Problems 14301 to 14400

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


#	ODE	CAS classiﬁcation	Solved?	time (sec)

14301	$y^{'} = \frac{1}{\sqrt{15 - x^{2} - y^{2}}}$	[‘y=_G(x,y’)‘]	✗	1.610

14302	$y^{'} = \frac{3 y}{(x - 5) (3 + x)} + e^{- x}$	[_linear]	✓	2.232

14303	$y^{'} = \frac{x y}{x^{2} + y^{2}}$	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	3.338

14304	$y^{'} = \frac{1}{x y}$	[_separable]	✓	1.929

14305	$y^{'} = \ln (- 1 + y)$	[_quadrature]	✓	0.728

14306	$y^{'} = \sqrt{(y + 2) (- 1 + y)}$	[_quadrature]	✓	10.725

14307	$y^{'} = \frac{y}{y - x}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	4.053

14308	$y^{'} = \frac{x}{y^{2}}$	[_separable]	✓	2.328

14309	$y^{'} = \frac{\sqrt{y}}{x}$	[_separable]	✓	2.045

14310	$y^{'} = \frac{x y}{1 - y}$	[_separable]	✓	1.419

14311	$y^{'} = {(x y)}^{1 / 3}$	[[_homogeneous, ‘class G‘]]	✓	4.932

14312	$y^{'} = \sqrt{\frac{y - 4}{x}}$	[[_homogeneous, ‘class C‘], _dAlembert]	✓	5.340

14313	$y^{'} = - \frac{y}{x} + y^{1 / 4}$	[[_homogeneous, ‘class G‘], _rational, _Bernoulli]	✓	12.484

14314	$y^{'} = 4 y - 5$ i.c.	[_quadrature]	✓	1.173

14315	$y^{'} + 3 y = 1$ i.c.	[_quadrature]	✓	1.279

14316	$y^{'} = b + a y$ i.c.	[_quadrature]	✓	0.989

14317	$y^{'} = x^{2} + e^{x} - \sin (x)$ i.c.	[_quadrature]	✓	0.717

14318	$y^{'} = x y + \frac{1}{x^{2} + 1}$ i.c.	[_linear]	✓	2.151

14319	$y^{'} = \cos (x) + \frac{y}{x}$ i.c.	[_linear]	✓	1.419

14320	$y^{'} = \frac{y}{x} + \tan (x)$ i.c.	[_linear]	✓	2.288

14321	$y^{'} = \frac{y}{- x^{2} + 4} + \sqrt{x}$ i.c.	[_linear]	✓	2.840

14322	$y^{'} = \frac{y}{- x^{2} + 4} + \sqrt{x}$ i.c.	[_linear]	✓	2.773

14323	$y^{'} = \cot (x) y + \csc (x)$ i.c.	[_linear]	✓	1.843

14324	$y^{'} = - x \sqrt{1 - y^{2}}$ i.c.	[_separable]	✓	5.354

14325	$y^{'} = - \frac{x}{2} + \frac{\sqrt{x^{2} + 4 y}}{2}$ i.c.	[[_1st_order, _with_linear_symmetries], _Clairaut]	✓	2.270

14326	$y^{'} = 3 x + 1$ i.c.	[_quadrature]	✓	0.506

14327	$y^{'} = x + \frac{1}{x}$ i.c.	[_quadrature]	✓	0.591

14328	$y^{'} = 2 \sin (x)$ i.c.	[_quadrature]	✓	0.642

14329	$y^{'} = x \sin (x)$ i.c.	[_quadrature]	✓	0.650

14330	$y^{'} = \frac{1}{x - 1}$ i.c.	[_quadrature]	✓	0.595

14331	$y^{'} = \frac{1}{x - 1}$ i.c.	[_quadrature]	✓	0.436

14332	$y^{'} = \frac{1}{x^{2} - 1}$ i.c.	[_quadrature]	✓	0.548

14333	$y^{'} = \frac{1}{x^{2} - 1}$ i.c.	[_quadrature]	✓	0.633

14334	$y^{'} = \tan (x)$ i.c.	[_quadrature]	✓	0.880

14335	$y^{'} = \tan (x)$ i.c.	[_quadrature]	✓	0.602

14336	$y^{'} = 3 y$ i.c.	[_quadrature]	✓	2.305

14337	$y^{'} = 1 - y$ i.c.	[_quadrature]	✓	0.853

14338	$y^{'} = 1 - y$ i.c.	[_quadrature]	✓	0.945

14339	$y^{'} = x e^{y - x^{2}}$ i.c.	[_separable]	✓	1.976

14340	$y^{'} = \frac{y}{x}$ i.c.	[_separable]	✓	1.504

14341	$y^{'} = \frac{2 x}{y}$ i.c.	[_separable]	✓	6.979

14342	$y^{'} = - 2 y + y^{2}$ i.c.	[_quadrature]	✓	1.455

14343	$y^{'} = x + x y$ i.c.	[_separable]	✓	1.533

14344	$x e^{y} + y^{'} = 0$ i.c.	[_separable]	✓	2.100

14345	$y - x^{2} y^{'} = 0$ i.c.	[_separable]	✓	1.687

14346	$2 y y^{'} = 1$	[_quadrature]	✓	1.016

14347	$2 x y^{'} y + y^{2} = - 1$	[_separable]	✓	2.462

14348	$y^{'} = \frac{1 - x y}{x^{2}}$	[_linear]	✓	0.944

14349	$y^{'} = - \frac{y (2 x + y)}{x (x + 2 y)}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	5.438

