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]	✓	40.228

1202	$\frac{y}{x} + 6 x + (\ln (x) - 2) y^{'} = 0$	[_linear]	✓	1.596

1203	$x \ln (x) + x y + (y \ln (x) + x y) y^{'} = 0$	[[_Abel, ‘2nd type‘, ‘class B‘]]	✗	1.630

1204	$\frac{x}{{(x^{2} + y^{2})}^{3 / 2}} + \frac{y y^{'}}{{(x^{2} + y^{2})}^{3 / 2}} = 0$	[_separable]	✓	8.418

1205	$2 x - y + (- x + 2 y) y^{'} = 0$ i.c.	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	5.146

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‘]]	✓	1.987

1207	$x^{2} y^{3} + x (1 + y^{2}) y^{'} = 0$	[_separable]	✓	4.194

1208	$y + (2 x - e^{y} y) y^{'} = 0$	[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	1.406

1209	$(x + 2) \sin (y) + x \cos (y) y^{'} = 0$	[_separable]	✓	2.437

1210	$2 x y + 3 x^{2} y + y^{3} + (x^{2} + y^{2}) y^{'} = 0$	[[_homogeneous, ‘class D‘], _rational]	✓	2.130

1211	$y^{'} = - 1 + e^{2 x} + y$	[[_linear, ‘class A‘]]	✓	1.122

1212	$1 + (- \sin (y) + \frac{x}{y}) y^{'} = 0$	[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	1.618

1213	$y + (- e^{- 2 y} + 2 x y) y^{'} = 0$	[[_1st_order, _with_exponential_symmetries]]	✓	1.678

1214	$e^{x} + (e^{x} \cot (y) + 2 \csc (y) y) y^{'} = 0$	[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	4.001

1215	$\frac{4 x^{3}}{y^{2}} + \frac{3}{y} + (\frac{3 x}{y^{2}} + 4 y) y^{'} = 0$	[_rational]	✓	1.446

1216	$3 x + \frac{6}{y} + (\frac{x^{2}}{y} + \frac{3 y}{x}) y^{'} = 0$	[_rational]	✓	1.479

1217	$3 x y + y^{2} + (x^{2} + x y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	4.572

1218	$y^{'} = \frac{x^{3} - 2 y}{x}$	[_linear]	✓	1.256

1219	$y^{'} = \frac{\cos (x) + 1}{2 - \sin (y)}$	[_separable]	✓	2.994

1220	$y^{'} = \frac{2 x + y}{3 - x + 3 y^{2}}$ i.c.	[_rational]	✓	3.175

1221	$y^{'} = 3 - 6 x + y - 2 x y$	[_separable]	✓	1.345

1222	$y^{'} = \frac{- 1 - 2 x y - y^{2}}{x^{2} + 2 x y}$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	1.649

1223	$x y + y^{'} x = 1 - y$ i.c.	[_linear]	✓	1.279

1224	$y^{'} = \frac{4 x^{3} + 1}{y (2 + 3 y)}$	[_separable]	✓	1.489

1225	$y^{'} x + 2 y = \frac{\sin (x)}{x}$ i.c.	[_linear]	✓	1.636

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‘]]	✓	1.251

1227	$\frac{- x^{2} + x + 1}{x^{2}} + \frac{y y^{'}}{- 2 + y} = 0$	[_separable]	✓	1.862

1228	$x^{2} + y + (e^{y} + x) y^{'} = 0$	[_exact]	✓	1.748

1229	$y^{'} + y = \frac{1}{e^{x} + 1}$	[_linear]	✓	1.699

1230	$y^{'} = 1 + 2 x + y^{2} + 2 x y^{2}$	[_separable]	✓	2.308

1231	$x + y + (x + 2 y) y^{'} = 0$ i.c.	[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	4.211

1232	$(e^{x} + 1) y^{'} = y - y e^{x}$	[_separable]	✓	1.923

1233	$y^{'} = \frac{- e^{2 y} \cos (x) + \cos (y) e^{- x}}{2 e^{2 y} \sin (x) - \sin (y) e^{- x}}$	[NONE]	✓	44.961

1234	$y^{'} = e^{2 x} + 3 y$	[[_linear, ‘class A‘]]	✓	1.066

1235	$2 y + y^{'} = e^{- x^{2} - 2 x}$	[[_linear, ‘class A‘]]	✓	1.418

1236	$y^{'} = \frac{3 x^{2} - 2 y - y^{3}}{2 x + 3 x y^{2}}$	[_rational]	✓	1.443

1237	$y^{'} = e^{x + y}$	[_separable]	✓	2.139

1238	$\frac{- 4 + 6 x y + 2 y^{2}}{3 x^{2} + 4 x y + 3 y^{2}} + y^{'} = 0$	[_rational]	✓	1.456

1239	$y^{'} = \frac{x^{2} - 1}{1 + y^{2}}$ i.c.	[_separable]	✓	2.886

1240	$(1 + t) y + y^{'} t = e^{2 t}$	[_linear]	✓	1.386

1241	$2 \cos (x) \sin (x) \sin (y) + \cos (y) \sin {(x)}^{2} y^{'} = 0$	[_separable]	✓	2.608

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]	✓	2.009

1243	$y^{'} x = e^{\frac{y}{x}} x + y$	[[_homogeneous, ‘class A‘], _dAlembert]	✓	4.878

1244	$y^{'} = \frac{x}{x^{2} + y + y^{3}}$	[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]	✓	1.367

