6.145 Problems 14401 to 14500

Table 6.289: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

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

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

14444

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

14445

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

14446

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

14447

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

14448

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

14449

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

14450

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

14451

\[ {} t^{2} x^{\prime \prime }-3 t x^{\prime }+3 x = 4 t^{7} \]

14452

\[ {} x^{\prime \prime }-x = \frac {{\mathrm e}^{t}}{1+{\mathrm e}^{t}} \]

14453

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

14454

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

14455

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

14456

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

14457

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

14458

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

14459

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

14460

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

14461

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

14462

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

14463

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

14464

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

14465

\[ {} x^{\prime }+5 x = \operatorname {Heaviside}\left (t -2\right ) \]

14466

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

14467

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

14468

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

14469

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

14470

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

14471

\[ {} x^{\prime \prime }+\frac {2 x^{\prime }}{5}+2 x = 1-\operatorname {Heaviside}\left (t -5\right ) \]

14472

\[ {} x^{\prime \prime }+9 x = \sin \left (3 t \right ) \]

14473

\[ {} x^{\prime \prime }-2 x = 1 \]

14474

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

14475

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

14476

\[ {} x^{\prime } = x-2 \operatorname {Heaviside}\left (t -1\right ) \]

14477

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

14478

\[ {} x^{\prime \prime }+\pi ^{2} x = \pi ^{2} \operatorname {Heaviside}\left (1-t \right ) \]

14479

\[ {} x^{\prime \prime }-4 x = 1-\operatorname {Heaviside}\left (t -1\right ) \]

14480

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

14481

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

14482

\[ {} x^{\prime \prime }-x = \delta \left (t -5\right ) \]

14483

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

14484

\[ {} x^{\prime \prime }+4 x = \delta \left (t -2\right )-\delta \left (t -5\right ) \]

14485

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

14486

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

14487

\[ {} x^{\prime \prime }+4 x = \frac {\operatorname {Heaviside}\left (t -5\right ) \left (t -5\right )}{5}+\left (2-\frac {t}{5}\right ) \operatorname {Heaviside}\left (t -10\right ) \]

14488

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

14489

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

14490

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

14491

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

14492

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

14493

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

14494

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

14495

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

14496

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

14497

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

14498

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

14499

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

14500

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