Problems 13201 to 13300

Table 2.267: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

13201	$3 x + 2 y + (2 x + y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	4.105

13202	$y^{2} + 3 + (2 x y - 4) y^{'} = 0$	[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]]	✓	1.664

13203	$2 x y + 1 + (x^{2} + 4 y) y^{'} = 0$	[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.309

13204	$3 x^{2} y + 2 - (x^{3} + y) y^{'} = 0$	[_rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✗	1.275

13205	$6 x y + 2 y^{2} - 5 + (3 x^{2} + 4 x y - 6) y^{'} = 0$	[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	1.835

13206	$y \sec {(x)}^{2} + \sec (x) \tan (x) + (\tan (x) + 2 y) y^{'} = 0$	[_exact, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	13.102

13207	$\frac{x}{y^{2}} + x + (\frac{x^{2}}{y^{3}} + y) y^{'} = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	1.902

13208	$\frac{(2 s - 1) s^{'}}{t} + \frac{s - s^{2}}{t^{2}} = 0$	[_separable]	✓	3.758

13209	$\frac{2 y^{3 / 2} + 1}{\sqrt{x}} + (3 \sqrt{x} \sqrt{y} - 1) y^{'} = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	3.035

13210	$2 x y - 3 + (x^{2} + 4 y) y^{'} = 0$ i.c.	[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.619

13211	$3 x^{2} y^{2} - y^{3} + 2 x + (2 x^{3} y - 3 x y^{2} + 1) y^{'} = 0$ i.c.	[_exact, _rational]	✓	7.663

13212	$2 \sin (x) \cos (x) y + \sin (x) y^{2} + (\sin {(x)}^{2} - 2 \cos (x) y) y^{'} = 0$ i.c.	[_exact, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	76.193

13213	$y e^{x} + 2 e^{x} + y^{2} + (e^{x} + 2 x y) y^{'} = 0$ i.c.	[_exact, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	2.561

13214	$\frac{3 - y}{x^{2}} + \frac{(y^{2} - 2 x) y^{'}}{x y^{2}} = 0$ i.c.	[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	3.044

13215	$\frac{1 + 8 x y^{2 / 3}}{x^{2 / 3} y^{1 / 3}} + \frac{(2 x^{4 / 3} y^{2 / 3} - x^{1 / 3}) y^{'}}{y^{4 / 3}} = 0$ i.c.	[[_homogeneous, ‘class G‘], _exact, _rational]	✓	4.486

13216	$4 x + 3 y^{2} + 2 x y^{'} y = 0$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	2.314

13217	$y^{2} + 2 x y - x^{2} y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	2.174

13218	$y + x {(x^{2} + y^{2})}^{2} + (y {(x^{2} + y^{2})}^{2} - x) y^{'} = 0$	[[_1st_order, _with_linear_symmetries], _rational]	✓	1.698

13219	$(x^{2} + 1) y^{'} + 4 x y = 0$	[_separable]	✓	1.234

13220	$x y + 2 x + y + 2 + (x^{2} + 2 x) y^{'} = 0$	[_separable]	✓	1.891

13221	$2 r (s^{2} + 1) + (r^{4} + 1) s^{'} = 0$	[_separable]	✓	2.438

13222	$\csc (y) + \sec (x) y^{'} = 0$	[_separable]	✓	2.355

13223	$\tan (θ) + 2 r θ^{'} = 0$	[_separable]	✓	2.258

13224	$(e^{v} + 1) \cos (u) + e^{v} (1 + \sin (u)) v^{'} = 0$	[_separable]	✓	2.668

13225	$(x + 4) (1 + y^{2}) + y (x^{2} + 3 x + 2) y^{'} = 0$	[_separable]	✓	2.935

13226	$x + y - y^{'} x = 0$	[_linear]	✓	1.314

13227	$2 x y + 3 y^{2} - (x^{2} + 2 x y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	4.124

13228	$v^{3} + (u^{3} - u v^{2}) v^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	93.671

13229	$x \tan (\frac{y}{x}) + y - y^{'} x = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	3.829

13230	$(2 s^{2} + 2 s t + t^{2}) s^{'} + s^{2} + 2 s t - t^{2} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓	6.361

13231	$x^{3} + y^{2} \sqrt{x^{2} + y^{2}} - x y \sqrt{x^{2} + y^{2}} y^{'} = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	9.692