1245	$3 t + 2 y = - y^{'} t$	[_linear]	✓	2.227

1246	$y^{'} = \frac{x + y}{x - y}$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	3.376

1247	$2 x y + 3 y^{2} - (x^{2} + 2 x y) y^{'} = 0$	[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	3.931

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‘]]	✓	3.203

1249	$y^{''} + 2 y^{'} - 3 y = 0$	[[_2nd_order, _missing_x]]	✓	0.367

1250	$y^{''} + 3 y^{'} + 2 y = 0$	[[_2nd_order, _missing_x]]	✓	0.368

1251	$6 y^{''} - y^{'} - y = 0$	[[_2nd_order, _missing_x]]	✓	0.367

1252	$2 y^{''} - 3 y^{'} + y = 0$	[[_2nd_order, _missing_x]]	✓	0.335

1253	$y^{''} + 5 y^{'} = 0$	[[_2nd_order, _missing_x]]	✓	1.111

1254	$4 y^{''} - 9 y = 0$	[[_2nd_order, _missing_x]]	✓	1.594

1255	$y^{''} - 9 y^{'} + 9 y = 0$	[[_2nd_order, _missing_x]]	✓	0.428

1256	$y^{''} - 2 y^{'} - 2 y = 0$	[[_2nd_order, _missing_x]]	✓	0.377

1257	$y^{''} + y^{'} - 2 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.575

1258	$y^{''} + 4 y^{'} + 3 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.556

1259	$6 y^{''} - 5 y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.603

1260	$y^{''} + 3 y^{'} = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.397

1261	$y^{''} + 5 y^{'} + 3 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.728

1262	$2 y^{''} + y^{'} - 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.748

1263	$y^{''} + 8 y^{'} - 9 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.632

1264	$4 y^{''} - y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	2.026

1265	$y^{''} - y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.862

1266	$2 y^{''} - 3 y^{'} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.576

1267	$y^{''} - y^{'} - 2 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.418

1268	$4 y^{''} - y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.703

1269	$y^{''} - (2 α - 1) y^{'} + α (α - 1) y = 0$	[[_2nd_order, _missing_x]]	✓	0.331

1270	$y^{''} + (3 - α) y^{'} - 2 (α - 1) y = 0$	[[_2nd_order, _missing_x]]	✓	0.648

1271	$2 y^{''} + 3 y^{'} - 2 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.450

1272	$y^{''} + 5 y^{'} + 6 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.412

1273	$y^{''} - 2 y^{'} + 2 y = 0$	[[_2nd_order, _missing_x]]	✓	0.492

1274	$y^{''} - 2 y^{'} + 6 y = 0$	[[_2nd_order, _missing_x]]	✓	0.567

1275	$y^{''} + 2 y^{'} - 8 y = 0$	[[_2nd_order, _missing_x]]	✓	0.360

1276	$y^{''} + 2 y^{'} + 2 y = 0$	[[_2nd_order, _missing_x]]	✓	0.468

1277	$y^{''} + 6 y^{'} + 13 y = 0$	[[_2nd_order, _missing_x]]	✓	0.519

1278	$4 y^{''} + 9 y = 0$	[[_2nd_order, _missing_x]]	✓	1.510

1279	$y^{''} + 2 y^{'} + \frac{5 y}{4} = 0$	[[_2nd_order, _missing_x]]	✓	0.505

1280	$9 y^{''} + 9 y^{'} - 4 y = 0$	[[_2nd_order, _missing_x]]	✓	0.344

1281	$y^{''} + y^{'} + \frac{5 y}{4} = 0$	[[_2nd_order, _missing_x]]	✓	0.534

1282	$y^{''} + 4 y^{'} + \frac{25 y}{4} = 0$	[[_2nd_order, _missing_x]]	✓	0.555

1283	$y^{''} + 4 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	1.363

1284	$y^{''} + 4 y^{'} + 5 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.620

1285	$y^{''} - 2 y^{'} + 5 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.831

1286	$y^{''} + y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	2.072

1287	$y^{''} + y^{'} + \frac{5 y}{4} = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.871

1288	$y^{''} + 2 y^{'} + 2 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.834

1289	$u^{''} - u^{'} + 2 u = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.941

1290	$5 u^{''} + 2 u^{'} + 7 u = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.927

1291	$y^{''} + 2 y^{'} + 6 y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.704

1292	$y^{''} + 2 a y^{'} + (a^{2} + 1) y = 0$ i.c.	[[_2nd_order, _missing_x]]	✓	0.619

1293	$t^{2} y^{''} + y^{'} t + y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.953

1294	$t^{2} y^{''} + 4 y^{'} t + 2 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	1.148

1295	$t^{2} y^{''} + 3 y^{'} t + \frac{5 y}{4} = 0$	[[_Emden, _Fowler]]	✓	1.023

1296	$t^{2} y^{''} - 4 y^{'} t - 6 y = 0$	[[_2nd_order, _exact, _linear, _homogeneous]]	✓	1.008

1297	$t^{2} y^{''} - 4 y^{'} t + 6 y = 0$	[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	0.936

1298	$t^{2} y^{''} - y^{'} t + 5 y = 0$	[[_Emden, _Fowler]]	✓	1.097

1299	$t^{2} y^{''} + 3 y^{'} t - 3 y = 0$	[[_Emden, _Fowler]]	✓	0.848

1300	$t^{2} y^{''} + 7 y^{'} t + 10 y = 0$	[[_Emden, _Fowler]]	✓	1.094

2.2.13 Problems 1201 to 1300