Problems 14301 to 14400

Table 2.289: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

14301	$y^{'} = \frac{\sqrt{y}}{x}$	[_separable]	✓	3.310

14302	$y^{'} = \frac{x y}{1 - y}$	[_separable]	✓	1.406

14303	$y^{'} = {(x y)}^{1 / 3}$	[[_homogeneous, ‘class G‘]]	✓	5.214

14304	$y^{'} = \sqrt{\frac{y - 4}{x}}$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	6.358

14305	$y^{'} = - \frac{y}{x} + y^{1 / 4}$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	16.587

14306	$y^{'} = 4 y - 5$ i.c.	[_quadrature]	✓	2.080

14307	$y^{'} + 3 y = 1$ i.c.	[_quadrature]	✓	2.175

14308	$y^{'} = a y + b$ i.c.	[_quadrature]	✓	1.047

14309	$y^{'} = x^{2} + e^{x} - \sin (x)$ i.c.	[_quadrature]	✓	0.905

14310	$y^{'} = x y + \frac{1}{x^{2} + 1}$ i.c.	[_linear]	✓	2.220

14311	$y^{'} = \frac{y}{x} + \cos (x)$ i.c.	[_linear]	✓	1.778

14312	$y^{'} = \frac{y}{x} + \tan (x)$ i.c.	[_linear]	✓	2.036

14313	$y^{'} = \frac{y}{- x^{2} + 4} + \sqrt{x}$ i.c.	[_linear]	✓	2.713

14314	$y^{'} = \frac{y}{- x^{2} + 4} + \sqrt{x}$ i.c.	[_linear]	✓	2.571

14315	$y^{'} = \cot (x) y + \csc (x)$ i.c.	[_linear]	✓	2.009

14316	$y^{'} = - x \sqrt{1 - y^{2}}$ i.c.	[_separable]	✓	6.395

14317	$y^{'} = - \frac{x}{2} + \frac{\sqrt{x^{2} + 4 y}}{2}$ i.c.	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	2.348

14318	$y^{'} = 3 x + 1$ i.c.	[_quadrature]	✓	0.674

14319	$y^{'} = x + \frac{1}{x}$ i.c.	[_quadrature]	✓	0.743

14320	$y^{'} = 2 \sin (x)$ i.c.	[_quadrature]	✓	0.749

14321	$y^{'} = x \sin (x)$ i.c.	[_quadrature]	✓	0.796

14322	$y^{'} = \frac{1}{- 1 + x}$ i.c.	[_quadrature]	✓	0.730

14323	$y^{'} = \frac{1}{- 1 + x}$ i.c.	[_quadrature]	✓	0.634

14324	$y^{'} = \frac{1}{x^{2} - 1}$ i.c.	[_quadrature]	✓	0.674

14325	$y^{'} = \frac{1}{x^{2} - 1}$ i.c.	[_quadrature]	✓	0.744

14326	$y^{'} = \tan (x)$ i.c.	[_quadrature]	✓	1.121

14327	$y^{'} = \tan (x)$ i.c.	[_quadrature]	✓	0.710

14328	$y^{'} = 3 y$ i.c.	[_quadrature]	✓	3.223

14329	$y^{'} = 1 - y$ i.c.	[_quadrature]	✓	1.314

14330	$y^{'} = 1 - y$ i.c.	[_quadrature]	✓	1.795

14331	$y^{'} = x e^{y - x^{2}}$ i.c.	[_separable]	✓	2.316

14332	$y^{'} = \frac{y}{x}$ i.c.	[_separable]	✓	2.039

14333	$y^{'} = \frac{2 x}{y}$ i.c.	[_separable]	✓	8.974

14334	$y^{'} = - 2 y + y^{2}$ i.c.	[_quadrature]	✓	2.740

14335	$y^{'} = x y + x$ i.c.	[_separable]	✓	1.961

14336	$x e^{y} + y^{'} = 0$ i.c.	[_separable]	✓	2.711

14337	$y - x^{2} y^{'} = 0$ i.c.	[_separable]	✓	1.751

14338	$2 y y^{'} = 1$	[_quadrature]	✓	1.887

14339	$2 x y y^{'} + y^{2} = - 1$	[_separable]	✓	2.777

14340	$y^{'} = \frac{1 - x y}{x^{2}}$	[_linear]	✓	1.252

14341	$y^{'} = - \frac{y (2 x + y)}{x (x + 2 y)}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	62.497

14342	$y^{'} = \frac{y^{2}}{1 - x y}$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	1.636

