2.2.3 Problems 201 to 300

Table 2.23: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

201

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

[_exact]

6.032

202

\begin{align*} 9 x^{2} y^{2}+x^{{3}/{2}} y^{\prime }&=y^{2} \\ \end{align*}

[_separable]

3.352

203

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

[_linear]

3.023

204

\begin{align*} 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 \\ \end{align*}

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

72.585

205

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

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

3.293

206

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

[_linear]

1.967

207

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

[_linear]

4.539

208

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

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

3.250

209

\begin{align*} y^{\prime }&=3 \left (y+7\right ) x^{2} \\ \end{align*}

[_separable]

2.554

210

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

[_separable]

5.265

211

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

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

9.550

212

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

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

13.902

213

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

[_separable]

2.600

214

\begin{align*} y^{\prime }&=\frac {\sqrt {y}-y}{\tan \left (x \right )} \\ \end{align*}

[_separable]

5.911

215

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

[[_2nd_order, _missing_x]]

1.707

216

\begin{align*} y^{\prime \prime }-9 y&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 15 \\ \end{align*}

[[_2nd_order, _missing_x]]

1.798

217

\begin{align*} 4 y+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 8 \\ \end{align*}

[[_2nd_order, _missing_x]]

1.468

218

\begin{align*} y^{\prime \prime }+25 y&=0 \\ y \left (0\right ) &= 10 \\ y^{\prime }\left (0\right ) &= -10 \\ \end{align*}

[[_2nd_order, _missing_x]]

1.674

219

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

[[_2nd_order, _missing_x]]

0.410

220

\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=0 \\ y \left (0\right ) &= 7 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.417

221

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

[[_2nd_order, _missing_x]]

1.154

222

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

[[_2nd_order, _missing_x]]

1.175

223

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

[[_2nd_order, _missing_x]]

0.514

224

\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 13 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.536

225

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

[[_2nd_order, _missing_x]]

0.516

226

\begin{align*} y^{\prime \prime }+6 y^{\prime }+13 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.506

227

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

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

1.791

228

\begin{align*} x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y&=0 \\ y \left (2\right ) &= 10 \\ y^{\prime }\left (2\right ) &= 15 \\ \end{align*}

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

1.057

229

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

[[_Emden, _Fowler]]

1.525

230

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

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

1.468

231

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

[_quadrature]

2.010

232

\begin{align*} y y^{\prime \prime }&=6 x^{4} \\ \end{align*}

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

0.516

233

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

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

0.747

234

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

[[_2nd_order, _missing_x]]

0.283

235

\begin{align*} y^{\prime \prime }+2 y^{\prime }-15 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.297

236

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

[[_2nd_order, _missing_x]]

1.003

237

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

[[_2nd_order, _missing_x]]

1.030

238

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

[[_2nd_order, _missing_x]]

0.293

239

\begin{align*} 4 y^{\prime \prime }+8 y^{\prime }+3 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.295

240

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

[[_2nd_order, _missing_x]]

0.349

241

\begin{align*} 9 y^{\prime \prime }-12 y^{\prime }+4 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.365

242

\begin{align*} 6 y^{\prime \prime }-7 y^{\prime }-20 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.297

243

\begin{align*} 35 y^{\prime \prime }-y^{\prime }-12 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.297

244

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

[[_2nd_order, _exact, _linear, _homogeneous]]

1.528

245

\begin{align*} x^{2} y^{\prime \prime }+2 x y^{\prime }-12 y&=0 \\ \end{align*}

[[_Emden, _Fowler]]

0.816

246

\begin{align*} 4 x^{2} y^{\prime \prime }+8 x y^{\prime }-3 y&=0 \\ \end{align*}

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

0.112

247

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

[[_2nd_order, _missing_y]]

0.520

248

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

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

1.118

249

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

[[_3rd_order, _missing_x]]

0.109

250

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 3 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.097

251

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

[[_3rd_order, _missing_x]]

0.095

252

\begin{align*} y^{\prime \prime \prime }-5 y^{\prime \prime }+8 y^{\prime }-4 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 4 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.099

