2.2.13 Problems 1201 to 1300

Table 2.39: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

1201

\begin{align*} 2 x -2 \,{\mathrm e}^{y x} \sin \left (2 x \right )+{\mathrm e}^{y x} \cos \left (2 x \right ) y+\left (-3+{\mathrm e}^{y x} x \cos \left (2 x \right )\right ) y^{\prime }&=0 \\ \end{align*}

[_exact]

5.112

1202

\begin{align*} \frac {y}{x}+6 x +\left (\ln \left (x \right )-2\right ) y^{\prime }&=0 \\ \end{align*}

[_linear]

2.011

1203

\begin{align*} x \ln \left (x \right )+y x +\left (y \ln \left (x \right )+y x \right ) y^{\prime }&=0 \\ \end{align*}

[[_Abel, ‘2nd type‘, ‘class B‘]]

9.362

1204

\begin{align*} \frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}&=0 \\ \end{align*}

[_separable]

4.360

1205

\begin{align*} 2 x -y+\left (-x +2 y\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 3 \\ \end{align*}

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

5.577

1206

\begin{align*} -1+9 x^{2}+y+\left (x -4 y\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 0 \\ \end{align*}

[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]]

1.698

1207

\begin{align*} x^{2} y^{3}+x \left (1+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

1.794

1208

\begin{align*} y+\left (2 x -{\mathrm e}^{y} y\right ) y^{\prime }&=0 \\ \end{align*}

[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]

1.506

1209

\begin{align*} \left (2+x \right ) \sin \left (y\right )+x \cos \left (y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

2.273

1210

\begin{align*} 2 y x +3 x^{2} y+y^{3}+\left (x^{2}+y^{2}\right ) y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class D‘], _rational]

2.372

1211

\begin{align*} y^{\prime }&=-1+{\mathrm e}^{2 x}+y \\ \end{align*}

[[_linear, ‘class A‘]]

1.691

1212

\begin{align*} 1+\left (-\sin \left (y\right )+\frac {x}{y}\right ) y^{\prime }&=0 \\ \end{align*}

[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]

1.718

1213

\begin{align*} y+\left (-{\mathrm e}^{-2 y}+2 y x \right ) y^{\prime }&=0 \\ \end{align*}

[[_1st_order, _with_exponential_symmetries]]

2.268

1214

\begin{align*} {\mathrm e}^{x}+\left ({\mathrm e}^{x} \cot \left (y\right )+2 \csc \left (y\right ) y\right ) y^{\prime }&=0 \\ \end{align*}

[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]

3.708

1215

\begin{align*} \frac {4 x^{3}}{y^{2}}+\frac {3}{y}+\left (\frac {3 x}{y^{2}}+4 y\right ) y^{\prime }&=0 \\ \end{align*}

[_rational]

1.792

1216

\begin{align*} 3 x +\frac {6}{y}+\left (\frac {x^{2}}{y}+\frac {3 y}{x}\right ) y^{\prime }&=0 \\ \end{align*}

[_rational]

1.817

1217

\begin{align*} 3 y x +y^{2}+\left (y x +x^{2}\right ) y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

6.507

1218

\begin{align*} y^{\prime }&=\frac {x^{3}-2 y}{x} \\ \end{align*}

[_linear]

2.171

1219

\begin{align*} y^{\prime }&=\frac {\cos \left (x \right )+1}{2-\sin \left (y\right )} \\ \end{align*}

[_separable]

2.836

1220

\begin{align*} y^{\prime }&=\frac {2 x +y}{3-x +3 y^{2}} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_rational]

3.181

1221

\begin{align*} y^{\prime }&=3-6 x +y-2 y x \\ \end{align*}

[_separable]

1.942

1222

\begin{align*} y^{\prime }&=\frac {-1-2 y x -y^{2}}{x^{2}+2 y x} \\ \end{align*}

[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]

2.187

1223

\begin{align*} y x +y^{\prime } x&=1-y \\ y \left (1\right ) &= 0 \\ \end{align*}

