Problems 14101 to 14200

Table 2.285: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

14101	$y^{'} \sqrt{- x^{2} + 1} - \sqrt{1 - y^{2}} = 0$	[_separable]	✓	4.956

14102	$3 e^{x} \tan (y) + (1 - e^{x}) \sec {(y)}^{2} y^{'} = 0$	[_separable]	✓	3.489

14103	$x - x y^{2} + (y - x^{2} y) y^{'} = 0$	[_separable]	✓	2.753

14104	$y - x + (x + y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.834

14105	$y^{'} x + x + y = 0$	[_linear]	✓	2.515

14106	$x + y + (y - x) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.570

14107	$y^{'} x - y = \sqrt{x^{2} + y^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	5.498

14108	$(7 x + 5 y) y^{'} + 10 x + 8 y = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	4.701

14109	$2 \sqrt{s t} - s + t s^{'} = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	6.457

14110	$t - s + t s^{'} = 0$	[_linear]	✓	1.454

14111	$x y^{2} y^{'} = x^{3} + y^{3}$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	11.761

14112	$x \cos (\frac{y}{x}) (y^{'} x + y) = y \sin (\frac{y}{x}) (y^{'} x - y)$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	7.355

14113	$3 y - 7 x + 7 - (3 x - 7 y - 3) y^{'} = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.207

14114	$x + 2 y + 1 - (3 + 2 x + 4 y) y^{'} = 0$	[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	2.045

14115	$x + 2 y + 1 - (2 x - 3) y^{'} = 0$	[_linear]	✓	1.373

14116	$\frac{y - y^{'} x}{\sqrt{x^{2} + y^{2}}} = m$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	88.362

14117	$\frac{y y^{'} + x}{\sqrt{x^{2} + y^{2}}} = m$	[[_homogeneous, ‘class A‘], _exact, _dAlembert]	✓	134.278

14118	$y + \frac{x}{y^{'}} = \sqrt{x^{2} + y^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	5.441

14119	$y y^{'} = \sqrt{x^{2} + y^{2}} - x$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	6.634

14120	$y^{'} - \frac{2 y}{x + 1} = {(x + 1)}^{3}$	[_linear]	✓	1.415

14121	$y^{'} - \frac{a y}{x} = \frac{x + 1}{x}$	[_linear]	✓	2.238

14122	$(- x^{2} + x) y^{'} + (2 x^{2} - 1) y - a x^{3} = 0$	[_linear]	✓	1.750

14123	$s^{'} \cos (t) + s \sin (t) = 1$	[_linear]	✓	2.112

14124	$s^{'} + s \cos (t) = \frac{\sin (2 t)}{2}$	[_linear]	✓	2.405

14125	$y^{'} - \frac{n y}{x} = e^{x} x^{n}$	[_linear]	✓	1.479

14126	$y^{'} + \frac{n y}{x} = a x^{- n}$	[_linear]	✓	1.238

14127	$y^{'} + y = e^{- x}$	[[_linear, ‘class A‘]]	✓	0.948

14128	$y^{'} + \frac{(- 2 x + 1) y}{x^{2}} - 1 = 0$	[_linear]	✓	1.610

14129	$y^{'} + x y = x^{3} y^{3}$	[_Bernoulli]	✓	1.444

14130	$(- x^{2} + 1) y^{'} - x y + a x y^{2} = 0$	[_separable]	✓	3.122

14131	$3 y^{2} y^{'} - a y^{3} - x - 1 = 0$	[_rational, _Bernoulli]	✓	2.150

14132	$(x^{2} y^{3} + x y) y^{'} = 1$	[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	1.760

14133	$y^{'} x = (y \ln (x) - 2) y$	[_Bernoulli]	✓	2.170

14134	$y - \cos (x) y^{'} = y^{2} \cos (x) (1 - \sin (x))$	[_Bernoulli]	✓	5.752

14135	$x^{2} + y + (x - 2 y) y^{'} = 0$	[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.281

14136	$y - 3 x^{2} - (4 y - x) y^{'} = 0$	[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.376

