2.2.153 Problems 15201 to 15300

Table 2.307: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

15201

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

[[_2nd_order, _missing_x]]

0.301

15202

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

[[_2nd_order, _exact, _linear, _homogeneous]]

0.097

15203

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

[[_2nd_order, _with_linear_symmetries]]

0.122

15204

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

[[_2nd_order, _with_linear_symmetries]]

0.151

15205

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

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

0.094

15206

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

[[_2nd_order, _with_linear_symmetries]]

0.166

15207

\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = 9 \,{\mathrm e}^{2 x} \]

[[_2nd_order, _with_linear_symmetries]]

0.335

15208

\[ {}y^{\prime \prime }-6 y^{\prime }+8 y = {\mathrm e}^{4 x} \]

[[_2nd_order, _with_linear_symmetries]]

0.441

15209

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

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

0.175

15210

\[ {}x^{2} y^{\prime \prime }-20 y = 27 x^{5} \]

[[_2nd_order, _with_linear_symmetries]]

0.177

15211

\[ {}x y^{\prime \prime }+\left (2+2 x \right ) y^{\prime }+2 y = 8 \,{\mathrm e}^{2 x} \]

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

0.215

15212

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

[[_2nd_order, _with_linear_symmetries]]

0.213

15213

\[ {}y^{\prime \prime \prime }-9 y^{\prime \prime }+27 y^{\prime }-27 y = 0 \]

[[_3rd_order, _missing_x]]

0.053

15214

\[ {}y^{\prime \prime \prime }-9 y^{\prime \prime }+27 y^{\prime }-27 y = {\mathrm e}^{3 x} \sin \left (x \right ) \]

[[_3rd_order, _linear, _nonhomogeneous]]

0.132

15215

\[ {}y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+24 y^{\prime \prime }-32 y^{\prime }+16 y = 0 \]

[[_high_order, _missing_x]]

0.061

15216

\[ {}x^{3} y^{\prime \prime \prime }-4 y^{\prime \prime }+10 y^{\prime }-12 y = 0 \]

[[_3rd_order, _with_linear_symmetries]]

0.040

15217

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

[[_2nd_order, _missing_x]]

3.272

15218

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

[[_2nd_order, _missing_x]]

2.247

15219

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

[[_2nd_order, _missing_x]]

1.436

15220

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

[[_2nd_order, _missing_x]]

1.339

15221

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

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

1.770

15222

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

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

1.507

15223

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

[[_Emden, _Fowler]]

1.876

15224

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

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

2.154

15225

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

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

1.869

15226

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

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

0.936

15227

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

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

1.197

15228

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

[[_3rd_order, _missing_x]]

0.068

15229

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

[[_high_order, _missing_x]]

0.077

15230

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

[[_2nd_order, _missing_x]]

2.594

15231

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

[[_2nd_order, _missing_x]]

1.429

15232

\[ {}y^{\prime \prime }-10 y^{\prime }+9 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1.439

15233

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

[[_2nd_order, _missing_x]]

1.169

15234

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

[[_3rd_order, _missing_x]]

0.048

15235

\[ {}y^{\prime \prime \prime \prime }-10 y^{\prime \prime }+9 y = 0 \]

[[_high_order, _missing_x]]

0.059

15236

\[ {}y^{\prime \prime }-7 y^{\prime }+10 y = 0 \]

[[_2nd_order, _missing_x]]

0.884

15237

\[ {}y^{\prime \prime }+2 y^{\prime }-24 y = 0 \]

[[_2nd_order, _missing_x]]

0.944

15238

\[ {}y^{\prime \prime }-25 y = 0 \]

[[_2nd_order, _missing_x]]

2.072

15239

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

[[_2nd_order, _missing_x]]

1.958

15240

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

[[_2nd_order, _missing_x]]

2.215

15241

\[ {}3 y^{\prime \prime }+7 y^{\prime }-6 y = 0 \]

[[_2nd_order, _missing_x]]

0.911

15242

\[ {}y^{\prime \prime }-8 y^{\prime }+15 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1.454

15243

\[ {}y^{\prime \prime }-8 y^{\prime }+15 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1.473

15244

\[ {}y^{\prime \prime }-8 y^{\prime }+15 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1.476

15245

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

[[_2nd_order, _missing_x]]

2.915

15246

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

[[_2nd_order, _missing_x]]

2.300

15247

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

[[_2nd_order, _missing_x]]

2.852

15248

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

[[_2nd_order, _missing_x]]

1.012

15249

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

[[_2nd_order, _missing_x]]

0.967

15250

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

[[_2nd_order, _missing_x]]

0.974

15251

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

[[_2nd_order, _missing_x]]

