4.20.21 Problems 2001 to 2100

Table 4.943: Second or higher order ODE with constant coefficients

#

ODE

Mathematica

Maple

Sympy

13314

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

13317

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

13318

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+5 y^{\prime }+12 y = 0 \]

13326

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

13327

\[ {} y^{\prime \prime }-5 y^{\prime }+6 y = 2-12 x +6 \,{\mathrm e}^{x} \]

13328

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

13329

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

13330

\[ {} 4 y^{\prime \prime }-12 y^{\prime }+5 y = 0 \]

13331

\[ {} 3 y^{\prime \prime }-14 y^{\prime }-5 y = 0 \]

13332

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

13333

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+5 y^{\prime }+12 y = 0 \]

13334

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

13335

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

13336

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

13337

\[ {} y^{\prime \prime }+6 y^{\prime }+25 y = 0 \]

13338

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

13339

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

13340

\[ {} y^{\prime \prime \prime }-5 y^{\prime \prime }+7 y^{\prime }-3 y = 0 \]

13341

\[ {} 4 y^{\prime \prime \prime }+4 y^{\prime \prime }-7 y^{\prime }+2 y = 0 \]

13342

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

13343

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

13344

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

13345

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

13346

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

13347

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

13348

\[ {} y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }-2 y^{\prime \prime }+2 y^{\prime }+12 y = 0 \]

13349

\[ {} y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+15 y^{\prime \prime }+20 y^{\prime }+12 y = 0 \]

13350

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

13351

\[ {} y^{\left (5\right )} = 0 \]

13352

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

13353

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

13354

\[ {} y^{\prime \prime }-6 y^{\prime }+8 y = 0 \]

13355

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

13356

\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = 0 \]

13357

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

13358

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

13359

\[ {} 9 y^{\prime \prime }-6 y^{\prime }+y = 0 \]

13360

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

13361

\[ {} y^{\prime \prime }+6 y^{\prime }+58 y = 0 \]

13362

\[ {} y^{\prime \prime }+6 y^{\prime }+13 y = 0 \]

13363

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

13364

\[ {} 9 y^{\prime \prime }+6 y^{\prime }+5 y = 0 \]

13365

\[ {} 4 y^{\prime \prime }+4 y^{\prime }+37 y = 0 \]

13366

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

13367

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

13368

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

13369

\[ {} y^{\prime \prime \prime }-5 y^{\prime \prime }+9 y^{\prime }-5 y = 0 \]

13370

\[ {} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+6 y^{\prime \prime }+2 y^{\prime }+5 y = 0 \]

13371

\[ {} y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+y^{\prime \prime }+13 y^{\prime }+30 y = 0 \]

13372

\[ {} y^{\prime \prime }-3 y^{\prime }+8 y = 4 x^{2} \]

13373

\[ {} y^{\prime \prime }-2 y^{\prime }-8 y = 4 \,{\mathrm e}^{2 x}-21 \,{\mathrm e}^{-3 x} \]

13374

\[ {} y^{\prime \prime }+2 y^{\prime }+5 y = 6 \sin \left (2 x \right )+7 \cos \left (2 x \right ) \]

13375

\[ {} y^{\prime \prime }+2 y^{\prime }+2 y = 10 \sin \left (4 x \right ) \]

13376

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

13377

\[ {} y^{\prime \prime }-3 y^{\prime }-4 y = 16 x -12 \,{\mathrm e}^{2 x} \]

13378

\[ {} y^{\prime \prime }+6 y^{\prime }+5 y = 2 \,{\mathrm e}^{x}+10 \,{\mathrm e}^{5 x} \]

13379

\[ {} y^{\prime \prime }+2 y^{\prime }+10 y = 5 x \,{\mathrm e}^{-2 x} \]

13380

\[ {} y^{\prime \prime \prime }+4 y^{\prime \prime }+y^{\prime }-6 y = -18 x^{2}+1 \]

13381

\[ {} y^{\prime \prime \prime }+2 y^{\prime \prime }-3 y^{\prime }-10 y = 8 x \,{\mathrm e}^{-2 x} \]

13382

\[ {} y^{\prime \prime \prime }+y^{\prime \prime }+3 y^{\prime }-5 y = 5 \sin \left (2 x \right )+10 x^{2}+3 x +7 \]

13383

\[ {} 4 y^{\prime \prime \prime }-4 y^{\prime \prime }-5 y^{\prime }+3 y = 3 x^{3}-8 x \]

13384

\[ {} y^{\prime \prime }+y^{\prime }-6 y = 10 \,{\mathrm e}^{2 x}-18 \,{\mathrm e}^{3 x}-6 x -11 \]

