4.3.50 Problems 4901 to 5000

Table 4.463: Second order ode

#

ODE

Mathematica

Maple

Sympy

14254

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

14255

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

14256

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

14257

\[ {} y+3 x^{5} y^{\prime }+x^{6} y^{\prime \prime } = \frac {1}{x^{2}} \]

14258

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

14259

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

14260

\[ {} \left (x -3\right ) y^{\prime \prime }-\left (4 x -9\right ) y^{\prime }+\left (3 x -6\right ) y = 0 \]

14261

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

14262

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

14263

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

14264

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

14265

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

14266

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

14267

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

14268

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

14269

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

14271

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

14272

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

14273

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

14274

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

14275

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

14276

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

14277

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

14281

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

14282

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

14285

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

14286

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

14288

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

14289

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

14290

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

14291

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

14292

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

14293

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

14294

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

14295

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

14297

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

14298

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

14299

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

14300

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

14301

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

14302

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

14304

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

14309

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

14313

\[ {} t^{2} x^{\prime \prime }-6 x = 0 \]

14314

\[ {} 2 x^{\prime \prime }-5 x^{\prime }-3 x = 0 \]

14319

\[ {} x^{\prime \prime } = -3 \sqrt {t} \]

14324

\[ {} x^{\prime }+t x^{\prime \prime } = 1 \]

14353

\[ {} \frac {x^{\prime }+t x^{\prime \prime }}{t} = -2 \]

14377

\[ {} x^{\prime \prime }+x^{\prime } = 3 t \]

14393

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

14394

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

14395

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

14396

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

14397

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

14398

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

14399

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

14400

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

14401

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

14402

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

14403

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

14404

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

14405

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

14406

\[ {} \frac {x^{\prime \prime }}{2}+\frac {5 x^{\prime }}{6}+\frac {2 x}{9} = 0 \]

14407

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

14408

\[ {} x^{\prime \prime }+\frac {x^{\prime }}{8}+x = 0 \]

14409

\[ {} x^{\prime \prime }+x^{\prime }+x = 3 t^{3}-1 \]

14410

\[ {} x^{\prime \prime }+x^{\prime }+x = 3 \cos \left (t \right )-2 \sin \left (t \right ) \]

14411

\[ {} x^{\prime \prime }+x^{\prime }+x = 12 \]

14412

\[ {} x^{\prime \prime }+x^{\prime }+x = t^{2} {\mathrm e}^{3 t} \]

14413

\[ {} x^{\prime \prime }+x^{\prime }+x = 5 \sin \left (7 t \right ) \]

14414

\[ {} x^{\prime \prime }+x^{\prime }+x = {\mathrm e}^{2 t} \cos \left (t \right )+t^{2} \]

14415

\[ {} x^{\prime \prime }+x^{\prime }+x = t \,{\mathrm e}^{-t} \sin \left (\pi t \right ) \]

14416

\[ {} x^{\prime \prime }+x^{\prime }+x = \left (t +2\right ) \sin \left (\pi t \right ) \]

14417

\[ {} x^{\prime \prime }+x^{\prime }+x = 4 t +5 \,{\mathrm e}^{-t} \]

14418

\[ {} x^{\prime \prime }+x^{\prime }+x = 5 \sin \left (2 t \right )+t \,{\mathrm e}^{t} \]

14419

\[ {} x^{\prime \prime }+x^{\prime }+x = t^{3}+1-4 \cos \left (t \right ) t \]

14420

\[ {} x^{\prime \prime }+x^{\prime }+x = -6+2 \,{\mathrm e}^{2 t} \sin \left (t \right ) \]

14421

\[ {} x^{\prime \prime }+7 x = t \,{\mathrm e}^{3 t} \]

14422

\[ {} x^{\prime \prime }-x^{\prime } = 6+{\mathrm e}^{2 t} \]

14423

\[ {} x^{\prime \prime }+x = t^{2} \]

14424

\[ {} x^{\prime \prime }-3 x^{\prime }-4 x = 2 t^{2} \]

14425

\[ {} x^{\prime \prime }+x = 9 \,{\mathrm e}^{-t} \]

14426

\[ {} x^{\prime \prime }-4 x = \cos \left (2 t \right ) \]

14427

\[ {} x^{\prime \prime }+x^{\prime }+2 x = t \sin \left (2 t \right ) \]

14428

\[ {} x^{\prime \prime }-b x^{\prime }+x = \sin \left (2 t \right ) \]

14429

\[ {} x^{\prime \prime }-3 x^{\prime }-40 x = 2 \,{\mathrm e}^{-t} \]

14430

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

14431

\[ {} x^{\prime \prime }+2 x = \cos \left (\sqrt {2}\, t \right ) \]

14432

\[ {} x^{\prime \prime }+\frac {x^{\prime }}{100}+4 x = \cos \left (2 t \right ) \]

14433

\[ {} x^{\prime \prime }+w^{2} x = \cos \left (\beta t \right ) \]

14434

\[ {} x^{\prime \prime }+3025 x = \cos \left (45 t \right ) \]

14435

\[ {} x^{\prime \prime } = -\frac {x}{t^{2}} \]

14436

\[ {} x^{\prime \prime } = \frac {4 x}{t^{2}} \]

14437

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

14438

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

14439

\[ {} t^{2} x^{\prime \prime }-7 t x^{\prime }+16 x = 0 \]

14440

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

14441

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

14442

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

14443

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