14137	$(y^{3} - x) y^{'} = y$	[[_homogeneous, ‘class G‘], _exact, _rational]	✓	2.426

14138	$\frac{y^{2}}{{(x - y)}^{2}} - \frac{1}{x} + (\frac{1}{y} - \frac{x^{2}}{{(x - y)}^{2}}) y^{'} = 0$	[_exact, _rational]	✓	2.176

14139	$6 x y^{2} + 4 x^{3} + 3 (2 x^{2} y + y^{2}) y^{'} = 0$	[_exact, _rational]	✓	1.430

14140	$\frac{x}{{(x + y)}^{2}} + \frac{(2 x + y) y^{'}}{{(x + y)}^{2}} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]	✓	2.612

14141	$\frac{1}{x^{2}} + \frac{3 y^{2}}{x^{4}} = \frac{2 y y^{'}}{x^{3}}$	[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli]	✓	4.502

14142	$\frac{x^{2} y^{'}}{{(x - y)}^{2}} - \frac{y^{2}}{{(x - y)}^{2}} = 0$	[_separable]	✓	2.340

14143	$y y^{'} + x = \frac{y}{x^{2} + y^{2}} - \frac{x y^{'}}{x^{2} + y^{2}}$	[[_1st_order, _with_linear_symmetries], _exact, _rational]	✓	1.524

14144	$y = 2 y^{'} x + {y^{'}}^{2}$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	0.555

14145	$y = x {y^{'}}^{2} + {y^{'}}^{2}$	[[_homogeneous, ‘class C‘], _rational, _dAlembert]	✓	0.660

14146	$y = x (y^{'} + 1) + {y^{'}}^{2}$	[[_1st_order, _with_linear_symmetries], _dAlembert]	✓	0.612

14147	$y = y {y^{'}}^{2} + 2 y^{'} x$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	1.924

14148	$y = y y^{'} + y^{'} - {y^{'}}^{2}$	[_quadrature]	✓	0.291

14149	$y = y^{'} x + \sqrt{1 - {y^{'}}^{2}}$	[[_1st_order, _with_linear_symmetries], _rational, _Clairaut]	✓	1.996

14150	$y = y^{'} x + y^{'}$	[_separable]	✓	1.393

14151	$y = y^{'} x + \frac{1}{y^{'}}$	[[_homogeneous, ‘class G‘], _rational, _Clairaut]	✓	0.541

14152	$y = y^{'} x - \frac{1}{{y^{'}}^{2}}$	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	0.780

14153	$y^{'} = \frac{2 y}{x} - \sqrt{3}$	[_linear]	✓	1.939

14154	$y^{'''} - 2 y^{''} - y^{'} + 2 y = 0$	[[_3rd_order, _missing_x]]	✓	0.080

14155	$y^{''} = \frac{1}{2 y^{'}}$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_poly_yn]]	✓	1.112

14156	$x y^{'''} = 2$	[[_3rd_order, _quadrature]]	✓	1.121

14157	$y^{''} = a^{2} y$	[[_2nd_order, _missing_x]]	✓	1.549

14158	$y^{''} = \frac{a}{y^{3}}$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	1.845

14159	$x y^{''} - y^{'} = x^{2} e^{x}$ i.c.	[[_2nd_order, _missing_y]]	✓	1.326

14160	$y y^{''} + {y^{'}}^{3} - {y^{'}}^{2} = 0$ i.c.	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]	✓	0.598

14161	$y^{''} + y^{'} \tan (x) = \sin (2 x)$ i.c.	[[_2nd_order, _missing_y]]	✓	0.789

14162	${y^{''}}^{2} + {y^{'}}^{2} = a^{2}$ i.c.	[[_2nd_order, _missing_x]]	✓	3.530

14163	$y^{''} = \frac{1}{2 y^{'}}$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_poly_yn]]	✓	1.092

14164	$y^{'''} = {y^{''}}^{2}$	[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]	✓	0.646

14165	$y^{'''} y^{'} - 3 {y^{''}}^{2} = 0$	[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]	✓	0.901

