2.4 Problems 301 to 400

Table 2.4: Main lookup table

#

ODE

Mathematica result

Maple result

301

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

302

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

303

\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }+4 y^{\prime }-8 y = 0 \]

304

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

305

\[ {}y^{\prime \prime \prime }-5 y^{\prime \prime }+100 y^{\prime }-500 y = 0 \]

306

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

307

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

308

\[ {}x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+4 x y^{\prime } = 0 \]

309

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

310

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

311

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

312

\[ {}x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+7 x y^{\prime }+y = 0 \]

313

\[ {}[x_{1}^{\prime }\relax (t ) = 6 x_{1}\relax (t ), x_{2}^{\prime }\relax (t ) = -3 x_{1}\relax (t )-x_{2}\relax (t )] \]

314

\[ {}[x_{1}^{\prime }\relax (t ) = -3 x_{1}\relax (t )+2 x_{2}\relax (t ), x_{2}^{\prime }\relax (t ) = -3 x_{1}\relax (t )+4 x_{2}\relax (t )] \]

315

\[ {}[x_{1}^{\prime }\relax (t ) = x_{1}\relax (t )+2 x_{2}\relax (t ), x_{2}^{\prime }\relax (t ) = 2 x_{1}\relax (t )+x_{2}\relax (t )] \]

316

\[ {}[x_{1}^{\prime }\relax (t ) = 2 x_{1}\relax (t )+3 x_{2}\relax (t ), x_{2}^{\prime }\relax (t ) = 2 x_{1}\relax (t )+x_{2}\relax (t )] \]

317

\[ {}[x_{1}^{\prime }\relax (t ) = 3 x_{1}\relax (t )+4 x_{2}\relax (t ), x_{2}^{\prime }\relax (t ) = 3 x_{1}\relax (t )+2 x_{2}\relax (t )] \]

318

\[ {}[x_{1}^{\prime }\relax (t ) = 4 x_{1}\relax (t )+x_{2}\relax (t ), x_{2}^{\prime }\relax (t ) = 6 x_{1}\relax (t )-x_{2}\relax (t )] \]

319

\[ {}[x_{1}^{\prime }\relax (t ) = 6 x_{1}\relax (t )-7 x_{2}\relax (t ), x_{2}^{\prime }\relax (t ) = x_{1}\relax (t )-2 x_{2}\relax (t )] \]

320

\[ {}[x_{1}^{\prime }\relax (t ) = 9 x_{1}\relax (t )+5 x_{2}\relax (t ), x_{2}^{\prime }\relax (t ) = -6 x_{1}\relax (t )-2 x_{2}\relax (t )] \]

321

\[ {}[x_{1}^{\prime }\relax (t ) = -3 x_{1}\relax (t )+4 x_{2}\relax (t ), x_{2}^{\prime }\relax (t ) = 6 x_{1}\relax (t )-5 x_{2}\relax (t )] \]

322

\[ {}[x_{1}^{\prime }\relax (t ) = x_{1}\relax (t )-5 x_{2}\relax (t ), x_{2}^{\prime }\relax (t ) = x_{1}\relax (t )-x_{2}\relax (t )] \]

323

\[ {}[x_{1}^{\prime }\relax (t ) = 2 x_{1}\relax (t )-5 x_{2}\relax (t ), x_{2}^{\prime }\relax (t ) = 4 x_{1}\relax (t )-2 x_{2}\relax (t )] \]

324

\[ {}[x_{1}^{\prime }\relax (t ) = -3 x_{1}\relax (t )-2 x_{2}\relax (t ), x_{2}^{\prime }\relax (t ) = 9 x_{1}\relax (t )+3 x_{2}\relax (t )] \]

325

\[ {}[x_{1}^{\prime }\relax (t ) = x_{1}\relax (t )-2 x_{2}\relax (t ), x_{2}^{\prime }\relax (t ) = 2 x_{1}\relax (t )+x_{2}\relax (t )] \]

326

\[ {}[x_{1}^{\prime }\relax (t ) = x_{1}\relax (t )-5 x_{2}\relax (t ), x_{2}^{\prime }\relax (t ) = x_{1}\relax (t )+3 x_{2}\relax (t )] \]

327

\[ {}[x_{1}^{\prime }\relax (t ) = 5 x_{1}\relax (t )-9 x_{2}\relax (t ), x_{2}^{\prime }\relax (t ) = 2 x_{1}\relax (t )-x_{2}\relax (t )] \]

328

\[ {}[x_{1}^{\prime }\relax (t ) = 3 x_{1}\relax (t )-4 x_{2}\relax (t ), x_{2}^{\prime }\relax (t ) = 4 x_{1}\relax (t )+3 x_{2}\relax (t )] \]

