6.214 Problems 21301 to 21400

Table 6.427: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

21301

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

21302

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

21303

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

21304

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

21305

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

21306

\[ {} x^{\prime \prime \prime \prime }-8 x^{\prime \prime \prime }+23 x^{\prime \prime }-28 x^{\prime }+12 x = 0 \]

21307

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

21308

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

21309

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

21310

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

21311

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

21312

\[ {} x^{\left (6\right )}-64 x = 0 \]

21313

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

21314

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

21315

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

21316

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

21317

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

21318

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

21319

\[ {} t^{3} x^{\prime \prime \prime }+4 t^{2} x^{\prime \prime }+3 t x^{\prime }+x = 0 \]

21320

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

21321

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

21322

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

21323

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

21324

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

21325

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

21326

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

21327

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

21328

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

21329

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

21330

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

21331

\[ {} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+6 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right )] \]

21332

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

21333

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

21334

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

21335

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

21336

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

21337

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

21338

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

21339

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

21340

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

21341

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

21342

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

21343

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

21344

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

21345

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

21346

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

21347

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

21348

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

21349

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

21350

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

21351

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

21352

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

21353

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

21354

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

21355

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

21356

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

21357

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

21358

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

21359

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

21360

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

21361

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

21362

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

21363

\[ {} [x^{\prime }\left (t \right ) = x \left (t \right )-6 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )-y \left (t \right )] \]

21364

\[ {} L x^{\prime \prime }+g \sin \left (x\right ) = 0 \]

21365

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

21366

\[ {} [x^{\prime }\left (t \right ) = 2 x \left (t \right )-7 x \left (t \right ) y \left (t \right )-a x \left (t \right ), y^{\prime }\left (t \right ) = -y \left (t \right )+4 x \left (t \right ) y \left (t \right )-a y \left (t \right )] \]

21367

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

21368

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

21369

\[ {} [x^{\prime }\left (t \right ) = x \left (t \right ) \left (3-y \left (t \right )\right ), y^{\prime }\left (t \right ) = y \left (t \right ) \left (x \left (t \right )-5\right )] \]

21370

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

21371

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

21372

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

21373

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

21374

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

21375

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

21376

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

21377

\[ {} x^{\prime \prime }+x+8 x^{7} = 0 \]

21378

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

21379

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

21380

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

21381

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

21382

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

21383

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

21384

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

21385

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

21386

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

21387

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

21388

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

21389

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

21390

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

21391

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

21392

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

21393

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

21394

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

21395

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

21396

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

21397

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

21398

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

21399

\[ {} x^{\prime \prime }-4 x^{\prime }+3 x = 1 \]

21400

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