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]

4.510

1202

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

[_linear]

2.004

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‘]]

7.579

1204

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

[_separable]

3.998

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‘]]

4.322

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‘]]

1.816

1207

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

[_separable]

1.812

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]‘]]

1.602

1209

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

[_separable]

2.371

1210

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

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

2.355

1211

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

[[_linear, ‘class A‘]]

1.780

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]‘]]

1.779

1213

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

[[_1st_order, _with_exponential_symmetries]]

2.379

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]‘]]

3.815

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]

1.767

1216

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

[_rational]

1.818

1217

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

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

4.971

1218

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

[_linear]

2.092

1219

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

[_separable]

3.103

1220

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

[_rational]

3.059

1221

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

[_separable]

1.744

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‘]]

1.990

1223

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

[_linear]

0.897

1224

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

[_separable]

1.562

1225

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

[_linear]

1.704

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‘]]

1.381

1227

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

[_separable]

2.451

1228

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

[_exact]

1.658

1229

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

[_linear]

1.606

1230

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

[_separable]

2.346

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‘]]

5.979

1232

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

[_separable]

2.868

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]

32.668

1234

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

[[_linear, ‘class A‘]]

1.065

1235

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

[[_linear, ‘class A‘]]

1.530

1236

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

[_rational]

1.885

1237

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

[_separable]

1.374

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]

1.938

1239

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

[_separable]

0.893

1240

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

[_linear]

1.702

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]

2.643

1242

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

[_exact, _rational]

2.289

1243

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

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

3.560

1244

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

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

1.635

1245

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

[_linear]

2.783

1246

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

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

3.743

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‘]]

5.053

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‘]]

4.156

1249

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

[[_2nd_order, _missing_x]]

0.195

1250

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

[[_2nd_order, _missing_x]]

0.194

1251

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

[[_2nd_order, _missing_x]]

0.202

1252

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

[[_2nd_order, _missing_x]]

0.194

1253

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

[[_2nd_order, _missing_x]]

0.819

1254

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

[[_2nd_order, _missing_x]]

0.988

1255

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

[[_2nd_order, _missing_x]]

0.237

1256

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

[[_2nd_order, _missing_x]]

0.228

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]]

0.309

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]]

0.343

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]]

0.322

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]]

1.996

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]]

0.402

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]]

0.373

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]]

0.332

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]]

1.177

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]]

1.099

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]]

0.309

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]]

0.290

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]]

0.750

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]]

0.233

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]]

0.292

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]]

0.277

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]]

0.286

1273

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

[[_2nd_order, _missing_x]]

0.292

1274

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

[[_2nd_order, _missing_x]]

0.298

1275

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

[[_2nd_order, _missing_x]]

0.224

1276

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

[[_2nd_order, _missing_x]]

0.301

1277

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

[[_2nd_order, _missing_x]]

0.241

1278

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

[[_2nd_order, _missing_x]]

1.036

1279

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

[[_2nd_order, _missing_x]]

0.246

1280

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

[[_2nd_order, _missing_x]]

0.207

1281

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

[[_2nd_order, _missing_x]]

0.239

1282

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

[[_2nd_order, _missing_x]]

0.259

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]]

0.690

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]]

0.475

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]]

0.372

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]]

1.309

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]]

0.354

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]]

0.379

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]]

0.461

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]]

0.458

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]]

0.384

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]]

0.509

1293

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

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

0.869

1294

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

[[_2nd_order, _exact, _linear, _homogeneous]]

1.262

1295

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

[[_Emden, _Fowler]]

1.029

1296

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

[[_2nd_order, _exact, _linear, _homogeneous]]

0.865

1297

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

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

0.999

1298

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

[[_Emden, _Fowler]]

0.997

1299

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

[[_Emden, _Fowler]]

0.721

1300

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

[[_Emden, _Fowler]]

0.940