Problems 18101 to 18200

Table 2.365: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

18101	$x y^{2} y^{'} + y^{3} = x \cos (x)$	[_Bernoulli]	✓	41.779

18102	$x y^{'} + y = x y^{2}$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	1.674

18103	$(e^{y} - 2 x y) y^{'} = y^{2}$	[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	1.364

18104	$y - x y^{'} = y^{'} y^{2} e^{y}$	[[_1st_order, _with_linear_symmetries]]	✓	1.375

18105	$x y^{'} + 2 = x^{3} (y - 1) y^{'}$	[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]]	✓	2.622

18106	$x y^{'} = 2 x^{2} y + y \ln (y)$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	1.858

18107	$y^{'} \sin (2 x) = 2 y + 2 \cos (x)$	[_linear]	✓	3.618

18108	$y y^{''} + {y^{'}}^{2} = 0$	[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	1.163

18109	$x y^{''} = y^{'} + {y^{'}}^{3}$	[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]	✓	0.424

18110	$y^{''} - k y = 0$	[[_2nd_order, _missing_x]]	✓	3.887

18111	$x^{2} y^{''} = 2 x y^{'} + {y^{'}}^{2}$	[[_2nd_order, _missing_y]]	✓	0.472

18112	$2 y y^{''} = 1 + {y^{'}}^{2}$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	1.075

18113	$y y^{''} - {y^{'}}^{2} = 0$	[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	0.333

18114	$x y^{''} + y^{'} = 4 x$	[[_2nd_order, _missing_y]]	✓	1.015

18115	$(x^{2} + 2 y^{'}) y^{''} + 2 x y^{'} = 0$ i.c.	[[_2nd_order, _missing_y], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_poly_yn]]	✗	3.611

18116	$y y^{''} = y^{2} y^{'} + {y^{'}}^{2}$ i.c.	[[_2nd_order, _missing_x], [_2nd_order, _with_potential_symmetries], [_2nd_order, _reducible, _mu_xy]]	✓	0.964

18117	$y^{''} = y^{'} e^{y}$ i.c.	[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]]	✓	2.926

18118	$y^{''} = 1 + {y^{'}}^{2}$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]	✓	1.555

18119	$y^{''} + {y^{'}}^{2} = 1$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]	✓	1.694

18120	$y y^{''} = {y^{'}}^{2}$	[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	0.268

18121	$(1 - x y) y^{'} = y^{2}$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	1.827

18122	$2 x + 3 y + 1 + (2 y - 3 x + 5) y^{'} = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	37.517

18123	$x y^{'} = \sqrt{x^{2} + y^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	9.830

18124	$y^{2} = (x^{3} - x y) y^{'}$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	2.822

18125	$x^{2} y^{3} + y = (x^{3} y^{2} - x) y^{'}$	[[_homogeneous, ‘class G‘], _rational]	✓	3.132

18126	$y y^{''} + {y^{'}}^{2} - 2 y y^{'} = 0$	[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	2.080

18127	$x y^{'} + y = x^{2} y^{'} + y^{2}$	[_separable]	✓	2.729

18128	$x y y^{'} = x^{2} y^{'} + y^{2}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	73.605

18129	$(e^{x} - 3 y^{2} x^{2}) y^{'} + y e^{x} = 2 x y^{3}$	[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	2.175

18130	$y^{''} + 2 x {y^{'}}^{2} = 0$	[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]	✓	0.223

18131	$x^{2} + y = x y^{'}$	[_linear]	✓	1.660

18132	$x y^{'} + y = x^{2} \cos (x)$	[_linear]	✓	1.552

18133	$6 x + 4 y + 3 + (3 x + 2 y + 2) y^{'} = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.968

18134	$\cos (x + y) = x \sin (x + y) + x \sin (x + y) y^{'}$	[[_1st_order, _with_linear_symmetries], _exact]	✓	4.826

18135	$x^{2} y^{''} + x y^{'} = 1$	[[_2nd_order, _missing_y]]	✓	0.821

18136	$y^{2} e^{x y} + \cos (x) + (e^{x y} + x y e^{x y}) y^{'} = 0$	[_exact]	✓	35.752

18137	$y^{'} \ln (x - y) = 1 + \ln (x - y)$	[[_homogeneous, ‘class C‘], _exact, _dAlembert]	✓	2.214

18138	$y^{'} + 2 x y = e^{- x^{2}}$	[_linear]	✓	1.725

18139	$y^{2} - 3 x y - 2 x^{2} = (x^{2} - x y) y^{'}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	80.409

18140	$(x^{2} + 1) y^{'} + 2 x y = 4 x^{3}$	[_linear]	✓	1.810

18141	$e^{x} \sin (y) + e^{x} \cos (y) y^{'} = y \sin (x y) + x \sin (x y) y^{'}$	[_exact]	✓	40.325

18142	$(x^{2} + 1) y^{''} + x y^{'} = 0$	[[_2nd_order, _missing_y]]	✓	0.780

18143	$(x e^{y} + y - x^{2}) y^{''} = 2 x y - e^{y} - x$	[NONE]	✗	0.212

18144	$(x + 1) e^{x} = (x e^{x} - y e^{y}) y^{'}$	[‘y=_G(x,y’)‘]	✓	1.939

18145	$x^{2} y^{4} + x^{6} - x^{3} y^{3} y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	6.251

18146	$y^{'} = 1 + 3 \tan (x) y$	[_linear]	✓	1.577

18147	$y^{'} = 1 + \frac{y}{x} - \frac{y^{2}}{x^{2}}$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓	2.995

18148	$y^{'} = \frac{2 x y e^{\frac{x^{2}}{y^{2}}}}{y^{2} + y^{2} e^{\frac{x^{2}}{y^{2}}} + 2 x^{2} e^{\frac{x^{2}}{y^{2}}}}$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	71.808

