Problems 13201 to 13300

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


#	ODE	CAS classiﬁcation	Solved?	time (sec)

13201	$\frac{2 y^{3 / 2} + 1}{\sqrt{x}} + (3 \sqrt{x} \sqrt{y} - 1) y^{'} = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	9.736

13202	$2 x y - 3 + (x^{2} + 4 y) y^{'} = 0$ i.c.	[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.665

13203	$3 y^{2} x^{2} - y^{3} + 2 x + (2 x^{3} y - 3 x y^{2} + 1) y^{'} = 0$ i.c.	[_exact, _rational]	✓	7.228

13204	$2 y \sin (x) \cos (x) + y^{2} \sin (x) + (\sin {(x)}^{2} - 2 y \cos (x)) y^{'} = 0$ i.c.	[_exact, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	46.792

13205	$y e^{x} + 2 e^{x} + y^{2} + (e^{x} + 2 x y) y^{'} = 0$ i.c.	[_exact, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	3.596

13206	$\frac{3 - y}{x^{2}} + \frac{(y^{2} - 2 x) y^{'}}{x y^{2}} = 0$ i.c.	[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	3.513

13207	$\frac{1 + 8 x y^{2 / 3}}{x^{2 / 3} y^{1 / 3}} + \frac{(2 x^{4 / 3} y^{2 / 3} - x^{1 / 3}) y^{'}}{y^{4 / 3}} = 0$ i.c.	[[_homogeneous, ‘class G‘], _exact, _rational]	✓	3.853

13208	$4 x + 3 y^{2} + 2 x y y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	2.750

13209	$y^{2} + 2 x y - x^{2} y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	3.021

13210	$y + x {(x^{2} + y^{2})}^{2} + (y {(x^{2} + y^{2})}^{2} - x) y^{'} = 0$	[[_1st_order, _with_linear_symmetries], _rational]	✓	2.186

13211	$4 x y + (x^{2} + 1) y^{'} = 0$	[_separable]	✓	1.721

13212	$x y + 2 x + y + 2 + (x^{2} + 2 x) y^{'} = 0$	[_separable]	✓	1.998

13213	$2 r (s^{2} + 1) + (r^{4} + 1) s^{'} = 0$	[_separable]	✓	2.776

13214	$\csc (y) + \sec (x) y^{'} = 0$	[_separable]	✓	2.029

13215	$\tan (θ) + 2 r θ^{'} = 0$	[_separable]	✓	3.076

13216	$(e^{v} + 1) \cos (u) + e^{v} (1 + \sin (u)) v^{'} = 0$	[_separable]	✓	2.688

13217	$(x + 4) (1 + y^{2}) + y (x^{2} + 3 x + 2) y^{'} = 0$	[_separable]	✓	3.069

13218	$x + y - x y^{'} = 0$	[_linear]	✓	1.592

13219	$2 x y + 3 y^{2} - (2 x y + x^{2}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	118.247

13220	$v^{3} + (u^{3} - u v^{2}) v^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	35.987

13221	$x \tan (\frac{y}{x}) + y - x y^{'} = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	3.869

13222	$(2 s^{2} + 2 s t + t^{2}) s^{'} + s^{2} + 2 s t - t^{2} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓	5.008

13223	$x^{3} + y^{2} \sqrt{x^{2} + y^{2}} - x y \sqrt{x^{2} + y^{2}} y^{'} = 0$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	6.658

13224	$\sqrt{x + y} + \sqrt{x - y} + (\sqrt{x - y} - \sqrt{x + y}) y^{'} = 0$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	15.913

13225	$y + 2 + y (x + 4) y^{'} = 0$ i.c.	[_separable]	✓	2.889

13226	$8 \cos {(y)}^{2} + \csc {(x)}^{2} y^{'} = 0$ i.c.	[_separable]	✓	2.975

13227	$(3 x + 8) (y^{2} + 4) - 4 y (x^{2} + 5 x + 6) y^{'} = 0$ i.c.	[_separable]	✓	3.602

13228	$x^{2} + 3 y^{2} - 2 x y y^{'} = 0$ i.c.	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	8.215

13229	$2 x - 5 y + (4 x - y) y^{'} = 0$ i.c.	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	4.524

13230	$3 x^{2} + 9 x y + 5 y^{2} - (6 x^{2} + 4 x y) y^{'} = 0$ i.c.	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	73.135

13231	$x + 2 y + (2 x - y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	4.528

13232	$3 x - y - (x + y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	4.781

