2.2.93 Problems 9201 to 9300

Table 2.187: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

9201

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

[[_2nd_order, _with_linear_symmetries]]

0.163

9202

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

[[_2nd_order, _with_linear_symmetries]]

0.395

9203

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

[[_2nd_order, _with_linear_symmetries]]

0.122

9204

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

[[_2nd_order, _with_linear_symmetries]]

0.090

9205

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

[[_2nd_order, _with_linear_symmetries]]

0.312

9206

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

[[_2nd_order, _with_linear_symmetries]]

0.161

9207

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

[[_2nd_order, _with_linear_symmetries]]

0.161

9208

\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.118

9209

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

[[_2nd_order, _with_linear_symmetries]]

0.177

9210

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

[[_2nd_order, _with_linear_symmetries]]

0.098

9211

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

[[_2nd_order, _with_linear_symmetries]]

0.106

9212

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

[[_2nd_order, _with_linear_symmetries]]

0.108

9213

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

[[_2nd_order, _with_linear_symmetries]]

0.167

9214

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

[[_2nd_order, _with_linear_symmetries]]

0.257

9215

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

[[_2nd_order, _with_linear_symmetries]]

0.130

9216

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

[[_2nd_order, _with_linear_symmetries]]

0.329

9217

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

[[_2nd_order, _with_linear_symmetries]]

0.381

9218

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

[[_2nd_order, _with_linear_symmetries]]

0.320

9219

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

[[_2nd_order, _with_linear_symmetries]]

0.323

9220

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

[[_2nd_order, _with_linear_symmetries]]

0.451

9221

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

[[_2nd_order, _with_linear_symmetries]]

0.495

9222

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

[[_2nd_order, _with_linear_symmetries]]

0.358

9223

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

[[_2nd_order, _with_linear_symmetries]]

0.364

9224

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-8 x y^{\prime }+20 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.367

9225

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-8 x y^{\prime }-12 y = 0 \]

[_Gegenbauer]

0.211

9226

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

[[_2nd_order, _with_linear_symmetries]]

0.426

9227

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

[_Gegenbauer]

0.329

9228

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-10 x y^{\prime }+28 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.413

9229

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

[[_2nd_order, _with_linear_symmetries]]

0.257

9230

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

[[_2nd_order, _with_linear_symmetries]]

0.497

9231

\[ {}\left (2 x^{2}-8 x +11\right ) y^{\prime \prime }-16 \left (-2+x \right ) y^{\prime }+36 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.675

9232

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

[[_2nd_order, _with_linear_symmetries]]

0.385

9233

\[ {}\left (x^{2}-8 x +14\right ) y^{\prime \prime }-8 \left (x -4\right ) y^{\prime }+20 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.342

9234

\[ {}\left (2 x^{2}+4 x +5\right ) y^{\prime \prime }-20 \left (x +1\right ) y^{\prime }+60 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.691

9235

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

[[_2nd_order, _with_linear_symmetries]]

0.480

9236

\[ {}\left (2 x^{5}+1\right ) y^{\prime \prime }+14 x^{4} y^{\prime }+10 x^{3} y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

1.252

9237

\[ {}y^{\prime \prime }+x^{6} y^{\prime }+7 x^{5} y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.500

9238

\[ {}\left (x^{8}+1\right ) y^{\prime \prime }-16 x^{7} y^{\prime }+72 x^{6} y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

425.257

9239

\[ {}y^{\prime \prime }+x^{5} y^{\prime }+6 x^{4} y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.440

9240

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

[[_2nd_order, _with_linear_symmetries]]

30.487

9241

\[ {}\left (3 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+15 x \right ) y^{\prime }+12 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.926

9242

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

[[_2nd_order, _with_linear_symmetries]]

0.386

9243

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

[[_2nd_order, _with_linear_symmetries]]

0.379

9244

\[ {}\left (2 x^{2}+3 x \right ) y^{\prime \prime }+10 \left (x +1\right ) y^{\prime }+8 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.383

9245

\[ {}x^{2} y^{\prime \prime }-\left (6-7 x \right ) y^{\prime }+8 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.355

9246

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

[[_2nd_order, _with_linear_symmetries]]

1.200

9247

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

[[_2nd_order, _with_linear_symmetries]]

0.197

9248

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

[[_2nd_order, _with_linear_symmetries]]

0.348

9249

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

[[_2nd_order, _with_linear_symmetries]]

0.322

9250

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

[[_2nd_order, _with_linear_symmetries]]

0.334

9251

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

[[_2nd_order, _with_linear_symmetries]]

0.214

9252

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

[[_2nd_order, _with_linear_symmetries]]

0.092

9253

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

[[_2nd_order, _with_linear_symmetries]]

0.089

9254

\[ {}2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

1.210

9255

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

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

0.447

9256

\[ {}12 x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (3 x^{2}+35 x +11\right ) y^{\prime }-\left (-5 x^{2}-10 x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.441