18149	$y^{'} = \frac{x + 2 y + 2}{- 2 x + y}$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.569

18150	$3 x^{2} \ln (y) + \frac{x^{3} y^{'}}{y} = 0$	[_separable]	✓	2.262

18151	$\frac{3 y^{2}}{x^{2} + 3 x} + (2 y \ln (\frac{5 x}{x + 3}) + 3 \sin (y)) y^{'} = 0$	[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	38.766

18152	$\frac{y - x}{{(x + y)}^{3}} - \frac{2 x y^{'}}{{(x + y)}^{3}} = 0$	[_linear]	✓	4.513

18153	$x y^{2} + y + x y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	1.617

18154	$x^{2} y^{''} = y^{'} (3 x - 2 y^{'})$	[[_2nd_order, _missing_y]]	✓	0.427

18155	$3 x^{2} y - y^{3} - (3 x y^{2} - x^{3}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓	8.557

18156	$x (x^{2} + 1) y^{'} + 2 y = {(x^{2} + 1)}^{3}$	[_linear]	✓	1.540

18157	$y^{'} = \frac{- 3 x - 2 y - 1}{2 x + 3 y - 1}$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.295

18158	$e^{x^{2} y} (1 + 2 x^{2} y) + x^{3} e^{x^{2} y} y^{'} = 0$	[_linear]	✓	1.369

18159	$3 x^{2} e^{y} - 2 x + (x^{3} e^{y} - \sin (y)) y^{'} = 0$	[_exact]	✓	2.508

18160	$y^{2} y^{''} + {y^{'}}^{3} = 0$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]	✓	0.374

18161	$3 x y + y^{2} + (3 x y + x^{2}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	70.917

18162	$x^{2} y^{'} = y^{2} + x y + x^{2}$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓	2.546

18163	$x y^{'} + y = y^{2} \ln (x)$	[_Bernoulli]	✓	2.559

18164	$\frac{\cos (y)}{x + 3} - (\sin (y) \ln (5 x + 15) - \frac{1}{y}) y^{'} = 0$	[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	38.746

18165	$x^{2} y^{''} + {y^{'}}^{2} = 0$	[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]	✓	0.201

18166	$x y + y - 1 + x y^{'} = 0$	[_linear]	✓	1.207

18167	$x^{2} y^{'} - y^{2} = 2 x y$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	2.981

18168	$y^{''} = 2 y {y^{'}}^{3}$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]	✓	0.304

18169	$x^{'} + x \cot (y) = \sec (y)$	[_linear]	✓	1.911

18170	$x y^{''} - y^{'} = 3 x^{2}$	[[_2nd_order, _missing_y]]	✓	0.979

18171	$x y^{''} + y^{'} = 0$	[[_2nd_order, _missing_y]]	✓	0.743

18172	$y^{''} - y^{'} - 2 y = 4 x$	[[_2nd_order, _with_linear_symmetries]]	✓	1.122

18173	$x^{3} y^{''} + x^{2} y^{'} + x y = 1$	[[_2nd_order, _with_linear_symmetries]]	✓	3.049

18174	$y^{''} - 2 y^{'} = 6$	[[_2nd_order, _missing_x]]	✓	2.046

18175	$y^{''} - 2 y = \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.582

18176	$y^{''} = e^{x}$	[[_2nd_order, _quadrature]]	✓	1.777

18177	$y^{''} - 2 y^{'} = 4$	[[_2nd_order, _missing_x]]	✓	2.064

18178	$y^{''} - y = \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.418

18179	$(- 1 + x) y^{''} - x y^{'} + y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.224

18180	$y^{''} + 2 y^{'} = 6 e^{x}$	[[_2nd_order, _missing_y]]	✓	1.994

18181	$x^{2} y^{''} - 3 x y^{'} - 5 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.981

18182	$x^{2} y^{''} - 4 x y^{'} + (x^{2} + 6) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	1.365

18183	$y^{''} - y = 0$	[[_2nd_order, _missing_x]]	✓	2.061

18184	$x^{2} y^{''} - 2 x y^{'} + 2 y = 0$ i.c.	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.880

18185	$y^{''} - 3 y^{'} + 2 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.163

18186	$y^{''} - 4 y^{'} + 4 y = 0$	[[_2nd_order, _missing_x]]	✓	0.967

18187	$x^{2} y^{''} - 2 y = 0$ i.c.	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	1.079

18188	$y^{''} + y^{'} - 2 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.421

18189	$y^{''} + 5 y^{'} + 6 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.169

18190	$y^{''} + y^{'} = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	2.515

18191	$y^{''} + {y^{'}}^{2} = 0$	[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]]	✓	0.391

18192	$y^{''} + 2 x y^{'} + (x^{2} + 1) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.543

18193	$y^{''} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.287

18194	$y^{''} - y = 0$	[[_2nd_order, _missing_x]]	✓	0.248

18195	$x y^{''} + 3 y^{'} = 0$	[[_2nd_order, _missing_y]]	✓	0.078

18196	$x^{2} y^{''} + x y^{'} - 4 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.086

18197	$(- x^{2} + 1) y^{''} - 2 x y^{'} + 2 y = 0$	[_Gegenbauer]	✓	0.104

18198	$x^{2} y^{''} + x y^{'} + (x^{2} - \frac{1}{4}) y = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.145

18199	$y^{''} - \frac{x y^{'}}{- 1 + x} + \frac{y}{- 1 + x} = 0$	[[_2nd_order, _with_linear_symmetries]]	✓	0.100

18200	$x^{2} y^{''} + 2 x y^{'} - 2 y = 0$	[[_Emden, _Fowler]]	✓	0.082

2.2.182 Problems 18101 to 18200