13233	$x^{2} + 2 y^{2} + (4 x y - y^{2}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]	✓	107.096

13234	$2 x^{2} + 2 x y + y^{2} + (2 x y + x^{2}) y^{'} = 0$	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	75.517

13235	$y^{'} + \frac{3 y}{x} = 6 x^{2}$	[_linear]	✓	1.635

13236	$x^{4} y^{'} + 2 x^{3} y = 1$	[_linear]	✓	1.530

13237	$y^{'} + 3 y = 3 x^{2} e^{- 3 x}$	[[_linear, ‘class A‘]]	✓	1.889

13238	$y^{'} + 4 x y = 8 x$	[_separable]	✓	1.519

13239	$x^{'} + \frac{x}{t^{2}} = \frac{1}{t^{2}}$	[_separable]	✓	1.535

13240	$(u^{2} + 1) v^{'} + 4 v u = 3 u$	[_separable]	✓	1.904

13241	$x y^{'} + \frac{(2 x + 1) y}{x + 1} = - 1 + x$	[_linear]	✓	1.555

13242	$(x^{2} + x - 2) y^{'} + 3 (x + 1) y = - 1 + x$	[_linear]	✓	1.652

13243	$x y^{'} + x y + y - 1 = 0$	[_linear]	✓	1.259

13244	$y + (x y^{2} + x - y) y^{'} = 0$	[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	1.294

13245	$r^{'} + r \tan (t) = \cos (t)$	[_linear]	✓	1.833

13246	$\cos (t) r^{'} + r \sin (t) - \cos {(t)}^{4} = 0$	[_linear]	✓	3.352

13247	$\cos {(x)}^{2} - y \cos (x) - (\sin (x) + 1) y^{'} = 0$	[_linear]	✓	3.227

13248	$y \sin (2 x) - \cos (x) + (1 + \sin {(x)}^{2}) y^{'} = 0$	[_linear]	✓	4.539

13249	$y^{'} - \frac{y}{x} = - \frac{y^{2}}{x}$	[_separable]	✓	2.566

13250	$x y^{'} + y = - 2 x^{6} y^{4}$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	4.004

13251	$y^{'} + (4 y - \frac{8}{y^{3}}) x = 0$	[_separable]	✓	3.271

13252	$x^{'} + \frac{(t + 1) x}{2 t} = \frac{t + 1}{t x}$	[_separable]	✓	2.428

13253	$x y^{'} - 2 y = 2 x^{4}$ i.c.	[_linear]	✓	2.020

13254	$y^{'} + 3 x^{2} y = x^{2}$ i.c.	[_separable]	✓	1.361

13255	$e^{x} (y - 3 {(e^{x} + 1)}^{2}) + (e^{x} + 1) y^{'} = 0$ i.c.	[_linear]	✓	2.021

13256	$2 x (y + 1) - (x^{2} + 1) y^{'} = 0$ i.c.	[_separable]	✓	1.980

13257	$r^{'} + r \tan (t) = \cos {(t)}^{2}$ i.c.	[_linear]	✓	2.227

13258	$x^{'} - x = \sin (2 t)$ i.c.	[[_linear, ‘class A‘]]	✓	1.895

13259	$y^{'} + \frac{y}{2 x} = \frac{x}{y^{3}}$ i.c.	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	3.730

13260	$x y^{'} + y = {(x y)}^{3 / 2}$ i.c.	[[_homogeneous, ‘class G‘], _rational]	✓	17.087

13261	$y^{'} + y = {\begin{array}{cc} 2 & 0 \leq x < 1 \\ 0 & 1 \leq x \end{array}$ i.c.	[[_linear, ‘class A‘]]	✓	0.788

13262	$y^{'} + y = {\begin{array}{cc} 5 & 0 \leq x < 10 \\ 1 & 10 \leq x \end{array}$ i.c.	[[_linear, ‘class A‘]]	✓	1.229

13263	$y^{'} + y = {\begin{array}{cc} e^{- x} & 0 \leq x < 2 \\ e^{- 2} & 2 \leq x \end{array}$ i.c.	[[_linear, ‘class A‘]]	✓	0.911

13264	$(x + 2) y^{'} + y = {\begin{array}{cc} 2 x & 0 \leq x < 2 \\ 4 & 2 \leq x \end{array}$ i.c.	[_linear]	✓	0.739