[_linear]

2.048

1224

\begin{align*} y^{\prime }&=\frac {4 x^{3}+1}{y \left (2+3 y\right )} \\ \end{align*}

[_separable]

1.749

1225

\begin{align*} y^{\prime } x +2 y&=\frac {\sin \left (x \right )}{x} \\ y \left (2\right ) &= 1 \\ \end{align*}

[_linear]

1.862

1226

\begin{align*} y^{\prime }&=\frac {-1-2 y x}{x^{2}+2 y} \\ \end{align*}

[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]]

1.545

1227

\begin{align*} \frac {-x^{2}+x +1}{x^{2}}+\frac {y y^{\prime }}{y-2}&=0 \\ \end{align*}

[_separable]

2.928

1228

\begin{align*} x^{2}+y+\left ({\mathrm e}^{y}+x \right ) y^{\prime }&=0 \\ \end{align*}

[_exact]

1.780

1229

\begin{align*} y^{\prime }+y&=\frac {1}{{\mathrm e}^{x}+1} \\ \end{align*}

[_linear]

1.717

1230

\begin{align*} y^{\prime }&=1+2 x +y^{2}+2 x y^{2} \\ \end{align*}

[_separable]

2.559

1231

\begin{align*} x +y+\left (x +2 y\right ) y^{\prime }&=0 \\ y \left (2\right ) &= 3 \\ \end{align*}

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

4.272

1232

\begin{align*} \left ({\mathrm e}^{x}+1\right ) y^{\prime }&=y-{\mathrm e}^{x} y \\ \end{align*}

[_separable]

3.084

1233

\begin{align*} y^{\prime }&=\frac {-{\mathrm e}^{2 y} \cos \left (x \right )+\cos \left (y\right ) {\mathrm e}^{-x}}{2 \,{\mathrm e}^{2 y} \sin \left (x \right )-\sin \left (y\right ) {\mathrm e}^{-x}} \\ \end{align*}

[NONE]

76.002

1234

\begin{align*} y^{\prime }&={\mathrm e}^{2 x}+3 y \\ \end{align*}

[[_linear, ‘class A‘]]

1.092

1235

\begin{align*} 2 y+y^{\prime }&={\mathrm e}^{-x^{2}-2 x} \\ \end{align*}

[[_linear, ‘class A‘]]

1.456

1236

\begin{align*} y^{\prime }&=\frac {3 x^{2}-2 y-y^{3}}{2 x +3 x y^{2}} \\ \end{align*}

[_rational]

1.892

1237

\begin{align*} y^{\prime }&={\mathrm e}^{x +y} \\ \end{align*}

[_separable]

1.524

1238

\begin{align*} \frac {-4+6 y x +2 y^{2}}{3 x^{2}+4 y x +3 y^{2}}+y^{\prime }&=0 \\ \end{align*}

[_rational]

1.910

1239

\begin{align*} y^{\prime }&=\frac {x^{2}-1}{1+y^{2}} \\ y \left (-1\right ) &= 1 \\ \end{align*}

[_separable]

0.968

1240

\begin{align*} \left (1+t \right ) y+y^{\prime } t&={\mathrm e}^{2 t} \\ \end{align*}

[_linear]

1.625

1241

\begin{align*} 2 \cos \left (x \right ) \sin \left (x \right ) \sin \left (y\right )+\cos \left (y\right ) \sin \left (x \right )^{2} y^{\prime }&=0 \\ \end{align*}

[_separable]

2.519

1242

\begin{align*} \frac {2 x}{y}-\frac {y}{x^{2}+y^{2}}+\left (-\frac {x^{2}}{y^{2}}+\frac {x}{x^{2}+y^{2}}\right ) y^{\prime }&=0 \\ \end{align*}

[_exact, _rational]

2.233

1243

\begin{align*} y^{\prime } x&={\mathrm e}^{\frac {y}{x}} x +y \\ \end{align*}

[[_homogeneous, ‘class A‘], _dAlembert]

