Problems 18001 to 18100

Table 2.363: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

18001	$y^{'} = x e^{x^{2}}$	[_quadrature]	✓	0.390

18002	$y^{'} = \arcsin (x)$	[_quadrature]	✓	0.349

18003	$(x + 1) y^{'} = x$	[_quadrature]	✓	0.353

18004	$(x^{2} + 1) y^{'} = x$	[_quadrature]	✓	0.373

18005	$(x^{3} + 1) y^{'} = x$	[_quadrature]	✓	0.660

18006	$(x^{2} + 1) y^{'} = \arctan (x)$	[_quadrature]	✓	0.457

18007	$x y^{'} y = - 1 + y$	[_separable]	✓	1.619

18008	$x^{5} y^{'} + y^{5} = 0$	[_separable]	✓	8.533

18009	$y^{'} x = (- 2 x^{2} + 1) \tan (y)$	[_separable]	✓	2.130

18010	$y^{'} = 2 x y$	[_separable]	✓	1.138

18011	$y^{'} \sin (y) = x^{2}$	[_separable]	✓	1.449

18012	$y^{'} \sin (x) = 1$	[_quadrature]	✓	0.537

18013	$y^{'} + y \tan (x) = 0$	[_separable]	✓	1.322

18014	$y^{'} - y \tan (x) = 0$	[_separable]	✓	1.368

18015	$1 + y^{2} + (x^{2} + 1) y^{'} = 0$	[_separable]	✓	1.860

18016	$y \ln (y) - y^{'} x = 0$	[_separable]	✓	1.669

18017	$y^{'} = x e^{x}$ i.c.	[_quadrature]	✓	0.584

18018	$y^{'} = 2 \sin (x) \cos (x)$ i.c.	[_quadrature]	✓	0.632

18019	$y^{'} = \ln (x)$ i.c.	[_quadrature]	✓	0.570

18020	$(x^{2} - 1) y^{'} = 1$ i.c.	[_quadrature]	✓	0.623

18021	$x (x^{2} - 4) y^{'} = 1$ i.c.	[_quadrature]	✓	0.750

18022	$(x + 1) (x^{2} + 1) y^{'} = 2 x^{2} + x$ i.c.	[_quadrature]	✓	1.030

18023	$y^{'} = e^{3 x - 2 y}$ i.c.	[_separable]	✓	2.692

18024	$y^{'} x = 2 x^{2} + 1$ i.c.	[_quadrature]	✓	0.623

18025	$e^{- y} + (x^{2} + 1) y^{'} = 0$ i.c.	[_separable]	✓	2.117

18026	$3 \cos (3 x) \cos (2 y) - 2 \sin (3 x) \sin (2 y) y^{'} = 0$ i.c.	[_separable]	✓	4.914

18027	$y^{'} = e^{x} \cos (x)$ i.c.	[_quadrature]	✓	0.710

18028	$x y^{'} y = (x + 1) (1 + y)$ i.c.	[_separable]	✓	1.784

18029	$y^{'} = 1 + 2 x y$	[_linear]	✓	1.068

18030	$y^{''} - 5 y^{'} + 6 y = 0$	[[_2nd_order, _missing_x]]	✓	0.323

18031	$2 y^{'''} + y^{''} - 5 y^{'} + 2 y = 0$	[[_3rd_order, _missing_x]]	✓	0.078

18032	$v^{'} = g - \frac{k v^{2}}{m}$	[_quadrature]	✓	2.246

18033	$x^{2} - 2 y^{2} + x y^{'} y = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	72.549

18034	$x^{2} y^{'} - 3 x y - 2 y^{2} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	2.500

18035	$x^{2} y^{'} = 3 (x^{2} + y^{2}) \arctan (\frac{y}{x}) + x y$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	10.548

18036	$x \sin (\frac{y}{x}) y^{'} = y \sin (\frac{y}{x}) + x$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	5.619

18037	$y^{'} x = y + 2 e^{- \frac{y}{x}} x$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	8.534

