2.2.3 Problems 201 to 300

Table 2.7: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

201

\[ {}{\mathrm e}^{y}+y \cos \left (x \right )+\left (x \,{\mathrm e}^{y}+\sin \left (x \right )\right ) y^{\prime } = 0 \]

[_exact]

38.623

202

\[ {}9 y^{2} x^{2}+x^{{3}/{2}} y^{\prime } = y^{2} \]

[_separable]

2.149

203

\[ {}2 y+\left (x +1\right ) y^{\prime } = 3 x +3 \]

[_linear]

2.075

204

\[ {}9 \sqrt {x}\, y^{{4}/{3}}-12 x^{{1}/{5}} y^{{3}/{2}}+\left (8 x^{{3}/{2}} y^{{1}/{3}}-15 x^{{6}/{5}} \sqrt {y}\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _exact, _rational]

37.398

205

\[ {}3 y+x^{3} y^{4}+3 x y^{\prime } = 0 \]

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

2.949

206

\[ {}x y^{\prime }+y = 2 \,{\mathrm e}^{2 x} \]

[_linear]

1.306

207

\[ {}\left (2 x +1\right ) y^{\prime }+y = \left (2 x +1\right )^{{3}/{2}} \]

[_linear]

4.616

208

\[ {}y^{\prime } = \sqrt {x +y} \]

[[_homogeneous, ‘class C‘], _dAlembert]

2.865

209

\[ {}y^{\prime } = 3 \left (y+7\right ) x^{2} \]

[_separable]

1.672

210

\[ {}y^{\prime } = x y^{3}-x y \]

[_separable]

4.427

211

\[ {}y^{\prime } = -\frac {3 x^{2}+2 y^{2}}{4 x y} \]

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

75.006

212

\[ {}y^{\prime } = \frac {x +3 y}{y-3 x} \]

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

4.620

213

\[ {}y^{\prime } = \frac {2 x y+2 x}{x^{2}+1} \]

[_separable]

1.602

214

\[ {}y^{\prime } = \frac {\sqrt {y}-y}{\tan \left (x \right )} \]

[_separable]

8.595

215

\[ {}y^{\prime \prime }-y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2.214

216

\[ {}y^{\prime \prime }-9 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2.520

217

\[ {}y^{\prime \prime }+4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

3.302

218

\[ {}y^{\prime \prime }+25 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

18.688

219

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1.166

220

\[ {}y^{\prime \prime }+y^{\prime }-6 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1.446

221

\[ {}y^{\prime \prime }+y^{\prime } = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2.574

222

\[ {}y^{\prime \prime }-3 y^{\prime } = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2.541

223

\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1.377

224

\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1.358

225

\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2.161

226

\[ {}y^{\prime \prime }+6 y^{\prime }+13 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2.958

227

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \]
i.c.

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

1.869

228

\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 0 \]
i.c.

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

1.118

229

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+y = 0 \]
i.c.

[[_Emden, _Fowler]]

1.763

230

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+y = 0 \]
i.c.

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

1.510

231

\[ {}y^{\prime }+y^{2} = 0 \]

[_quadrature]

2.038

232

\[ {}y y^{\prime \prime } = 6 x^{4} \]

[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]]

0.118

233

\[ {}y y^{\prime \prime }+{y^{\prime }}^{2} = 0 \]

[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

1.190

234

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 0 \]

[[_2nd_order, _missing_x]]

0.884

235

\[ {}y^{\prime \prime }+2 y^{\prime }-15 y = 0 \]

[[_2nd_order, _missing_x]]

0.917

236

\[ {}y^{\prime \prime }+5 y^{\prime } = 0 \]

[[_2nd_order, _missing_x]]

2.010

237

\[ {}2 y^{\prime \prime }+3 y^{\prime } = 0 \]

[[_2nd_order, _missing_x]]

2.099

238

\[ {}2 y^{\prime \prime }-y^{\prime }-y = 0 \]

[[_2nd_order, _missing_x]]

0.909

239

\[ {}4 y^{\prime \prime }+8 y^{\prime }+3 y = 0 \]

[[_2nd_order, _missing_x]]

0.935

240

\[ {}4 y^{\prime \prime }+4 y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

1.029

241

\[ {}9 y^{\prime \prime }-12 y^{\prime }+4 y = 0 \]

[[_2nd_order, _missing_x]]

1.007

242

\[ {}6 y^{\prime \prime }-7 y^{\prime }-20 y = 0 \]

[[_2nd_order, _missing_x]]

0.916

243

\[ {}35 y^{\prime \prime }-y^{\prime }-12 y = 0 \]

[[_2nd_order, _missing_x]]

0.889

244

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

1.262

245

\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-12 y = 0 \]

[[_Emden, _Fowler]]

0.778

246

\[ {}4 x^{2} y^{\prime \prime }+8 x y^{\prime }-3 y = 0 \]

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

0.803

247

\[ {}x^{2} y^{\prime \prime }+x y^{\prime } = 0 \]

[[_2nd_order, _missing_y]]

0.556

248

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0 \]

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

0.972

249

\[ {}y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y = 0 \]
i.c.

[[_3rd_order, _missing_x]]

0.135

250

\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = 0 \]
i.c.

[[_3rd_order, _missing_x]]

0.139

251

\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = 0 \]
i.c.

[[_3rd_order, _missing_x]]

0.129

252

\[ {}y^{\prime \prime \prime }-5 y^{\prime \prime }+8 y^{\prime }-4 y = 0 \]
i.c.