4.085

1244

\begin{align*} y^{\prime }&=\frac {x}{x^{2}+y+y^{3}} \\ \end{align*}

[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]

1.592

1245

\begin{align*} 3 t +2 y&=-y^{\prime } t \\ \end{align*}

[_linear]

2.930

1246

\begin{align*} y^{\prime }&=\frac {x +y}{x -y} \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

4.003

1247

\begin{align*} 2 y x +3 y^{2}-\left (x^{2}+2 y x \right ) y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

6.655

1248

\begin{align*} y^{\prime }&=\frac {-3 x^{2} y-y^{2}}{2 x^{3}+3 y x} \\ y \left (1\right ) &= -2 \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

4.464

1249

\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

3.877

1250

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

3.475

1251

\begin{align*} 6 y^{\prime \prime }-y^{\prime }-y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

3.727

1252

\begin{align*} 2 y^{\prime \prime }-3 y^{\prime }+y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

2.799

1253

\begin{align*} y^{\prime \prime }+5 y^{\prime }&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

1.556

1254

\begin{align*} 4 y^{\prime \prime }-9 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

1.578

1255

\begin{align*} y^{\prime \prime }-9 y^{\prime }+9 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

5.052

1256

\begin{align*} y^{\prime \prime }-2 y^{\prime }-2 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

4.044

1257

\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.826

1258

\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}

[[_2nd_order, _missing_x]]

1.852

1259

\begin{align*} 6 y^{\prime \prime }-5 y^{\prime }+y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.854

1260

\begin{align*} y^{\prime \prime }+3 y^{\prime }&=0 \\ y \left (0\right ) &= -2 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}

[[_2nd_order, _missing_x]]

1.188

1261

\begin{align*} y^{\prime \prime }+5 y^{\prime }+3 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.947

1262

\begin{align*} 2 y^{\prime \prime }+y^{\prime }-4 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.924

1263

\begin{align*} y^{\prime \prime }+8 y^{\prime }-9 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}

[[_2nd_order, _missing_x]]

7.023

1264

\begin{align*} 4 y^{\prime \prime }-y&=0 \\ y \left (-2\right ) &= 1 \\ y^{\prime }\left (-2\right ) &= -1 \\ \end{align*}

[[_2nd_order, _missing_x]]

2.324

1265

\begin{align*} y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= {\frac {5}{4}} \\ y^{\prime }\left (0\right ) &= -{\frac {3}{4}} \\ \end{align*}

[[_2nd_order, _missing_x]]

1.954

1266

\begin{align*} 2 y^{\prime \prime }-3 y^{\prime }+y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= {\frac {1}{2}} \\ \end{align*}

[[_2nd_order, _missing_x]]

1.599

1267

\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=0 \\ y \left (0\right ) &= \alpha \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.828

1268

\begin{align*} 4 y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= \beta \\ \end{align*}

[[_2nd_order, _missing_x]]

1.457

1269

\begin{align*} y^{\prime \prime }-\left (2 \alpha -1\right ) y^{\prime }+\alpha \left (\alpha -1\right ) y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

4.070

1270

\begin{align*} y^{\prime \prime }+\left (3-\alpha \right ) y^{\prime }-2 \left (\alpha -1\right ) y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

4.421

1271

\begin{align*} 2 y^{\prime \prime }+3 y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -\beta \\ \end{align*}

[[_2nd_order, _missing_x]]

0.830

1272

\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= \beta \\ \end{align*}

[[_2nd_order, _missing_x]]

0.705

1273

\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

3.674

1274

\begin{align*} y^{\prime \prime }-2 y^{\prime }+6 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

9.225

1275

\begin{align*} y^{\prime \prime }+2 y^{\prime }-8 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

3.498

1276

\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

4.353

1277

\begin{align*} y^{\prime \prime }+6 y^{\prime }+13 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