329

\[ {}[x_{1}^{\prime }\relax (t ) = 7 x_{1}\relax (t )-5 x_{2}\relax (t ), x_{2}^{\prime }\relax (t ) = 4 x_{1}\relax (t )+3 x_{2}\relax (t )] \]

330

\[ {}[x_{1}^{\prime }\relax (t ) = -50 x_{1}\relax (t )+20 x_{2}\relax (t ), x_{2}^{\prime }\relax (t ) = 100 x_{1}\relax (t )-60 x_{2}\relax (t )] \]

331

\[ {}[x_{1}^{\prime }\relax (t ) = 4 x_{1}\relax (t )+x_{2}\relax (t )+4 x_{3}\relax (t ), x_{2}^{\prime }\relax (t ) = x_{1}\relax (t )+7 x_{2}\relax (t )+x_{3}\relax (t ), x_{3}^{\prime }\relax (t ) = 4 x_{1}\relax (t )+x_{2}\relax (t )+4 x_{3}\relax (t )] \]

332

\[ {}[x_{1}^{\prime }\relax (t ) = x_{1}\relax (t )+2 x_{2}\relax (t )+2 x_{3}\relax (t ), x_{2}^{\prime }\relax (t ) = 2 x_{1}\relax (t )+7 x_{2}\relax (t )+x_{3}\relax (t ), x_{3}^{\prime }\relax (t ) = 2 x_{1}\relax (t )+x_{2}\relax (t )+7 x_{3}\relax (t )] \]

333

\[ {}[x_{1}^{\prime }\relax (t ) = 4 x_{1}\relax (t )+x_{2}\relax (t )+x_{3}\relax (t ), x_{2}^{\prime }\relax (t ) = x_{1}\relax (t )+4 x_{2}\relax (t )+x_{3}\relax (t ), x_{3}^{\prime }\relax (t ) = x_{1}\relax (t )+x_{2}\relax (t )+4 x_{3}\relax (t )] \]

334

\[ {}[x_{1}^{\prime }\relax (t ) = 5 x_{1}\relax (t )+x_{2}\relax (t )+3 x_{3}\relax (t ), x_{2}^{\prime }\relax (t ) = x_{1}\relax (t )+7 x_{2}\relax (t )+x_{3}\relax (t ), x_{3}^{\prime }\relax (t ) = 3 x_{1}\relax (t )+x_{2}\relax (t )+5 x_{3}\relax (t )] \]

335

\[ {}[x_{1}^{\prime }\relax (t ) = 5 x_{1}\relax (t )-6 x_{3}\relax (t ), x_{2}^{\prime }\relax (t ) = 2 x_{1}\relax (t )-x_{2}\relax (t )-2 x_{3}\relax (t ), x_{3}^{\prime }\relax (t ) = 4 x_{1}\relax (t )-2 x_{2}\relax (t )-4 x_{3}\relax (t )] \]

336

\[ {}[x_{1}^{\prime }\relax (t ) = 3 x_{1}\relax (t )+2 x_{2}\relax (t )+2 x_{3}\relax (t ), x_{2}^{\prime }\relax (t ) = -5 x_{1}\relax (t )-4 x_{2}\relax (t )-2 x_{3}\relax (t ), x_{3}^{\prime }\relax (t ) = 5 x_{1}\relax (t )+5 x_{2}\relax (t )+3 x_{3}\relax (t )] \]

337

\[ {}[x_{1}^{\prime }\relax (t ) = 3 x_{1}\relax (t )+x_{2}\relax (t )+x_{3}\relax (t ), x_{2}^{\prime }\relax (t ) = -5 x_{1}\relax (t )-3 x_{2}\relax (t )-x_{3}\relax (t ), x_{3}^{\prime }\relax (t ) = 5 x_{1}\relax (t )+5 x_{2}\relax (t )+3 x_{3}\relax (t )] \]

338

\[ {}[x_{1}^{\prime }\relax (t ) = 2 x_{1}\relax (t )+x_{2}\relax (t )-x_{3}\relax (t ), x_{2}^{\prime }\relax (t ) = -4 x_{1}\relax (t )-3 x_{2}\relax (t )-x_{3}\relax (t ), x_{3}^{\prime }\relax (t ) = 4 x_{1}\relax (t )+4 x_{2}\relax (t )+2 x_{3}\relax (t )] \]

339

\[ {}[x_{1}^{\prime }\relax (t ) = 5 x_{1}\relax (t )+5 x_{2}\relax (t )+2 x_{3}\relax (t ), x_{2}^{\prime }\relax (t ) = -6 x_{1}\relax (t )-6 x_{2}\relax (t )-5 x_{3}\relax (t ), x_{3}^{\prime }\relax (t ) = 6 x_{1}\relax (t )+6 x_{2}\relax (t )+5 x_{3}\relax (t )] \]