14166	$y^{''} = 9 y$	[[_2nd_order, _missing_x]]	✓	1.433

14167	$y^{''} + y = 0$	[[_2nd_order, _missing_x]]	✓	1.338

14168	$y^{''} - y = 0$	[[_2nd_order, _missing_x]]	✓	1.635

14169	$y^{''} + 12 y = 7 y^{'}$	[[_2nd_order, _missing_x]]	✓	0.354

14170	$y^{''} - 4 y^{'} + 4 y = 0$	[[_2nd_order, _missing_x]]	✓	0.361

14171	$y^{''} + 2 y^{'} + 10 y = 0$	[[_2nd_order, _missing_x]]	✓	0.464

14172	$y^{''} + 3 y^{'} - 2 y = 0$	[[_2nd_order, _missing_x]]	✓	0.387

14173	$4 y^{''} - 12 y^{'} + 9 y = 0$	[[_2nd_order, _missing_x]]	✓	0.390

14174	$y^{''} + y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.584

14175	$y^{''''} - 5 y^{''} + 4 y = 0$	[[_high_order, _missing_x]]	✓	0.091

14176	$y^{'''} - 2 y^{''} - y^{'} + 2 y = 0$	[[_3rd_order, _missing_x]]	✓	0.080

14177	$y^{'''} - 3 a y^{''} + 3 a^{2} y^{'} - a^{3} y = 0$	[[_3rd_order, _missing_x]]	✓	0.087

14178	$y^{(5)} - 4 y^{'''} = 0$	[[_high_order, _missing_x]]	✓	0.076

14179	$y^{''''} + 2 y^{''} + 9 y = 0$	[[_high_order, _missing_x]]	✓	0.087

14180	$y^{''''} - 8 y^{''} + 16 y = 0$	[[_high_order, _missing_x]]	✓	0.085

14181	$y^{''''} + y = 0$	[[_high_order, _missing_x]]	✓	0.113

14182	$y^{''''} - a^{4} y = 0$	[[_high_order, _missing_x]]	✓	0.099

14183	$y^{''} - 7 y^{'} + 12 y = x$	[[_2nd_order, _with_linear_symmetries]]	✓	0.440

14184	$s^{''} - a^{2} s = 1 + t$	[[_2nd_order, _with_linear_symmetries]]	✓	0.629

14185	$y^{''} + y^{'} - 2 y = 8 \sin (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.586

14186	$y^{''} - y = 5 x + 2$	[[_2nd_order, _with_linear_symmetries]]	✓	0.524

14187	$y^{''} - 2 a y^{'} + a^{2} y = e^{x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.499

14188	$y^{''} + 6 y^{'} + 5 y = e^{2 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.506

14189	$y^{''} + 9 y = 6 e^{3 x}$	[[_2nd_order, _with_linear_symmetries]]	✓	0.718

14190	$y^{''} - 3 y^{'} = 2 - 6 x$	[[_2nd_order, _missing_y]]	✓	1.128

14191	$y^{''} - 2 y^{'} + 3 y = e^{- x} \cos (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.758

14192	$y^{''} + 4 y = 2 \sin (2 x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.773

14193	$y^{'''} - 4 y^{''} + 5 y^{'} - 2 y = 2 x + 3$	[[_3rd_order, _with_linear_symmetries]]	✓	0.134

14194	$y^{''''} - a^{4} y = 5 a^{4} e^{a x} \sin (a x)$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.230

14195	$y^{''''} + 2 a^{2} y^{''} + a^{4} y = 8 \cos (a x)$	[[_high_order, _linear, _nonhomogeneous]]	✓	0.957

14196	$y^{''} + 2 h y^{'} + n^{2} y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	2.409

14197	$y^{''} + n^{2} y = h \sin (r x)$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.969

14198	$y^{''} - 7 y^{'} + 6 y = \sin (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.584

14199	$y^{''} + y = \sec (x)$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	0.668

14200	$y^{''} + y = \frac{1}{\cos {(2 x)}^{3 / 2}}$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	1.137

2.2.142 Problems 14101 to 14200