2.2.94 Problems 9301 to 9400

Table 2.189: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

9301

\[ {}16 x^{2} y^{\prime \prime }+4 x \left (2 x^{2}+x +6\right ) y^{\prime }+\left (18 x^{2}+5 x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.548

9302

\[ {}9 x^{2} \left (x +1\right ) y^{\prime \prime }+3 x \left (-x^{2}+11 x +5\right ) y^{\prime }+\left (-7 x^{2}+16 x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.419

9303

\[ {}36 x^{2} \left (1-2 x \right ) y^{\prime \prime }+24 x \left (1-9 x \right ) y^{\prime }+\left (1-70 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.375

9304

\[ {}x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (3-x \right ) y^{\prime }+4 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.289

9305

\[ {}x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5-4 x \right ) y^{\prime }+\left (9-4 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.283

9306

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

[[_2nd_order, _with_linear_symmetries]]

0.267

9307

\[ {}2 x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (6-x \right ) y^{\prime }+\left (8-x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.273

9308

\[ {}x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (5+9 x \right ) y^{\prime }+\left (4+3 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.296

9309

\[ {}x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5+4 x \right ) y^{\prime }+\left (9+4 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.321

9310

\[ {}x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (7+x \right ) y^{\prime }+\left (9-x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.323

9311

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

[[_2nd_order, _with_linear_symmetries]]

0.321

9312

\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-3 x \left (-x^{2}+1\right ) y^{\prime }+4 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.388

9313

\[ {}4 x^{2} y^{\prime \prime }+2 x^{3} y^{\prime }+\left (3 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.300

9314

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

[[_2nd_order, _with_linear_symmetries]]

0.362

9315

\[ {}2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+7 x^{3} y^{\prime }+\left (3 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.369

9316

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

[[_2nd_order, _with_linear_symmetries]]

0.349

9317

\[ {}4 x^{2} \left (x^{2}+4\right ) y^{\prime \prime }+3 x \left (3 x^{2}+8\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.459

9318

\[ {}3 x^{2} \left (x^{2}+3\right ) y^{\prime \prime }+x \left (11 x^{2}+3\right ) y^{\prime }+\left (5 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.392

9319

\[ {}9 x^{2} y^{\prime \prime }-3 x \left (-2 x^{2}+7\right ) y^{\prime }+\left (2 x^{2}+25\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.342

9320

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

[[_2nd_order, _with_linear_symmetries]]

0.306

9321

\[ {}x^{2} \left (1-2 x \right ) y^{\prime \prime }+3 y^{\prime } x +\left (1+4 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.290

9322

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

[[_2nd_order, _with_linear_symmetries]]

0.284

9323

\[ {}x^{2} \left (1-x \right ) y^{\prime \prime }-x \left (3-5 x \right ) y^{\prime }+\left (4-5 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.280

9324

\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (9 x^{2}+1\right ) y^{\prime }+\left (25 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.372

9325

\[ {}9 x^{2} y^{\prime \prime }+3 x \left (-x^{2}+1\right ) y^{\prime }+\left (7 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

1.179

9326

\[ {}x \left (x^{2}+1\right ) y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }-8 x y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

0.421

9327

\[ {}4 x^{2} y^{\prime \prime }+2 x \left (-x^{2}+4\right ) y^{\prime }+\left (7 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.736

9328

\[ {}4 x^{2} \left (x +1\right ) y^{\prime \prime }+8 x^{2} y^{\prime }+\left (x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.223

9329

\[ {}9 x^{2} \left (x +3\right ) y^{\prime \prime }+3 x \left (3+7 x \right ) y^{\prime }+\left (3+4 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.289

9330

\[ {}x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-x \left (3 x^{2}+2\right ) y^{\prime }+\left (-x^{2}+2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.242

9331

\[ {}16 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 x \left (9 x^{2}+1\right ) y^{\prime }+\left (49 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.292

9332

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

[[_2nd_order, _with_linear_symmetries]]

0.224

9333

\[ {}4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }+8 x^{2} \left (2 x +3\right ) y^{\prime }+\left (9 x^{2}+3 x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.230

9334

\[ {}x^{2} \left (1-x \right )^{2} y^{\prime \prime }-x \left (-3 x^{2}+2 x +1\right ) y^{\prime }+\left (x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.227

9335

\[ {}9 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+7 x +1\right ) y^{\prime }+\left (25 x^{2}+4 x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.341

9336

\[ {}2 x^{2} \left (x +2\right ) y^{\prime \prime }-x \left (4-7 x \right ) y^{\prime }-\left (5-3 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.285

9337

\[ {}x^{2} \left (1-2 x \right ) y^{\prime \prime }+x \left (8-9 x \right ) y^{\prime }+\left (6-3 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.273

9338

\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (10 x^{2}+3\right ) y^{\prime }-\left (-14 x^{2}+15\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.397

9339

\[ {}x^{2} \left (-2 x^{2}+1\right ) y^{\prime \prime }+x \left (-13 x^{2}+7\right ) y^{\prime }-14 x^{2} y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.363

9340

\[ {}4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (2 x +1\right ) y^{\prime }-\left (1+3 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.283

9341

\[ {}2 x^{2} \left (2+3 x \right ) y^{\prime \prime }+x \left (4+21 x \right ) y^{\prime }-\left (1-9 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.289

9342

\[ {}x^{2} y^{\prime \prime }+x \left (x +2\right ) y^{\prime }-\left (2-3 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.294