13232	$\sqrt{x + y} + \sqrt{x - y} + (\sqrt{x - y} - \sqrt{x + y}) y^{'} = 0$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	8.860

13233	$y + 2 + y (x + 4) y^{'} = 0$ i.c.	[_separable]	✓	2.418

13234	$8 \cos {(y)}^{2} + \csc {(x)}^{2} y^{'} = 0$ i.c.	[_separable]	✓	3.214

13235	$(3 x + 8) (4 + y^{2}) - 4 y (x^{2} + 5 x + 6) y^{'} = 0$ i.c.	[_separable]	✓	3.332

13236	$x^{2} + 3 y^{2} - 2 x y^{'} y = 0$ i.c.	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	4.132

13237	$(4 x - y) y^{'} + 2 x - 5 y = 0$ i.c.	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.810

13238	$3 x^{2} + 9 x y + 5 y^{2} - (6 x^{2} + 4 x y) y^{'} = 0$ i.c.	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	5.163

13239	$x + 2 y + (2 x - y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	4.245

13240	$3 x - y - (x + y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	4.180

13241	$x^{2} + 2 y^{2} + (4 x y - y^{2}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓	6.711

13242	$2 x^{2} + 2 x y + y^{2} + (x^{2} + 2 x y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	4.359

13243	$y^{'} + \frac{3 y}{x} = 6 x^{2}$	[_linear]	✓	1.280

13244	$x^{4} y^{'} + 2 x^{3} y = 1$	[_linear]	✓	1.193

13245	$y^{'} + 3 y = 3 x^{2} e^{- 3 x}$	[[_linear, ‘class A‘]]	✓	1.598

13246	$y^{'} + 4 x y = 8 x$	[_separable]	✓	1.158

13247	$x^{'} + \frac{x}{t^{2}} = \frac{1}{t^{2}}$	[_separable]	✓	1.162

13248	$(u^{2} + 1) v^{'} + 4 u v = 3 u$	[_separable]	✓	1.556

13249	$y^{'} x + \frac{(2 x + 1) y}{x + 1} = x - 1$	[_linear]	✓	1.346

13250	$(x^{2} + x - 2) y^{'} + 3 (x + 1) y = x - 1$	[_linear]	✓	1.540

13251	$y^{'} x + x y + y - 1 = 0$	[_linear]	✓	1.045

13252	$y + (x y^{2} + x - y) y^{'} = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	1.225

13253	$r^{'} + r \tan (t) = \cos (t)$	[_linear]	✓	1.739

13254	$\cos (t) r^{'} + r \sin (t) - \cos {(t)}^{4} = 0$	[_linear]	✓	3.144

13255	$\cos {(x)}^{2} - \cos (x) y - (1 + \sin (x)) y^{'} = 0$	[_linear]	✓	2.978

13256	$y \sin (2 x) - \cos (x) + (1 + \sin {(x)}^{2}) y^{'} = 0$	[_linear]	✓	4.297

13257	$y^{'} - \frac{y}{x} = - \frac{y^{2}}{x}$	[_separable]	✓	1.927

13258	$y^{'} x + y = - 2 x^{6} y^{4}$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	3.908

13259	$y^{'} + (4 y - \frac{8}{y^{3}}) x = 0$	[_separable]	✓	2.984

13260	$x^{'} + \frac{(1 + t) x}{2 t} = \frac{1 + t}{t x}$	[_separable]	✓	2.417

13261	$y^{'} x - 2 y = 2 x^{4}$ i.c.	[_linear]	✓	1.622

13262	$y^{'} + 3 x^{2} y = x^{2}$ i.c.	[_separable]	✓	1.397

13263	$e^{x} (y - 3 {(e^{x} + 1)}^{2}) + (e^{x} + 1) y^{'} = 0$ i.c.	[_linear]	✓	1.914

13264	$2 x (1 + y) - (x^{2} + 1) y^{'} = 0$ i.c.	[_separable]	✓	1.524

13265	$r^{'} + r \tan (t) = \cos {(t)}^{2}$ i.c.	[_linear]	✓	2.292

13266	$x^{'} - x = \sin (2 t)$ i.c.	[[_linear, ‘class A‘]]	✓	1.669

13267	$y^{'} + \frac{y}{2 x} = \frac{x}{y^{3}}$ i.c.	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	3.110

13268	$y^{'} x + y = {(x y)}^{3 / 2}$ i.c.	[[_homogeneous, ‘class G‘], _rational]	✓	10.836

