_linear_symmetries]]	✓	2.484

5869	$e^{y} (y^{'} + 1) = e^{x}$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	1.531

5870	$y^{'} \sin (y) + \sin (x) \cos (y) = \sin (x)$	[_separable]	✓	39.913

5871	${(x - y)}^{2} y^{'} = 4$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	4.045

5872	$y^{'} x - y = \sqrt{x^{2} + y^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	5.557

5873	$(3 x + 2 y + 1) y^{'} + 4 x + 3 y + 2 = 0$	[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.028

5874	$(x^{2} - y^{2}) y^{'} = 2 x y$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	4.746

5875	$y + (1 + y^{2} e^{2 x}) y^{'} = 0$	[[_1st_order, _with_linear_symmetries]]	✓	1.519

5876	$x^{2} y + y^{2} + x^{3} y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	1.808

5877	$y^{2} e^{x y^{2}} + 4 x^{3} + (2 x y e^{x y^{2}} - 3 y^{2}) y^{'} = 0$	[_exact]	✓	37.051

5878	$y^{'} = {(x^{2} + 2 y - 1)}^{2 / 3} - x$	[[_1st_order, _with_linear_symmetries]]	✓	1.364

5879	$y^{'} x + y = x^{2} (e^{x} + 1) y^{2}$	[_Bernoulli]	✓	2.868

5880	$2 y - y \ln (x) x - 2 x \ln (x) y^{'} = 0$	[_separable]	✓	1.773

5881	$y^{'} + a y = k e^{b x}$	[[_linear, ‘class A‘]]	✓	1.309

5882	$y^{'} = {(x + y)}^{2}$	[[_homogeneous, ‘class C‘], _Riccati]	✓	1.541

5883	$y^{'} + 8 x^{3} y^{3} + 2 x y = 0$	[_Bernoulli]	✓	1.474

5884	$(x y \sqrt{x^{2} - y^{2}} + x) y^{'} = y - x^{2} \sqrt{x^{2} - y^{2}}$	[NONE]	✗	31.575

5885	$y^{'} + a y = b \sin (k x)$	[[_linear, ‘class A‘]]	✓	1.556

5886	$y^{'} x - y^{2} + 1 = 0$	[_separable]	✓	1.588

5887	$(y^{2} + a \sin (x)) y^{'} = \cos (x)$	[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	2.141

5888	$y^{'} x = x + y + e^{\frac{y}{x}} x$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	5.908

5889	$y^{'} + \cos (x) y = e^{- \sin (x)}$	[_linear]	✓	1.778

5890	$y^{'} x - y (\ln (x y) - 1) = 0$	[[_homogeneous, ‘class G‘]]	✓	2.142

5891	$x^{3} y^{'} - y^{2} - x^{2} y = 0$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓	1.755

5892	$y^{'} x + a y + b x^{n} = 0$	[_linear]	✓	1.362

5893	$y^{'} x - y - x \sin (\frac{y}{x}) = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	3.691

5894	$y^{2} - 3 x y - 2 x^{2} + (x y - x^{2}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	4.588

5895	$(3 + 6 x y + x^{2}) y^{'} + 2 x + 2 x y + 3 y^{2} = 0$	[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	1.544

5896	$x^{2} y^{'} + x^{2} + x y + y^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓	1.732

5897	$(x^{2} - 1) y^{'} + 2 x y - \cos (x) = 0$	[_linear]	✓	2.547

5898	$(x^{2} y - 1) y^{'} + x y^{2} - 1 = 0$	[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	1.502

5899	$(x^{2} - 1) y^{'} + x y - 3 x y^{2} = 0$	[_separable]	✓	2.699

5900	$(x^{2} - 1) y^{'} - 2 x y \ln (y) = 0$	[_separable]	✓	2.603

2.2.59 Problems 5801 to 5900