253

\begin{align*} y^{\prime \prime \prime }+9 y^{\prime }&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -1 \\ y^{\prime \prime }\left (0\right ) &= 2 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.116

254

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

[[_3rd_order, _missing_x]]

0.088

255

\begin{align*} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y&=0 \\ y \left (1\right ) &= 6 \\ y^{\prime }\left (1\right ) &= 14 \\ y^{\prime \prime }\left (1\right ) &= 22 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.189

256

\begin{align*} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+4 x y^{\prime }-4 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 5 \\ y^{\prime \prime }\left (1\right ) &= -11 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.191

257

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

[[_2nd_order, _with_linear_symmetries]]

0.642

258

\begin{align*} y^{\prime \prime }-4 y&=12 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 10 \\ \end{align*}

[[_2nd_order, _missing_x]]

1.985

259

\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=6 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 11 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.549

260

\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=2 x \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 8 \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.319

261

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

[[_2nd_order, _with_linear_symmetries]]

0.211

262

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

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

1.602

263

\begin{align*} y^{\prime \prime }-2 y^{\prime }-5 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.470

264

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-9 y&=0 \\ \end{align*}

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

0.112

265

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

[[_2nd_order, _missing_x]]

0.122

266

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

[[_2nd_order, _with_linear_symmetries]]

0.112

267

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

[[_2nd_order, _with_linear_symmetries]]

0.113

268

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

[_Gegenbauer]

0.119

269

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

[_Gegenbauer]

0.129

270

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

[[_2nd_order, _with_linear_symmetries]]

0.190

271

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

[[_2nd_order, _missing_x]]

1.705

272

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

[[_2nd_order, _missing_x]]

1.033

273

\begin{align*} y^{\prime \prime }+y^{\prime }-10 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.325

274

\begin{align*} 2 y^{\prime \prime }-7 y^{\prime }+3 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.305

275

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.351

276

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

[[_2nd_order, _missing_x]]

0.335

277

\begin{align*} 4 y^{\prime \prime }-12 y^{\prime }+9 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.361

278

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

[[_2nd_order, _missing_x]]

0.346

279

\begin{align*} y^{\prime \prime }+8 y^{\prime }+25 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.349

280

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

[[_high_order, _missing_x]]

0.051

281

\begin{align*} y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+16 y^{\prime \prime }&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.053

282

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

[[_high_order, _missing_x]]

0.067

283

\begin{align*} 9 y^{\prime \prime \prime }+12 y^{\prime \prime }+4 y^{\prime }&=0 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.055

284

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

[[_high_order, _missing_x]]

0.062

285

\begin{align*} y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+16 y&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.062

286

\begin{align*} y^{\prime \prime \prime \prime }+18 y^{\prime \prime }+81 y&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.064

287

\begin{align*} 6 y^{\prime \prime \prime \prime }+11 y^{\prime \prime }+4 y&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.072

288

\begin{align*} y^{\prime \prime \prime \prime }&=16 y \\ \end{align*}

[[_high_order, _missing_x]]

0.060

289

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

[[_3rd_order, _missing_x]]

0.052

290

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

[[_high_order, _missing_x]]

0.082

291

\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=0 \\ y \left (0\right ) &= 7 \\ y^{\prime }\left (0\right ) &= 11 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.424

292

\begin{align*} 9 y^{\prime \prime }+6 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.533

293

\begin{align*} y^{\prime \prime }-6 y^{\prime }+25 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.506

294

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

[[_3rd_order, _missing_x]]

0.095

295

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

[[_3rd_order, _missing_x]]

0.096

296

\begin{align*} y^{\prime \prime \prime }+10 y^{\prime \prime }+25 y^{\prime }&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 4 \\ y^{\prime \prime }\left (0\right ) &= 5 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.097

297

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

[[_3rd_order, _missing_x]]

0.049

298

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

[[_3rd_order, _missing_x]]

0.053

299

\begin{align*} y^{\prime \prime \prime }+27 y&=0 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.053

300

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

[[_high_order, _missing_x]]

0.079