0.960

15252

\[ {}16 y^{\prime \prime }-24 y^{\prime }+9 y = 0 \]

[[_2nd_order, _missing_x]]

0.986

15253

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

[[_2nd_order, _missing_x]]

0.994

15254

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

[[_2nd_order, _missing_x]]

1.380

15255

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

[[_2nd_order, _missing_x]]

1.313

15256

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

[[_2nd_order, _missing_x]]

1.372

15257

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

[[_2nd_order, _missing_x]]

1.386

15258

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

[[_2nd_order, _missing_x]]

1.388

15259

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

[[_2nd_order, _missing_x]]

1.401

15260

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

[[_2nd_order, _missing_x]]

2.222

15261

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

[[_2nd_order, _missing_x]]

2.666

15262

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

[[_2nd_order, _missing_x]]

2.757

15263

\[ {}y^{\prime \prime }-4 y^{\prime }+29 y = 0 \]

[[_2nd_order, _missing_x]]

2.800

15264

\[ {}9 y^{\prime \prime }+18 y^{\prime }+10 y = 0 \]

[[_2nd_order, _missing_x]]

1.848

15265

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

[[_2nd_order, _missing_x]]

2.291

15266

\[ {}y^{\prime \prime }+16 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

3.151

15267

\[ {}y^{\prime \prime }+16 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2.292

15268

\[ {}y^{\prime \prime }+16 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

3.406

15269

\[ {}y^{\prime \prime }-4 y^{\prime }+13 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

3.460

15270

\[ {}y^{\prime \prime }-4 y^{\prime }+13 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

3.612

15271

\[ {}y^{\prime \prime }-4 y^{\prime }+13 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

3.585

15272

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

[[_2nd_order, _missing_x]]

3.134

15273

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

[[_2nd_order, _missing_x]]

3.040

15274

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

[[_high_order, _missing_x]]

0.053

15275

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

[[_high_order, _missing_x]]

0.054

15276

\[ {}y^{\prime \prime \prime \prime }-34 y^{\prime \prime }+225 y = 0 \]

[[_high_order, _missing_x]]

0.058

15277

\[ {}y^{\prime \prime \prime \prime }-81 y = 0 \]

[[_high_order, _missing_x]]

0.060

15278

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

[[_high_order, _missing_x]]

0.063

15279

\[ {}y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime } = 0 \]

[[_high_order, _missing_x]]

0.076

15280

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

[[_3rd_order, _missing_x]]

0.063

15281

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

[[_3rd_order, _missing_x]]

0.070

15282

\[ {}y^{\prime \prime \prime }-8 y^{\prime \prime }+37 y^{\prime }-50 y = 0 \]

[[_3rd_order, _missing_x]]

0.062

15283

\[ {}y^{\prime \prime \prime }-9 y^{\prime \prime }+31 y^{\prime }-39 y = 0 \]

[[_3rd_order, _missing_x]]

0.063

15284

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

[[_high_order, _missing_x]]

0.066

15285

\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+10 y^{\prime \prime }+18 y^{\prime }+9 y = 0 \]

[[_high_order, _missing_x]]

0.074

15286

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

[[_3rd_order, _missing_x]]

0.069

15287

\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = 0 \]
i.c.

[[_3rd_order, _missing_x]]

0.135

15288

\[ {}y^{\prime \prime \prime \prime }+26 y^{\prime \prime }+25 y = 0 \]
i.c.

[[_high_order, _missing_x]]

0.093

15289

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

[[_high_order, _missing_x]]

0.089

15290

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

[[_3rd_order, _missing_x]]

0.069

15291

\[ {}y^{\prime \prime \prime }+216 y = 0 \]

[[_3rd_order, _missing_x]]

0.062

15292

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

[[_high_order, _missing_x]]

0.061

15293

\[ {}y^{\prime \prime \prime \prime }+13 y^{\prime \prime }+36 y = 0 \]

[[_high_order, _missing_x]]

0.067

15294

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

[[_high_order, _missing_x]]

0.071

15295

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

[[_high_order, _missing_x]]

0.102

15296

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

[[_high_order, _missing_x]]

0.063

15297

\[ {}4 y^{\prime \prime \prime \prime }+15 y^{\prime \prime }-4 y = 0 \]

[[_high_order, _missing_x]]

0.069

15298

\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+16 y^{\prime }-16 y = 0 \]

[[_high_order, _missing_x]]

0.064

15299

\[ {}y^{\left (6\right )}+16 y^{\prime \prime \prime }+64 y = 0 \]

[[_high_order, _missing_x]]

0.087

15300

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = 0 \]

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

1.101