Problems 1201 to 1300

Table 2.27: Main lookup table. Sorted sequentially by problem number.


#	ODE	CAS classiﬁcation	Solved?	time (sec)

1201	$2 x - 2 e^{x y} \sin (2 x) + e^{x y} \cos (2 x) y + (- 3 + e^{x y} x \cos (2 x)) y^{'} = 0$	[_exact]	✓	37.423

1202	$\frac{y}{x} + 6 x + (\ln (x) - 2) y^{'} = 0$	[_linear]	✓	1.574

1203	$\ln (x) x + x y + (y \ln (x) + x y) y^{'} = 0$	[[_Abel, ‘2nd type‘, ‘class B‘]]	✗	1.383

1204	$\frac{x}{{(x^{2} + y^{2})}^{3 / 2}} + \frac{y y^{'}}{{(x^{2} + y^{2})}^{3 / 2}} = 0$	[_separable]	✓	4.030

1205	$2 x - y + (- x + 2 y) y^{'} = 0$ i.c.	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	6.446

1206	$- 1 + 9 x^{2} + y + (x - 4 y) y^{'} = 0$ i.c.	[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.904

1207	$x^{2} y^{3} + x (1 + y^{2}) y^{'} = 0$	[_separable]	✓	1.636

1208	$y + (2 x - e^{y} y) y^{'} = 0$	[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	1.299

1209	$(x + 2) \sin (y) + x \cos (y) y^{'} = 0$	[_separable]	✓	2.569

1210	$2 x y + 3 x^{2} y + y^{3} + (x^{2} + y^{2}) y^{'} = 0$	[[_homogeneous, ‘class D‘], _rational]	✓	2.007

1211	$y^{'} = - 1 + e^{2 x} + y$	[[_linear, ‘class A‘]]	✓	1.350

1212	$1 + (- \sin (y) + \frac{x}{y}) y^{'} = 0$	[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	1.473

1213	$y + (- e^{- 2 y} + 2 x y) y^{'} = 0$	[[_1st_order, _with_exponential_symmetries]]	✓	1.823

1214	$e^{x} + (e^{x} \cot (y) + 2 \csc (y) y) y^{'} = 0$	[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	4.233

1215	$\frac{4 x^{3}}{y^{2}} + \frac{3}{y} + (\frac{3 x}{y^{2}} + 4 y) y^{'} = 0$	[_rational]	✓	1.372

1216	$3 x + \frac{6}{y} + (\frac{x^{2}}{y} + \frac{3 y}{x}) y^{'} = 0$	[_rational]	✓	1.361

1217	$3 x y + y^{2} + (x^{2} + x y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	62.626

1218	$y^{'} = \frac{x^{3} - 2 y}{x}$	[_linear]	✓	1.621

1219	$y^{'} = \frac{\cos (x) + 1}{2 - \sin (y)}$	[_separable]	✓	3.232

1220	$y^{'} = \frac{2 x + y}{3 - x + 3 y^{2}}$ i.c.	[_rational]	✓	4.121

1221	$y^{'} = 3 - 6 x + y - 2 x y$	[_separable]	✓	1.590

1222	$y^{'} = \frac{- 1 - 2 x y - y^{2}}{x^{2} + 2 x y}$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	1.535

1223	$x y + x y^{'} = 1 - y$ i.c.	[_linear]	✓	1.507

1224	$y^{'} = \frac{4 x^{3} + 1}{y (2 + 3 y)}$	[_separable]	✓	1.515

1225	$2 y + x y^{'} = \frac{\sin (x)}{x}$ i.c.	[_linear]	✓	1.841

1226	$y^{'} = \frac{- 1 - 2 x y}{x^{2} + 2 y}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]]	✓	1.223

1227	$\frac{- x^{2} + x + 1}{x^{2}} + \frac{y y^{'}}{- 2 + y} = 0$	[_separable]	✓	1.941

1228	$x^{2} + y + (e^{y} + x) y^{'} = 0$	[_exact]	✓	1.538

1229	$y + y^{'} = \frac{1}{e^{x} + 1}$	[_linear]	✓	1.726

1230	$y^{'} = 1 + 2 x + y^{2} + 2 x y^{2}$	[_separable]	✓	2.275

1231	$x + y + (x + 2 y) y^{'} = 0$ i.c.	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	5.249

1232	$(e^{x} + 1) y^{'} = y - y e^{x}$	[_separable]	✓	2.276

1233	$y^{'} = \frac{- e^{2 y} \cos (x) + \cos (y) e^{- x}}{2 e^{2 y} \sin (x) - \sin (y) e^{- x}}$	[NONE]	✓	40.228

1234	$y^{'} = e^{2 x} + 3 y$	[[_linear, ‘class A‘]]	✓	1.358

1235	$2 y + y^{'} = e^{- x^{2} - 2 x}$	[[_linear, ‘class A‘]]	✓	1.429

1236	$y^{'} = \frac{3 x^{2} - 2 y - y^{3}}{2 x + 3 x y^{2}}$	[_rational]	✓	1.421

1237	$y^{'} = e^{x + y}$	[_separable]	✓	2.655

1238	$\frac{- 4 + 6 x y + 2 y^{2}}{3 x^{2} + 4 x y + 3 y^{2}} + y^{'} = 0$	[_rational]	✓	1.474

1239	$y^{'} = \frac{x^{2} - 1}{1 + y^{2}}$ i.c.	[_separable]	✓	4.296

1240	$(t + 1) y + t y^{'} = e^{2 t}$	[_linear]	✓	1.454

1241	$2 \cos (x) \sin (x) \sin (y) + \cos (y) \sin {(x)}^{2} y^{'} = 0$	[_separable]	✓	3.229