13385

\[ {} y^{\prime \prime }+y^{\prime }-2 y = 6 \,{\mathrm e}^{-2 x}+3 \,{\mathrm e}^{x}-4 x^{2} \]

13386

\[ {} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y = 4 \,{\mathrm e}^{x}-18 \,{\mathrm e}^{-x} \]

13387

\[ {} y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y = 9 \,{\mathrm e}^{2 x}-8 \,{\mathrm e}^{3 x} \]

13388

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

13389

\[ {} y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+2 y^{\prime \prime } = 3 \,{\mathrm e}^{-x}+6 \,{\mathrm e}^{2 x}-6 x \]

13390

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = x \,{\mathrm e}^{x}-4 \,{\mathrm e}^{2 x}+6 \,{\mathrm e}^{4 x} \]

13391

\[ {} y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y = 3 x^{2} {\mathrm e}^{x}-7 \,{\mathrm e}^{x} \]

13392

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

13393

\[ {} y^{\prime \prime }+4 y = 12 x^{2}-16 x \cos \left (2 x \right ) \]

13394

\[ {} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-3 y^{\prime \prime } = 18 x^{2}+16 x \,{\mathrm e}^{x}+4 \,{\mathrm e}^{3 x}-9 \]

13395

\[ {} y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+7 y^{\prime \prime }-5 y^{\prime }+6 y = 5 \sin \left (x \right )-12 \sin \left (2 x \right ) \]

13396

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

13397

\[ {} y^{\prime \prime }+5 y^{\prime }+4 y = 16 x +20 \,{\mathrm e}^{x} \]

13398

\[ {} y^{\prime \prime }-8 y^{\prime }+15 y = 9 x \,{\mathrm e}^{2 x} \]

13399

\[ {} y^{\prime \prime }+7 y^{\prime }+10 y = 4 x \,{\mathrm e}^{-3 x} \]

13400

\[ {} y^{\prime \prime }+8 y^{\prime }+16 y = 8 \,{\mathrm e}^{-2 x} \]

13401

\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = 27 \,{\mathrm e}^{-6 x} \]

13402

\[ {} y^{\prime \prime }+4 y^{\prime }+13 y = 18 \,{\mathrm e}^{-2 x} \]

13403

\[ {} y^{\prime \prime }-10 y^{\prime }+29 y = 8 \,{\mathrm e}^{5 x} \]

13404

\[ {} y^{\prime \prime }-4 y^{\prime }+13 y = 8 \sin \left (3 x \right ) \]

13405

\[ {} y^{\prime \prime }-y^{\prime }-6 y = 8 \,{\mathrm e}^{2 x}-5 \,{\mathrm e}^{3 x} \]

13406

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

13407

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

13408

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

13409

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

13410

\[ {} y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }+6 y = 3 x \,{\mathrm e}^{x}+2 \,{\mathrm e}^{x}-\sin \left (x \right ) \]

13411

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+9 y^{\prime }-4 y = 8 x^{2}+3-6 \,{\mathrm e}^{2 x} \]

13412

\[ {} y^{\prime \prime }-6 y^{\prime }+8 y = x^{3}+x +{\mathrm e}^{-2 x} \]

13413

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

13414

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

13415

\[ {} y^{\prime \prime }-6 y^{\prime }+9 y = x^{4} {\mathrm e}^{x}+x^{3} {\mathrm e}^{2 x}+x^{2} {\mathrm e}^{3 x} \]

13416

\[ {} y^{\prime \prime }+6 y^{\prime }+13 y = x \,{\mathrm e}^{-3 x} \sin \left (2 x \right )+x^{2} {\mathrm e}^{-2 x} \sin \left (3 x \right ) \]

13417

\[ {} y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = x^{2} {\mathrm e}^{x}+3 x \,{\mathrm e}^{2 x}+5 x^{2} \]

13418

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = x \,{\mathrm e}^{2 x}+x^{2} {\mathrm e}^{3 x} \]

13419

\[ {} y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+4 y^{\prime \prime }+3 y^{\prime }+y = x^{2} {\mathrm e}^{-x}+3 \,{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right ) \]

13420

\[ {} y^{\prime \prime \prime \prime }-16 y = x^{2} \sin \left (2 x \right )+x^{4} {\mathrm e}^{2 x} \]

13421

\[ {} y^{\left (6\right )}+2 y^{\left (5\right )}+5 y^{\prime \prime \prime \prime } = x^{3}+x^{2} {\mathrm e}^{-x}+{\mathrm e}^{-x} \sin \left (2 x \right ) \]

13422

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