[[_3rd_order, _missing_x]]

0.132

253

\[ {}y^{\prime \prime \prime }+9 y^{\prime } = 0 \]
i.c.

[[_3rd_order, _missing_x]]

0.075

254

\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y = 0 \]
i.c.

[[_3rd_order, _missing_x]]

0.085

255

\[ {}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = 0 \]
i.c.

[[_3rd_order, _with_linear_symmetries]]

0.177

256

\[ {}x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+4 x y^{\prime }-4 y = 0 \]
i.c.

[[_3rd_order, _with_linear_symmetries]]

0.206

257

\[ {}y^{\prime \prime }+y = 3 x \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

2.259

258

\[ {}y^{\prime \prime }-4 y = 12 \]
i.c.

[[_2nd_order, _missing_x]]

4.151

259

\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 6 \]
i.c.

[[_2nd_order, _missing_x]]

1.584

260

\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = 2 x \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

3.850

261

\[ {}y^{\prime \prime }+2 y = 6 x +4 \]

[[_2nd_order, _with_linear_symmetries]]

3.139

262

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \]

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

1.012

263

\[ {}y^{\prime \prime }-2 y^{\prime }-5 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1.607

264

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 0 \]

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

0.084

265

\[ {}4 y^{\prime \prime }-4 y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

0.257

266

\[ {}x^{2} y^{\prime \prime }-x \left (x +2\right ) y^{\prime }+\left (x +2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.102

267

\[ {}\left (x +1\right ) y^{\prime \prime }-\left (x +2\right ) y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.109

268

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0 \]

[_Gegenbauer]

0.104

269

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \]

[_Gegenbauer]

0.108

270

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.147

271

\[ {}y^{\prime \prime }-4 y = 0 \]

[[_2nd_order, _missing_x]]

2.002

272

\[ {}2 y^{\prime \prime }-3 y^{\prime } = 0 \]

[[_2nd_order, _missing_x]]

1.848

273

\[ {}y^{\prime \prime }+y^{\prime }-10 y = 0 \]

[[_2nd_order, _missing_x]]

1.140

274

\[ {}2 y^{\prime \prime }-7 y^{\prime }+3 y = 0 \]

[[_2nd_order, _missing_x]]

0.876

275

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 0 \]

[[_2nd_order, _missing_x]]

0.982

276

\[ {}y^{\prime \prime }+5 y^{\prime }+5 y = 0 \]

[[_2nd_order, _missing_x]]

1.142

277

\[ {}4 y^{\prime \prime }-12 y^{\prime }+9 y = 0 \]

[[_2nd_order, _missing_x]]

0.980

278

\[ {}y^{\prime \prime }-6 y^{\prime }+13 y = 0 \]

[[_2nd_order, _missing_x]]

2.639

279

\[ {}y^{\prime \prime }+8 y^{\prime }+25 y = 0 \]

[[_2nd_order, _missing_x]]

2.755

280

\[ {}5 y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime } = 0 \]

[[_high_order, _missing_x]]

0.054

281

\[ {}y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+16 y^{\prime \prime } = 0 \]

[[_high_order, _missing_x]]

0.055

282

\[ {}y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime } = 0 \]

[[_high_order, _missing_x]]

0.056

283

\[ {}9 y^{\prime \prime \prime }+12 y^{\prime \prime }+4 y^{\prime } = 0 \]

[[_3rd_order, _missing_x]]

0.052

284

\[ {}y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-4 y = 0 \]

[[_high_order, _missing_x]]

0.067

285

\[ {}y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+16 y = 0 \]

[[_high_order, _missing_x]]

0.060

286

\[ {}y^{\prime \prime \prime \prime }+18 y^{\prime \prime }+81 y = 0 \]

[[_high_order, _missing_x]]

0.076

287

\[ {}6 y^{\prime \prime \prime \prime }+11 y^{\prime \prime }+4 y = 0 \]

[[_high_order, _missing_x]]

0.069

288

\[ {}y^{\prime \prime \prime \prime } = 16 y \]

[[_high_order, _missing_x]]

0.058

289

\[ {}y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y = 0 \]

[[_3rd_order, _missing_x]]

0.053

290

\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }+y = 0 \]

[[_high_order, _missing_x]]

0.083

291

\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1.419

292

\[ {}9 y^{\prime \prime }+6 y^{\prime }+4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2.954

293

\[ {}y^{\prime \prime }-6 y^{\prime }+25 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

3.654

294

\[ {}2 y^{\prime \prime \prime }-3 y^{\prime \prime }-2 y^{\prime } = 0 \]
i.c.

[[_3rd_order, _missing_x]]

0.129

295

\[ {}3 y^{\prime \prime \prime }+2 y^{\prime \prime } = 0 \]
i.c.

[[_3rd_order, _missing_x]]

0.125

296

\[ {}y^{\prime \prime \prime }+10 y^{\prime \prime }+25 y^{\prime } = 0 \]
i.c.

[[_3rd_order, _missing_x]]

0.125

297

\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y = 0 \]

[[_3rd_order, _missing_x]]

0.052

298

\[ {}2 y^{\prime \prime \prime }-y^{\prime \prime }-5 y^{\prime }-2 y = 0 \]

[[_3rd_order, _missing_x]]

0.056

299

\[ {}y^{\prime \prime \prime }+27 y = 0 \]

[[_3rd_order, _missing_x]]

0.063

300

\[ {}y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }+y^{\prime \prime }-3 y^{\prime }-6 y = 0 \]

[[_high_order, _missing_x]]

0.074