9343

\[ {}4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (3+8 x \right ) y^{\prime }-\left (5-49 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.296

9344

\[ {}x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (3+10 x \right ) y^{\prime }+30 x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.312

9345

\[ {}x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-3 \left (x +3\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.349

9346

\[ {}x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (9+13 x \right ) y^{\prime }+\left (7+5 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.309

9347

\[ {}4 x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (4-x \right ) y^{\prime }-\left (7+5 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.269

9348

\[ {}3 x^{2} \left (x +3\right ) y^{\prime \prime }-x \left (15+x \right ) y^{\prime }-20 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.294

9349

\[ {}x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (1-10 x \right ) y^{\prime }-\left (9-10 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.304

9350

\[ {}x^{2} \left (x +1\right ) y^{\prime \prime }+3 x^{2} y^{\prime }-\left (6-x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.277

9351

\[ {}x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (3+14 x \right ) y^{\prime }+\left (6+100 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.268

9352

\[ {}x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (6+11 x \right ) y^{\prime }+\left (6+32 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.283

9353

\[ {}4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (1+4 x \right ) y^{\prime }-\left (49+27 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.277

9354

\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-2 x^{2}+7\right ) y^{\prime }+12 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.368

9355

\[ {}x^{2} y^{\prime \prime }-x \left (-x^{2}+7\right ) y^{\prime }+12 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.332

9356

\[ {}x^{2} y^{\prime \prime }+x \left (2 x^{2}+1\right ) y^{\prime }-\left (-10 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.392

9357

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

[[_2nd_order, _with_linear_symmetries]]

0.313

9358

\[ {}x^{2} y^{\prime \prime }+x \left (-3 x^{2}+1\right ) y^{\prime }-4 \left (-3 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.645

9359

\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (11 x^{2}+5\right ) y^{\prime }+24 x^{2} y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.458

9360

\[ {}4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 y^{\prime } x -\left (-x^{2}+35\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.400

9361

\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-x^{2}+5\right ) y^{\prime }-\left (25 x^{2}+7\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.426

9362

\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+5\right ) y^{\prime }-21 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.389

9363

\[ {}4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (x^{2}+2\right ) y^{\prime }-\left (x^{2}+15\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.319

9364

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

[[_2nd_order, _with_linear_symmetries]]

0.337

9365

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

[[_2nd_order, _with_linear_symmetries]]

0.118

9366

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

[_Gegenbauer]

0.299

9367

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

[[_2nd_order, _with_linear_symmetries]]

0.319

9368

\[ {}\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+6 y = 0 \]

[_Gegenbauer]

0.334

9369

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

[[_2nd_order, _with_linear_symmetries]]

0.296

9370

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

[[_2nd_order, _with_linear_symmetries]]

0.198

9371

\[ {}y^{\prime \prime }-\frac {2 t y^{\prime }}{t^{2}+1}+\frac {2 y}{t^{2}+1} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.338

9372

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

[[_2nd_order, _with_linear_symmetries]]

0.330

9373

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

[_Laguerre]

0.286

9374

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

[[_2nd_order, _with_linear_symmetries]]

0.519

9375

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

[[_2nd_order, _with_linear_symmetries]]

0.273

9376

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

[[_2nd_order, _with_linear_symmetries]]

0.290

9377

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

[[_2nd_order, _with_linear_symmetries]]

0.267

9378

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

[_Lienard]

0.328

9379

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

[[_2nd_order, _with_linear_symmetries]]

0.266

9380

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

[_Laguerre]

0.315

9381

\[ {}t^{2} y^{\prime \prime }+\left (t^{2}-3 t \right ) y^{\prime }+3 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.308

9382

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

[[_2nd_order, _with_linear_symmetries]]

0.301

9383

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

[[_2nd_order, _with_linear_symmetries]]

0.723

9384

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

[[_2nd_order, _with_linear_symmetries]]

0.299

9385

\[ {}y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+6\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.224

9386

\[ {}\left (-z^{2}+1\right ) y^{\prime \prime }-3 z y^{\prime }+\lambda y = 0 \]

[_Gegenbauer]

0.541

9387

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

[[_2nd_order, _with_linear_symmetries]]

0.306

9388

\[ {}f^{\prime \prime }+2 \left (z -1\right ) f^{\prime }+4 f = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.291

9389

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

[_Lienard]

0.327

9390

\[ {}z y^{\prime \prime }+\left (2 z -3\right ) y^{\prime }+\frac {4 y}{z} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.337

9391

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

[_erf]

0.249

9392

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

[[_2nd_order, _with_linear_symmetries]]

0.305

9393

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

[[_2nd_order, _with_linear_symmetries]]

0.309

9394

\[ {}\left (-4 x^{2}+1\right ) y^{\prime \prime }-20 y^{\prime } x -16 y = 0 \]

[_Gegenbauer]

0.306

9395

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-6 y^{\prime } x +12 y = 0 \]

[_Gegenbauer]

0.258

9396

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

[[_2nd_order, _with_linear_symmetries]]

0.335

9397

\[ {}\left (2 x^{2}+1\right ) y^{\prime \prime }+7 y^{\prime } x +2 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.405

9398

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

[_Lienard]

0.309

9399

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

[[_2nd_order, _with_linear_symmetries]]

0.283

9400

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

[[_2nd_order, _with_linear_symmetries]]

0.289