14343	$y^{'} = 4 y + 1$ i.c.	[_quadrature]	✓	2.049

14344	$y^{'} = x y + 2$ i.c.	[_linear]	✓	1.462

14345	$y^{'} = \frac{y}{x}$ i.c.	[_separable]	✓	2.019

14346	$y^{'} = \frac{y}{- 1 + x} + x^{2}$ i.c.	[_linear]	✓	1.425

14347	$y^{'} = \frac{y}{x} + \sin (x^{2})$ i.c.	[_linear]	✓	2.204

14348	$y^{'} = \frac{2 y}{x} + e^{x}$ i.c.	[_linear]	✓	2.205

14349	$y^{'} = \cot (x) y + \sin (x)$ i.c.	[_linear]	✓	2.153

14350	$x - y y^{'} = 0$	[_separable]	✓	4.461

14351	$y - x y^{'} = 0$	[_separable]	✓	1.659

14352	$x^{2} - y + x y^{'} = 0$	[_linear]	✓	1.601

14353	$x y (1 - y) - 2 y^{'} = 0$	[_separable]	✓	2.507

14354	$x (1 - y^{3}) - 3 y^{2} y^{'} = 0$	[_separable]	✓	2.506

14355	$y (2 x - 1) + x (x + 1) y^{'} = 0$	[_separable]	✓	1.705

14356	$y^{'} = \frac{1}{- 1 + x}$ i.c.	[_quadrature]	✓	0.615

14357	$y^{'} = x + y$ i.c.	[[_linear, ‘class A‘]]	✓	1.505

14358	$y^{'} = \frac{y}{x}$ i.c.	[_separable]	✓	2.021

14359	$y^{'} = \frac{y}{x}$ i.c.	[_separable]	✓	2.007

14360	$y^{'} = \frac{y}{- x^{2} + 1} + \sqrt{x}$ i.c.	[_linear]	✓	2.208

14361	$y^{'} = \frac{y}{- x^{2} + 1} + \sqrt{x}$	[_linear]	✓	1.783

14362	$y^{'} = \frac{y}{- x^{2} + 1} + \sqrt{x}$ i.c.	[_linear]	✓	2.247

14363	$y^{'} = y^{2}$ i.c.	[_quadrature]	✓	2.297

14364	$y^{'} = y^{2}$ i.c.	[_quadrature]	✓	1.937

14365	$y^{'} = y^{2}$ i.c.	[_quadrature]	✓	2.214

14366	$y^{'} = y^{3}$ i.c.	[_quadrature]	✓	3.354

14367	$y^{'} = y^{3}$ i.c.	[_quadrature]	✓	4.831

14368	$y^{'} = y^{3}$ i.c.	[_quadrature]	✓	10.761

14369	$y^{'} = - \frac{3 x^{2}}{2 y}$ i.c.	[_separable]	✓	3.052

14370	$y^{'} = - \frac{3 x^{2}}{2 y}$ i.c.	[_separable]	✓	2.897

14371	$y^{'} = - \frac{3 x^{2}}{2 y}$ i.c.	[_separable]	✓	2.560

14372	$y^{'} = - \frac{3 x^{2}}{2 y}$ i.c.	[_separable]	✓	3.117

14373	$y^{'} = \frac{\sqrt{y}}{x}$ i.c.	[_separable]	✓	3.194

14374	$y^{'} = \frac{\sqrt{y}}{x}$ i.c.	[_separable]	✓	3.040

14375	$y^{'} = \frac{\sqrt{y}}{x}$ i.c.	[_separable]	✓	3.329

14376	$y^{'} = \frac{\sqrt{y}}{x}$ i.c.	[_separable]	✓	2.958

14377	$y^{'} = 3 x y^{1 / 3}$ i.c.	[_separable]	✓	40.444

14378	$y^{'} = 3 x y^{1 / 3}$ i.c.	[_separable]	✓	8.617

14379	$y^{'} = 3 x y^{1 / 3}$ i.c.	[_separable]	✓	114.345

14380	$y^{'} = 3 x y^{1 / 3}$ i.c.	[_separable]	✓	11.530

14381	$y^{'} = 3 x y^{1 / 3}$ i.c.	[_separable]	✓	14.012

14382	$y^{'} = \sqrt{(y + 2) (y - 1)}$ i.c.	[_quadrature]	✓	19.111

14383	$y^{'} = \sqrt{(y + 2) (y - 1)}$ i.c.	[_quadrature]	✓	3.829

14384	$y^{'} = \sqrt{(y + 2) (y - 1)}$ i.c.	[_quadrature]	✓	61.680

14385	$y^{'} = \frac{y}{y - x}$ i.c.	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	5.569

14386	$y^{'} = \frac{y}{y - x}$ i.c.	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	5.072

14387	$y^{'} = \frac{y}{y - x}$ i.c.	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	5.919

14388	$y^{'} = \frac{y}{y - x}$ i.c.	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	5.243

14389	$y^{'} = \frac{x y}{x^{2} + y^{2}}$ i.c.	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	5.011

14390	$y^{'} = \frac{x y}{x^{2} + y^{2}}$ i.c.	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	5.389

14391	$y^{'} = \frac{x y}{x^{2} + y^{2}}$ i.c.	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	4.907

14392	$y^{'} = x \sqrt{1 - y^{2}}$ i.c.	[_separable]	✓	4.109

14393	$y^{'} = x \sqrt{1 - y^{2}}$ i.c.	[_separable]	✓	84.826

14394	$y^{'} = x \sqrt{1 - y^{2}}$ i.c.	[_separable]	✓	7.483

14395	$y^{'} = x \sqrt{1 - y^{2}}$ i.c.	[_separable]	✓	3.225

14396	$y^{'} = - \frac{x}{2} + \frac{\sqrt{x^{2} + 4 y}}{2}$ i.c.	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	2.750

14397	$y^{'} = - \frac{x}{2} + \frac{\sqrt{x^{2} + 4 y}}{2}$ i.c.	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	2.522

14398	$y^{'} = - \frac{x}{2} + \frac{\sqrt{x^{2} + 4 y}}{2}$ i.c.	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	2.593

14399	$y^{'} = - \frac{x}{2} + \frac{\sqrt{x^{2} + 4 y}}{2}$ i.c.	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	3.022

14400	$y^{'} = - \frac{x}{2} + \frac{\sqrt{x^{2} + 4 y}}{2}$ i.c.	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	2.497

2.2.144 Problems 14301 to 14400