18038	$x - y - (x + y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.896

18039	$y^{'} x = 2 x + 3 y$	[_linear]	✓	1.914

18040	$y^{'} x = \sqrt{x^{2} + y^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	8.941

18041	$x^{2} y^{'} = y^{2} + 2 x y$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	2.237

18042	$x^{3} + y^{3} - x y^{2} y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	11.227

18043	$y^{'} = {(x + y)}^{2}$	[[_homogeneous, ‘class C‘], _Riccati]	✓	1.519

18044	$y^{'} = \sin {(x - y + 1)}^{2}$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	6.049

18045	$y^{'} = \frac{x + y + 4}{x - y - 6}$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.514

18046	$y^{'} = \frac{x + y + 4}{x + y - 6}$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.829

18047	$2 x - 2 y + (- 1 + y) y^{'} = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.155

18048	$y^{'} = \frac{x + y - 1}{x + 4 y + 2}$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	4.047

18049	$2 x + 3 y - 1 - 4 (x + 1) y^{'} = 0$	[_linear]	✓	1.651

18050	$y^{'} = \frac{1 - x y^{2}}{2 x^{2} y}$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	2.048

18051	$y^{'} = \frac{2 + 3 x y^{2}}{4 x^{2} y}$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	2.409

18052	$y^{'} = \frac{y - x y^{2}}{x + x^{2} y}$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	1.669

18053	$(x + \frac{2}{y}) y^{'} + y = 0$	[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	1.513

18054	$\sin (x) \tan (y) + 1 + \cos (x) \sec {(y)}^{2} y^{'} = 0$	[‘y=_G(x,y’)‘]	✓	42.684

18055	$y - x^{3} + (y^{3} + x) y^{'} = 0$	[_exact, _rational]	✓	1.270

18056	$y + y \cos (x y) + (x + x \cos (x y)) y^{'} = 0$	[_separable]	✓	1.740

18057	$\cos (x) \cos {(y)}^{2} + 2 \sin (x) \sin (y) \cos (y) y^{'} = 0$	[_separable]	✓	3.066

18058	$(\sin (x) \sin (y) - x e^{y}) y^{'} = e^{y} + \cos (x) \cos (y)$	[_exact]	✓	30.925

18059	$- \frac{\sin (\frac{x}{y})}{y} + \frac{x \sin (\frac{x}{y}) y^{'}}{y^{2}} = 0$	[_separable]	✓	1.698

18060	$1 + y + (1 - x) y^{'} = 0$	[_separable]	✓	1.467

18061	$2 x y^{3} + \cos (x) y + (3 x^{2} y^{2} + \sin (x)) y^{'} = 0$	[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	43.233

18062	$1 = \frac{y}{1 - x^{2} y^{2}} + \frac{x y^{'}}{1 - x^{2} y^{2}}$	[_exact, _rational, _Riccati]	✓	1.606

18063	$2 x y^{4} + \sin (y) + (4 x^{2} y^{3} + x \cos (y)) y^{'} = 0$	[_exact]	✓	2.845

18064	$\frac{y^{'} x + y}{1 - x^{2} y^{2}} + x = 0$	[_exact, _rational, _Riccati]	✓	2.060

18065	$2 x (1 + \sqrt{x^{2} - y}) = \sqrt{x^{2} - y} y^{'}$	[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	4.542

18066	$\ln (y) x + x y + (y \ln (x) + x y) y^{'} = 0$	[_separable]	✓	1.991

18067	$e^{y^{2}} - \csc (y) \csc {(x)}^{2} + (2 x y e^{y^{2}} - \csc (y) \cot (y) \cot (x)) y^{'} = 0$	[_exact]	✓	55.446

18068	$1 + y^{2} \sin (2 x) - 2 y \cos {(x)}^{2} y^{'} = 0$	[_exact, _Bernoulli]	✓	6.737

18069	$\frac{x}{{(x^{2} + y^{2})}^{3 / 2}} + \frac{y y^{'}}{{(x^{2} + y^{2})}^{3 / 2}} = 0$	[_separable]	✓	8.033