14350	$y^{'} = \frac{y^{2}}{1 - x y}$	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	1.475

14351	$y^{'} = 4 y + 1$ i.c.	[_quadrature]	✓	1.167

14352	$y^{'} = 2 + x y$ i.c.	[_linear]	✓	1.235

14353	$y^{'} = \frac{y}{x}$ i.c.	[_separable]	✓	1.518

14354	$y^{'} = \frac{y}{x - 1} + x^{2}$ i.c.	[_linear]	✓	1.182

14355	$y^{'} = \frac{y}{x} + \sin (x^{2})$ i.c.	[_linear]	✓	1.780

14356	$y^{'} = \frac{2 y}{x} + e^{x}$ i.c.	[_linear]	✓	1.757

14357	$y^{'} = \cot (x) y + \sin (x)$ i.c.	[_linear]	✓	1.968

14358	$x - y y^{'} = 0$	[_separable]	✓	3.620

14359	$y - y^{'} x = 0$	[_separable]	✓	1.319

14360	$y^{'} x + x^{2} - y = 0$	[_linear]	✓	1.223

14361	$x y (1 - y) - 2 y^{'} = 0$	[_separable]	✓	2.138

14362	$x (1 - y^{3}) - 3 y^{2} y^{'} = 0$	[_separable]	✓	2.726

14363	$(2 x - 1) y + x (x + 1) y^{'} = 0$	[_separable]	✓	1.400

14364	$y^{'} = \frac{1}{x - 1}$ i.c.	[_quadrature]	✓	0.433

14365	$y^{'} = x + y$ i.c.	[[_linear, ‘class A‘]]	✓	1.183

14366	$y^{'} = \frac{y}{x}$ i.c.	[_separable]	✓	1.474

14367	$y^{'} = \frac{y}{x}$ i.c.	[_separable]	✓	1.483

14368	$y^{'} = \frac{y}{- x^{2} + 1} + \sqrt{x}$ i.c.	[_linear]	✓	2.454

14369	$y^{'} = \frac{y}{- x^{2} + 1} + \sqrt{x}$	[_linear]	✓	1.964

14370	$y^{'} = \frac{y}{- x^{2} + 1} + \sqrt{x}$ i.c.	[_linear]	✓	2.581

14371	$y^{'} = y^{2}$ i.c.	[_quadrature]	✓	1.299

14372	$y^{'} = y^{2}$ i.c.	[_quadrature]	✓	1.322

14373	$y^{'} = y^{2}$ i.c.	[_quadrature]	✓	1.370

14374	$y^{'} = y^{3}$ i.c.	[_quadrature]	✓	1.696

14375	$y^{'} = y^{3}$ i.c.	[_quadrature]	✓	2.255

14376	$y^{'} = y^{3}$ i.c.	[_quadrature]	✓	12.268

14377	$y^{'} = - \frac{3 x^{2}}{2 y}$ i.c.	[_separable]	✓	2.638

14378	$y^{'} = - \frac{3 x^{2}}{2 y}$ i.c.	[_separable]	✓	2.259

14379	$y^{'} = - \frac{3 x^{2}}{2 y}$ i.c.	[_separable]	✓	2.193

14380	$y^{'} = - \frac{3 x^{2}}{2 y}$ i.c.	[_separable]	✓	3.129

14381	$y^{'} = \frac{\sqrt{y}}{x}$ i.c.	[_separable]	✓	3.642

14382	$y^{'} = \frac{\sqrt{y}}{x}$ i.c.	[_separable]	✓	3.592

14383	$y^{'} = \frac{\sqrt{y}}{x}$ i.c.	[_separable]	✓	3.695

14384	$y^{'} = \frac{\sqrt{y}}{x}$ i.c.	[_separable]	✓	3.057

14385	$y^{'} = 3 x y^{1 / 3}$ i.c.	[_separable]	✓	18.636

14386	$y^{'} = 3 x y^{1 / 3}$ i.c.	[_separable]	✓	36.229

14387	$y^{'} = 3 x y^{1 / 3}$ i.c.	[_separable]	✓	16.392

14388	$y^{'} = 3 x y^{1 / 3}$ i.c.	[_separable]	✓	6.631

14389	$y^{'} = 3 x y^{1 / 3}$ i.c.	[_separable]	✓	43.596

14390	$y^{'} = \sqrt{(y + 2) (- 1 + y)}$ i.c.	[_quadrature]	✓	7.828

14391	$y^{'} = \sqrt{(y + 2) (- 1 + y)}$ i.c.	[_quadrature]	✓	1.901

14392	$y^{'} = \sqrt{(y + 2) (- 1 + y)}$ i.c.	[_quadrature]	✓	94.335

14393	$y^{'} = \frac{y}{y - x}$ i.c.	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.818

14394	$y^{'} = \frac{y}{y - x}$ i.c.	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.846

14395	$y^{'} = \frac{y}{y - x}$ i.c.	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	4.319

14396	$y^{'} = \frac{y}{y - x}$ i.c.	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.850

14397	$y^{'} = \frac{x y}{x^{2} + y^{2}}$ i.c.	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	9.872

14398	$y^{'} = \frac{x y}{x^{2} + y^{2}}$ i.c.	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	7.184

14399	$y^{'} = \frac{x y}{x^{2} + y^{2}}$ i.c.	[[_homogeneous, ‘class A‘], _rational, _dAlembert]	✓	11.848

14400	$y^{'} = x \sqrt{1 - y^{2}}$ i.c.	[_separable]	✓	5.356

2.2.144 Problems 14301 to 14400