6.316

1278

\begin{align*} 4 y^{\prime \prime }+9 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

2.815

1279

\begin{align*} y^{\prime \prime }+2 y^{\prime }+\frac {5 y}{4}&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

7.781

1280

\begin{align*} 9 y^{\prime \prime }+9 y^{\prime }-4 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

3.748

1281

\begin{align*} y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

4.540

1282

\begin{align*} y^{\prime \prime }+4 y^{\prime }+\frac {25 y}{4}&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

11.665

1283

\begin{align*} y^{\prime \prime }+4 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

[[_2nd_order, _missing_x]]

1.623

1284

\begin{align*} y^{\prime \prime }+4 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

[[_2nd_order, _missing_x]]

4.265

1285

\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=0 \\ y \left (\frac {\pi }{2}\right ) &= 0 \\ y^{\prime }\left (\frac {\pi }{2}\right ) &= 2 \\ \end{align*}

[[_2nd_order, _missing_x]]

3.452

1286

\begin{align*} y^{\prime \prime }+y&=0 \\ y \left (\frac {\pi }{3}\right ) &= 2 \\ y^{\prime }\left (\frac {\pi }{3}\right ) &= -4 \\ \end{align*}

[[_2nd_order, _missing_x]]

1.782

1287

\begin{align*} y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

[[_2nd_order, _missing_x]]

64.398

1288

\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\ y \left (\frac {\pi }{4}\right ) &= 2 \\ y^{\prime }\left (\frac {\pi }{4}\right ) &= -2 \\ \end{align*}

[[_2nd_order, _missing_x]]

4.908

1289

\begin{align*} u^{\prime \prime }-u^{\prime }+2 u&=0 \\ u \left (0\right ) &= 2 \\ u^{\prime }\left (0\right ) &= 0 \\ \end{align*}

[[_2nd_order, _missing_x]]

5.763

1290

\begin{align*} 5 u^{\prime \prime }+2 u^{\prime }+7 u&=0 \\ u \left (0\right ) &= 2 \\ u^{\prime }\left (0\right ) &= 1 \\ \end{align*}

[[_2nd_order, _missing_x]]

8.291

1291

\begin{align*} y^{\prime \prime }+2 y^{\prime }+6 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= \alpha \\ \end{align*}

[[_2nd_order, _missing_x]]

8.434

1292

\begin{align*} y^{\prime \prime }+2 a y^{\prime }+\left (a^{2}+1\right ) y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

[[_2nd_order, _missing_x]]

4.941

1293

\begin{align*} t^{2} y^{\prime \prime }+y^{\prime } t +y&=0 \\ \end{align*}

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

3.969

1294

\begin{align*} t^{2} y^{\prime \prime }+4 y^{\prime } t +2 y&=0 \\ \end{align*}

[[_2nd_order, _exact, _linear, _homogeneous]]

5.572

1295

\begin{align*} t^{2} y^{\prime \prime }+3 y^{\prime } t +\frac {5 y}{4}&=0 \\ \end{align*}

[[_Emden, _Fowler]]

3.853

1296

\begin{align*} t^{2} y^{\prime \prime }-4 y^{\prime } t -6 y&=0 \\ \end{align*}

[[_2nd_order, _exact, _linear, _homogeneous]]

2.980

1297

\begin{align*} t^{2} y^{\prime \prime }-4 y^{\prime } t +6 y&=0 \\ \end{align*}

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

4.826

1298

\begin{align*} t^{2} y^{\prime \prime }-y^{\prime } t +5 y&=0 \\ \end{align*}

[[_Emden, _Fowler]]

3.395

1299

\begin{align*} t^{2} y^{\prime \prime }+3 y^{\prime } t -3 y&=0 \\ \end{align*}

[[_Emden, _Fowler]]

1.595

1300

\begin{align*} t^{2} y^{\prime \prime }+7 y^{\prime } t +10 y&=0 \\ \end{align*}

[[_Emden, _Fowler]]

13.076