340

\[ {}[x_{1}^{\prime }\relax (t ) = 3 x_{1}\relax (t )+x_{3}\relax (t ), x_{2}^{\prime }\relax (t ) = 9 x_{1}\relax (t )-x_{2}\relax (t )+2 x_{3}\relax (t ), x_{3}^{\prime }\relax (t ) = -9 x_{1}\relax (t )+4 x_{2}\relax (t )-x_{3}\relax (t )] \]

341

\[ {}[x_{1}^{\prime }\relax (t ) = x_{1}\relax (t ), x_{2}^{\prime }\relax (t ) = 2 x_{1}\relax (t )+2 x_{2}\relax (t ), x_{3}^{\prime }\relax (t ) = 3 x_{2}\relax (t )+3 x_{3}\relax (t ), x_{4}^{\prime }\relax (t ) = 4 x_{3}\relax (t )+4 x_{4}\relax (t )] \]

342

\[ {}[x_{1}^{\prime }\relax (t ) = -2 x_{1}\relax (t )+9 x_{4}\relax (t ), x_{2}^{\prime }\relax (t ) = 4 x_{1}\relax (t )+2 x_{2}\relax (t )-10 x_{4}\relax (t ), x_{3}^{\prime }\relax (t ) = -x_{3}\relax (t )+8 x_{4}\relax (t ), x_{4}^{\prime }\relax (t ) = x_{4}\relax (t )] \]

343

\[ {}[x_{1}^{\prime }\relax (t ) = 2 x_{1}\relax (t ), x_{2}^{\prime }\relax (t ) = -21 x_{1}\relax (t )-5 x_{2}\relax (t )-27 x_{3}\relax (t )-9 x_{4}\relax (t ), x_{3}^{\prime }\relax (t ) = 5 x_{3}\relax (t ), x_{4}^{\prime }\relax (t ) = -21 x_{3}\relax (t )-2 x_{4}\relax (t )] \]

344

\[ {}[x_{1}^{\prime }\relax (t ) = 4 x_{1}\relax (t )+x_{2}\relax (t )+x_{3}\relax (t )+7 x_{4}\relax (t ), x_{2}^{\prime }\relax (t ) = x_{1}\relax (t )+4 x_{2}\relax (t )+10 x_{3}\relax (t )+x_{4}\relax (t ), x_{3}^{\prime }\relax (t ) = x_{1}\relax (t )+10 x_{2}\relax (t )+4 x_{3}\relax (t )+x_{4}\relax (t ), x_{4}^{\prime }\relax (t ) = 7 x_{1}\relax (t )+x_{2}\relax (t )+x_{3}\relax (t )+4 x_{4}\relax (t )] \]

345

\[ {}[x_{1}^{\prime }\relax (t ) = -40 x_{1}\relax (t )-12 x_{2}\relax (t )+54 x_{3}\relax (t ), x_{2}^{\prime }\relax (t ) = 35 x_{1}\relax (t )+13 x_{2}\relax (t )-46 x_{3}\relax (t ), x_{3}^{\prime }\relax (t ) = -25 x_{1}\relax (t )-7 x_{2}\relax (t )+34 x_{3}\relax (t )] \]

346

\[ {}[x_{1}^{\prime }\relax (t ) = -20 x_{1}\relax (t )+11 x_{2}\relax (t )+13 x_{3}\relax (t ), x_{2}^{\prime }\relax (t ) = 12 x_{1}\relax (t )-x_{2}\relax (t )-7 x_{3}\relax (t ), x_{3}^{\prime }\relax (t ) = -48 x_{1}\relax (t )+21 x_{2}\relax (t )+31 x_{3}\relax (t )] \]

347

\[ {}[x_{1}^{\prime }\relax (t ) = 147 x_{1}\relax (t )+23 x_{2}\relax (t )-202 x_{3}\relax (t ), x_{2}^{\prime }\relax (t ) = -90 x_{1}\relax (t )-9 x_{2}\relax (t )+129 x_{3}\relax (t ), x_{3}^{\prime }\relax (t ) = 90 x_{1}\relax (t )+15 x_{2}\relax (t )-123 x_{3}\relax (t )] \]

348

\[ {}[x_{1}^{\prime }\relax (t ) = 9 x_{1}\relax (t )-7 x_{2}\relax (t )-5 x_{3}\relax (t ), x_{2}^{\prime }\relax (t ) = -12 x_{1}\relax (t )+7 x_{2}\relax (t )+11 x_{3}\relax (t )+9 x_{4}\relax (t ), x_{3}^{\prime }\relax (t ) = 24 x_{1}\relax (t )-17 x_{2}\relax (t )-19 x_{3}\relax (t )-9 x_{4}\relax (t ), x_{4}^{\prime }\relax (t ) = -18 x_{1}\relax (t )+13 x_{2}\relax (t )+17 x_{3}\relax (t )+9 x_{4}\relax (t )] \]