1242	$\frac{2 x}{y} - \frac{y}{x^{2} + y^{2}} + (- \frac{x^{2}}{y^{2}} + \frac{x}{x^{2} + y^{2}}) y^{'} = 0$	[_exact, _rational]	✓	1.955

1243	$x y^{'} = e^{\frac{y}{x}} x + y$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	202.954

1244	$y^{'} = \frac{x}{x^{2} + y + y^{3}}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	1.365

1245	$3 t + 2 y = - t y^{'}$	[_linear]	✓	2.652

1246	$y^{'} = \frac{x + y}{x - y}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	39.145

1247	$2 x y + 3 y^{2} - (x^{2} + 2 x y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	116.724

1248	$y^{'} = \frac{- 3 x^{2} y - y^{2}}{2 x^{3} + 3 x y}$ i.c.	[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	4.515

1249	$y^{''} + 2 y^{'} - 3 y = 0$	[[_2nd_order, _missing_x]]	✓	0.856

1250	$y^{''} + 3 y^{'} + 2 y = 0$	[[_2nd_order, _missing_x]]	✓	0.822

1251	$6 y^{''} - y^{'} - y = 0$	[[_2nd_order, _missing_x]]	✓	0.867

1252	$2 y^{''} - 3 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.851

1253	$y^{''} + 5 y^{'} = 0$	[[_2nd_order, _missing_x]]	✓	1.913

1254	$4 y^{''} - 9 y = 0$	[[_2nd_order, _missing_x]]	✓	2.091

1255	$y^{''} - 9 y^{'} + 9 y = 0$	[[_2nd_order, _missing_x]]	✓	1.125

1256	$y^{''} - 2 y^{'} - 2 y = 0$	[[_2nd_order, _missing_x]]	✓	1.011

1257	$y^{''} + y^{'} - 2 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.421

1258	$y^{''} + 4 y^{'} + 3 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.421

1259	$6 y^{''} - 5 y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.186

1260	$y^{''} + 3 y^{'} = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	2.022

1261	$y^{''} + 5 y^{'} + 3 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.611

1262	$2 y^{''} + y^{'} - 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.620

1263	$y^{''} + 8 y^{'} - 9 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.450

1264	$4 y^{''} - y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	2.665

1265	$y^{''} - y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	2.548

1266	$2 y^{''} - 3 y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.175

1267	$y^{''} - y^{'} - 2 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.926

1268	$4 y^{''} - y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	2.097

1269	$y^{''} - (2 α - 1) y^{'} + α (α - 1) y = 0$	[[_2nd_order, _missing_x]]	✓	0.472

1270	$y^{''} + (3 - α) y^{'} - 2 (α - 1) y = 0$	[[_2nd_order, _missing_x]]	✓	41.405

1271	$2 y^{''} + 3 y^{'} - 2 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.905

1272	$y^{''} + 5 y^{'} + 6 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.878

1273	$y^{''} - 2 y^{'} + 2 y = 0$	[[_2nd_order, _missing_x]]	✓	2.025

1274	$y^{''} - 2 y^{'} + 6 y = 0$	[[_2nd_order, _missing_x]]	✓	2.042

1275	$y^{''} + 2 y^{'} - 8 y = 0$	[[_2nd_order, _missing_x]]	✓	0.862

1276	$y^{''} + 2 y^{'} + 2 y = 0$	[[_2nd_order, _missing_x]]	✓	1.914

1277	$y^{''} + 6 y^{'} + 13 y = 0$	[[_2nd_order, _missing_x]]	✓	2.534

1278	$4 y^{''} + 9 y = 0$	[[_2nd_order, _missing_x]]	✓	2.222

1279	$y^{''} + 2 y^{'} + \frac{5 y}{4} = 0$	[[_2nd_order, _missing_x]]	✓	1.646

1280	$9 y^{''} + 9 y^{'} - 4 y = 0$	[[_2nd_order, _missing_x]]	✓	0.839

1281	$y^{''} + y^{'} + \frac{5 y}{4} = 0$	[[_2nd_order, _missing_x]]	✓	2.037

1282	$y^{''} + 4 y^{'} + \frac{25 y}{4} = 0$	[[_2nd_order, _missing_x]]	✓	1.715

1283	$y^{''} + 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	2.132

1284	$y^{''} + 4 y^{'} + 5 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	2.109

1285	$y^{''} - 2 y^{'} + 5 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	2.819

1286	$y^{''} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	3.119

1287	$y^{''} + y^{'} + \frac{5 y}{4} = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	2.408

1288	$y^{''} + 2 y^{'} + 2 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	2.364

1289	$u^{''} - u^{'} + 2 u = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	3.137

1290	$5 u^{''} + 2 u^{'} + 7 u = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	2.989

1291	$y^{''} + 2 y^{'} + 6 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	2.134

1292	$y^{''} + 2 a y^{'} + (a^{2} + 1) y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	2.084

1293	$t^{2} y^{''} + t y^{'} + y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	1.079

1294	$t^{2} y^{''} + 4 t y^{'} + 2 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	1.175

1295	$t^{2} y^{''} + 3 t y^{'} + \frac{5 y}{4} = 0$	[[_Emden, _Fowler]]	✓	1.826

1296	$t^{2} y^{''} - 4 t y^{'} - 6 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	0.951

1297	$t^{2} y^{''} - 4 t y^{'} + 6 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.899

1298	$t^{2} y^{''} - t y^{'} + 5 y = 0$	[[_Emden, _Fowler]]	✓	4.231

1299	$t^{2} y^{''} + 3 t y^{'} - 3 y = 0$	[[_Emden, _Fowler]]	✓	0.878

1300	$t^{2} y^{''} + 7 t y^{'} + 10 y = 0$	[[_Emden, _Fowler]]	✓	3.498

2.2.13 Problems 1201 to 1300