9257

\[ {}x^{2} \left (10 x^{2}+x +5\right ) y^{\prime \prime }+x \left (48 x^{2}+3 x +4\right ) y^{\prime }+\left (36 x^{2}+x \right ) y = 0 \]

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

1.154

9258

\[ {}18 x^{2} \left (x +1\right ) y^{\prime \prime }+3 x \left (x^{2}+11 x +5\right ) y^{\prime }-\left (-5 x^{2}-2 x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.428

9259

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

[[_2nd_order, _with_linear_symmetries]]

0.334

9260

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

[[_2nd_order, _with_linear_symmetries]]

0.361

9261

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

[[_2nd_order, _with_linear_symmetries]]

0.462

9262

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

[[_2nd_order, _with_linear_symmetries]]

0.185

9263

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

[[_2nd_order, _with_linear_symmetries]]

0.642

9264

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

[[_2nd_order, _with_linear_symmetries]]

0.374

9265

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

[[_2nd_order, _with_linear_symmetries]]

0.696

9266

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

[[_2nd_order, _with_linear_symmetries]]

0.315

9267

\[ {}6 x^{2} y^{\prime \prime }+x \left (10-x \right ) y^{\prime }-\left (x +2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.418

9268

\[ {}x^{2} \left (4 x +3\right ) y^{\prime \prime }+x \left (11+4 x \right ) y^{\prime }-\left (4 x +3\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.404

9269

\[ {}2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+11 x \right ) y^{\prime }-\left (1-x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.203

9270

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

[[_2nd_order, _with_linear_symmetries]]

0.864

9271

\[ {}8 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-13 x^{2}+1\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.434

9272

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

[[_2nd_order, _with_linear_symmetries]]

0.398

9273

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

[[_2nd_order, _exact, _linear, _homogeneous]]

0.367

9274

\[ {}4 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+x \left (-19 x^{2}+7\right ) y^{\prime }-\left (14 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.428

9275

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

[[_2nd_order, _with_linear_symmetries]]

0.466

9276

\[ {}2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }-x \left (-7 x^{2}+12\right ) y^{\prime }+\left (3 x^{2}+7\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.438

9277

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

[[_2nd_order, _with_linear_symmetries]]

0.416

9278

\[ {}2 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+5 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-40 x^{2}+2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.542

9279

\[ {}x \left (x^{2}+1\right ) y^{\prime \prime }+\left (7 x^{2}+4\right ) y^{\prime }+8 x y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

0.370

9280

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

[[_2nd_order, _with_linear_symmetries]]

0.420

9281

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

[[_2nd_order, _with_linear_symmetries]]

0.391

9282

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

[[_2nd_order, _with_linear_symmetries]]

0.444

9283

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

[[_2nd_order, _with_linear_symmetries]]

0.414

9284

\[ {}4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.373

9285

\[ {}8 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+2 x \left (34 x^{2}+5\right ) y^{\prime }-\left (-30 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.513

9286

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

[[_2nd_order, _with_linear_symmetries]]

0.182

9287

\[ {}6 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (50 x^{2}+1\right ) y^{\prime }+\left (30 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.198

9288

\[ {}28 x^{2} \left (1-3 x \right ) y^{\prime \prime }-7 x \left (5+9 x \right ) y^{\prime }+7 \left (2+9 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.196

9289

\[ {}8 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+2 x \left (-21 x^{2}+10\right ) y^{\prime }-\left (35 x^{2}+2\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.197

9290

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

[[_2nd_order, _with_linear_symmetries]]

0.145

9291

\[ {}3 x^{2} \left (x +1\right )^{2} y^{\prime \prime }-x \left (-11 x^{2}-10 x +1\right ) y^{\prime }+\left (5 x^{2}+1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.191

9292

\[ {}4 x^{2} \left (x^{2}+2 x +3\right ) y^{\prime \prime }-x \left (-15 x^{2}-14 x +3\right ) y^{\prime }+\left (7 x^{2}+3\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.210

9293

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

[[_2nd_order, _with_linear_symmetries]]

0.402

9294

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

[[_2nd_order, _with_linear_symmetries]]

0.292

9295

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

[[_2nd_order, _with_linear_symmetries]]

0.438

9296

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

[[_2nd_order, _with_linear_symmetries]]

0.507

9297

\[ {}4 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+12 x^{2} \left (x +1\right ) y^{\prime }+\left (3 x^{2}+3 x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.888

9298

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

[[_2nd_order, _with_linear_symmetries]]

0.970

9299

\[ {}9 x^{2} y^{\prime \prime }+3 x \left (-2 x^{2}+3 x +5\right ) y^{\prime }+\left (-14 x^{2}+12 x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.599

9300

\[ {}x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (3 x^{2}+14 x +5\right ) y^{\prime }+\left (12 x^{2}+18 x +4\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.629