18070	$3 x^{2} (1 + \ln (y)) + (\frac{x^{3}}{y} - 2 y) y^{'} = 0$	[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	1.725

18071	$\frac{y - y^{'} x}{{(x + y)}^{2}} + y^{'} = 1$	[[_1st_order, _with_linear_symmetries], _exact, _rational]	✓	4.311

18072	$\frac{4 y^{2} - 2 x^{2}}{4 x y^{2} - x^{3}} + \frac{(8 y^{2} - x^{2}) y^{'}}{4 y^{3} - x^{2} y} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓	156.465

18073	$(3 x^{2} - y^{2}) y^{'} - 2 x y = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	3.648

18074	$x y - 1 + (x^{2} - x y) y^{'} = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]]	✓	1.333

18075	$y^{'} x + y + 3 x^{3} y^{4} y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	11.811

18076	$e^{x} + (e^{x} \cot (y) + 2 \csc (y) y) y^{'} = 0$	[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	3.926

18077	$(x + 2) \sin (y) + x \cos (y) y^{'} = 0$	[_separable]	✓	2.356

18078	$y + (x - 2 x^{2} y^{3}) y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	3.055

18079	$x + 3 y^{2} + 2 x y^{'} y = 0$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	2.133

18080	$y + (2 x - e^{y} y) y^{'} = 0$	[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	1.389

18081	$y \ln (y) - 2 x y + (x + y) y^{'} = 0$	[‘y=_G(x,y’)‘]	✓	1.587

18082	$y^{2} + x y + 1 + (x^{2} + x y + 1) y^{'} = 0$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	1.561

18083	$x^{3} + x y^{3} + 3 y^{2} y^{'} = 0$	[_rational, _Bernoulli]	✓	1.877

18084	$y^{'} x - y = (1 + y^{2}) y^{'}$	[[_1st_order, _with_linear_symmetries], _rational]	✓	1.619

18085	$y - y^{'} x = x y^{3} y^{'}$	[_separable]	✓	2.430

18086	$y^{'} x = x^{5} + x^{3} y^{2} + y$	[[_homogeneous, ‘class D‘], _rational, _Riccati]	✓	2.365

18087	$(x + y) y^{'} = y - x$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.575

18088	$y^{'} x = y + x^{2} + 9 y^{2}$	[[_homogeneous, ‘class D‘], _rational, _Riccati]	✓	1.426

18089	$y^{'} x - y + y^{2} = 0$	[_separable]	✓	1.780

18090	$y^{'} x - y = 2 x^{2} - 3$	[_linear]	✓	0.973

18091	$y^{'} x + y = y^{'} \sqrt{x y}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	116.990

18092	$y - x y^{2} + (x^{2} y^{2} + x) y^{'} = 0$	[_rational]	✓	1.353

18093	$y^{'} x - y = x^{2} y^{4} (y^{'} x + y)$	[[_homogeneous, ‘class G‘], _rational]	✓	3.054

18094	$y^{'} x + y + x^{2} y^{5} y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational]	✓	2.102

18095	$2 x y^{2} - y + y^{'} x = 0$	[[_homogeneous, ‘class D‘], _rational, _Bernoulli]	✓	1.659

18096	$y^{'} + \frac{y}{x} = \sin (x)$	[_linear]	✓	1.322

18097	$y^{'} = \frac{2 y}{x} + \frac{x^{3}}{y} + x \tan (\frac{y}{x^{2}})$	[[_homogeneous, ‘class G‘]]	✓	5.426

18098	$y^{'} x - 3 y = x^{4}$	[_linear]	✓	1.625

18099	$y^{'} + y = \frac{1}{e^{2 x} + 1}$	[_linear]	✓	1.772

18100	$(x^{2} + 1) y^{'} + 2 x y = \cot (x)$	[_linear]	✓	1.733

2.2.181 Problems 18001 to 18100