13265	$a y^{'} + b y = k e^{- λ x}$	[[_linear, ‘class A‘]]	✓	1.233

13266	$y^{'} + y = 2 \sin (x) + 5 \sin (2 x)$	[[_linear, ‘class A‘]]	✓	2.310

13267	$\cos (y) y^{'} + \frac{\sin (y)}{x} = 1$	[‘y=_G(x,y’)‘]	✓	1.837

13268	$(y + 1) y^{'} + x (y^{2} + 2 y) = x$	[_separable]	✓	1.877

13269	$y^{'} = (1 - x) y^{2} + (2 x - 1) y - x$	[_Riccati]	✓	2.563

13270	$y^{'} = - y^{2} + x y + 1$	[_Riccati]	✓	1.347

13271	$y^{'} = - 8 x y^{2} + 4 x (4 x + 1) y - 8 x^{3} - 4 x^{2} + 1$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]	✓	2.684

13272	$6 x^{2} y - (x^{3} + 1) y^{'} = 0$	[_separable]	✓	1.712

13273	$(3 y^{2} x^{2} - x) y^{'} + 2 x y^{3} - y = 0$	[[_homogeneous, ‘class G‘], _exact, _rational]	✓	2.217

13274	$y - 1 + x (x + 1) y^{'} = 0$	[_separable]	✓	1.741

13275	$x^{2} - 2 y + x y^{'} = 0$	[_linear]	✓	1.258

13276	$3 x - 5 y + (x + y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	10.650

13277	$e^{2 x} y^{2} + (e^{2 x} y - 2 y) y^{'} = 0$	[_separable]	✓	2.260

13278	$8 x^{3} y - 12 x^{3} + (x^{4} + 1) y^{'} = 0$	[_separable]	✓	1.918

13279	$2 x^{2} + x y + y^{2} + 2 x^{2} y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, _Riccati]	✓	4.889

13280	$y^{'} = \frac{4 x^{3} y^{2} - 3 x^{2} y}{x^{3} - 2 x^{4} y}$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	4.204

13281	$(x + 1) y^{'} + x y = e^{- x}$	[_linear]	✓	2.123

13282	$y^{'} = \frac{2 x - 7 y}{3 y - 8 x}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	8.796

13283	$x^{2} y^{'} + x y = x y^{3}$	[_separable]	✓	5.668

13284	$(x^{3} + 1) y^{'} + 6 x^{2} y = 6 x^{2}$	[_separable]	✓	1.919

13285	$y^{'} = \frac{2 x^{2} + y^{2}}{2 x y - x^{2}}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	6.181

13286	$x^{2} + y^{2} - 2 x y y^{'} = 0$ i.c.	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	8.273

13287	$2 y^{2} + 8 + (- x^{2} + 1) y y^{'} = 0$ i.c.	[_separable]	✓	3.576

13288	$e^{2 x} y^{2} - 2 x + e^{2 x} y y^{'} = 0$ i.c.	[_exact, _Bernoulli]	✓	3.750

13289	$3 x^{2} + 2 x y^{2} + (2 x^{2} y + 6 y^{2}) y^{'} = 0$ i.c.	[_exact, _rational]	✓	38.005

13290	$4 x y y^{'} = 1 + y^{2}$ i.c.	[_separable]	✓	4.737

13291	$y^{'} = \frac{2 x + 7 y}{2 x - 2 y}$ i.c.	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	5.854

13292	$y^{'} = \frac{x y}{x^{2} + 1}$ i.c.	[_separable]	✓	2.369

13293	$y^{'} + y = {\begin{array}{cc} 1 & 0 \leq x < 2 \\ 0 & 0 < x \end{array}$ i.c.	[[_linear, ‘class A‘]]	✓	0.811

13294	$(x + 2) y^{'} + y = {\begin{array}{cc} 2 x & 0 \leq x \leq 2 \\ 4 & 2 < x \end{array}$ i.c.	[_linear]	✓	0.783

13295	$x^{2} y^{'} + x y = \frac{y^{3}}{x}$ i.c.	[[_homogeneous, ‘class A‘], _rational, _Bernoulli]	✓	144.209

13296	$5 x y + 4 y^{2} + 1 + (2 x y + x^{2}) y^{'} = 0$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	1.703

13297	$2 x + \tan (y) + (x - x^{2} \tan (y)) y^{'} = 0$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✓	2.561

13298	$(x + 1) y^{2} + y + (2 x y + 1) y^{'} = 0$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	1.444

13299	$2 x y^{2} + y + (2 y^{3} - x) y^{'} = 0$	[_rational]	✓	2.394

13300	$4 x y^{2} + 6 y + (5 x^{2} y + 8 x) y^{'} = 0$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	2.453

2.2.133 Problems 13201 to 13300