13269	$y^{'} + y = {\begin{array}{cc} 2 & 0 \leq x < 1 \\ 0 & 1 \leq x \end{array}$ i.c.	[[_linear, ‘class A‘]]	✓	0.897

13270	$y^{'} + y = {\begin{array}{cc} 5 & 0 \leq x < 10 \\ 1 & 10 \leq x \end{array}$ i.c.	[[_linear, ‘class A‘]]	✓	1.119

13271	$y^{'} + y = {\begin{array}{cc} e^{- x} & 0 \leq x < 2 \\ e^{- 2} & 2 \leq x \end{array}$ i.c.	[[_linear, ‘class A‘]]	✓	0.938

13272	$(x + 2) y^{'} + y = {\begin{array}{cc} 2 x & 0 \leq x < 2 \\ 4 & 2 \leq x \end{array}$ i.c.	[_linear]	✓	0.704

13273	$a y^{'} + b y = k e^{- λ x}$	[[_linear, ‘class A‘]]	✓	1.400

13274	$y^{'} + y = 2 \sin (x) + 5 \sin (2 x)$	[[_linear, ‘class A‘]]	✓	2.106

13275	$y^{'} \cos (y) + \frac{\sin (y)}{x} = 1$	[‘y=_G(x,y’)‘]	✓	1.835

13276	$(1 + y) y^{'} + x (2 y + y^{2}) = x$	[_separable]	✓	2.041

13277	$y^{'} = (1 - x) y^{2} + (2 x - 1) y - x$	[_Riccati]	✓	2.372

13278	$y^{'} = - y^{2} + x y + 1$	[_Riccati]	✓	1.712

13279	$y^{'} = - 8 x y^{2} + 4 x (1 + 4 x) y - 8 x^{3} - 4 x^{2} + 1$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]	✓	2.522

13280	$6 x^{2} y - (x^{3} + 1) y^{'} = 0$	[_separable]	✓	1.227

13281	$(3 x^{2} y^{2} - x) y^{'} + 2 x y^{3} - y = 0$	[[_homogeneous, ‘class G‘], _exact, _rational]	✓	1.928

13282	$y - 1 + x (x + 1) y^{'} = 0$	[_separable]	✓	1.399

13283	$x^{2} - 2 y + y^{'} x = 0$	[_linear]	✓	0.911

13284	$3 x - 5 y + (x + y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	13.434

13285	$y^{2} e^{2 x} + (e^{2 x} y - 2 y) y^{'} = 0$	[_separable]	✓	2.139

13286	$8 x^{3} y - 12 x^{3} + (x^{4} + 1) y^{'} = 0$	[_separable]	✓	1.620

13287	$2 x^{2} + x y + y^{2} + 2 x^{2} y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓	4.550

13288	$y^{'} = \frac{4 x^{3} y^{2} - 3 x^{2} y}{x^{3} - 2 y x^{4}}$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	2.923

13289	$(x + 1) y^{'} + x y = e^{- x}$	[_linear]	✓	1.833

13290	$y^{'} = \frac{2 x - 7 y}{3 y - 8 x}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	12.941

13291	$x y + x^{2} y^{'} = x y^{3}$	[_separable]	✓	4.210

13292	$(x^{3} + 1) y^{'} + 6 x^{2} y = 6 x^{2}$	[_separable]	✓	1.527

13293	$y^{'} = \frac{2 x^{2} + y^{2}}{2 x y - x^{2}}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	55.194

13294	$x^{2} + y^{2} - 2 x y^{'} y = 0$ i.c.	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	5.851

13295	$8 + 2 y^{2} + (- x^{2} + 1) y y^{'} = 0$ i.c.	[_separable]	✓	2.795

13296	$y^{2} e^{2 x} - 2 x + y e^{2 x} y^{'} = 0$ i.c.	[_exact, _Bernoulli]	✓	2.513

13297	$3 x^{2} + 2 x y^{2} + (2 x^{2} y + 6 y^{2}) y^{'} = 0$ i.c.	[_exact, _rational]	✓	8.207

13298	$4 x y^{'} y = 1 + y^{2}$ i.c.	[_separable]	✓	2.840

13299	$y^{'} = \frac{2 x + 7 y}{2 x - 2 y}$ i.c.	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	4.333

13300	$y^{'} = \frac{x y}{x^{2} + 1}$ i.c.	[_separable]	✓	1.706

2.2.133 Problems 13201 to 13300