349

\[ {}[x_{1}^{\prime }\relax (t ) = 13 x_{1}\relax (t )-42 x_{2}\relax (t )+106 x_{3}\relax (t )+139 x_{4}\relax (t ), x_{2}^{\prime }\relax (t ) = 2 x_{1}\relax (t )-16 x_{2}\relax (t )+52 x_{3}\relax (t )+70 x_{4}\relax (t ), x_{3}^{\prime }\relax (t ) = x_{1}\relax (t )+6 x_{2}\relax (t )-20 x_{3}\relax (t )-31 x_{4}\relax (t ), x_{4}^{\prime }\relax (t ) = -x_{1}\relax (t )-6 x_{2}\relax (t )+22 x_{3}\relax (t )+33 x_{4}\relax (t )] \]

350

\[ {}[x_{1}^{\prime }\relax (t ) = 23 x_{1}\relax (t )-18 x_{2}\relax (t )-16 x_{3}\relax (t ), x_{2}^{\prime }\relax (t ) = -8 x_{1}\relax (t )+6 x_{2}\relax (t )+7 x_{3}\relax (t )+9 x_{4}\relax (t ), x_{3}^{\prime }\relax (t ) = 34 x_{1}\relax (t )-27 x_{2}\relax (t )-26 x_{3}\relax (t )-9 x_{4}\relax (t ), x_{4}^{\prime }\relax (t ) = -26 x_{1}\relax (t )+21 x_{2}\relax (t )+25 x_{3}\relax (t )+12 x_{4}\relax (t )] \]

351

\[ {}[x_{1}^{\prime }\relax (t ) = 47 x_{1}\relax (t )-8 x_{2}\relax (t )+5 x_{3}\relax (t )-5 x_{4}\relax (t ), x_{2}^{\prime }\relax (t ) = -10 x_{1}\relax (t )+32 x_{2}\relax (t )+18 x_{3}\relax (t )-2 x_{4}\relax (t ), x_{3}^{\prime }\relax (t ) = 139 x_{1}\relax (t )-40 x_{2}\relax (t )-167 x_{3}\relax (t )-121 x_{4}\relax (t ), x_{4}^{\prime }\relax (t ) = -232 x_{1}\relax (t )+64 x_{2}\relax (t )+360 x_{3}\relax (t )+248 x_{4}\relax (t )] \]

352

\[ {}[x_{1}^{\prime }\relax (t ) = 139 x_{1}\relax (t )-14 x_{2}\relax (t )-52 x_{3}\relax (t )-14 x_{4}\relax (t )+28 x_{5}\relax (t ), x_{2}^{\prime }\relax (t ) = -22 x_{1}\relax (t )+5 x_{2}\relax (t )+7 x_{3}\relax (t )+8 x_{4}\relax (t )-7 x_{5}\relax (t ), x_{3}^{\prime }\relax (t ) = 370 x_{1}\relax (t )-38 x_{2}\relax (t )-139 x_{3}\relax (t )-38 x_{4}\relax (t )+76 x_{5}\relax (t ), x_{4}^{\prime }\relax (t ) = 152 x_{1}\relax (t )-16 x_{2}\relax (t )-59 x_{3}\relax (t )-13 x_{4}\relax (t )+35 x_{5}\relax (t ), x_{5}^{\prime }\relax (t ) = 95 x_{1}\relax (t )-10 x_{2}\relax (t )-38 x_{3}\relax (t )-7 x_{4}\relax (t )+23 x_{5}\relax (t )] \]

353

\[ {}[x_{1}^{\prime }\relax (t ) = 9 x_{1}\relax (t )+13 x_{2}\relax (t )-13 x_{6}\relax (t ), x_{2}^{\prime }\relax (t ) = -14 x_{1}\relax (t )+19 x_{2}\relax (t )-10 x_{3}\relax (t )-20 x_{4}\relax (t )+10 x_{5}\relax (t )+4 x_{6}\relax (t ), x_{3}^{\prime }\relax (t ) = -30 x_{1}\relax (t )+12 x_{2}\relax (t )-7 x_{3}\relax (t )-30 x_{4}\relax (t )+12 x_{5}\relax (t )+18 x_{6}\relax (t ), x_{4}^{\prime }\relax (t ) = -12 x_{1}\relax (t )+10 x_{2}\relax (t )-10 x_{3}\relax (t )-9 x_{4}\relax (t )+10 x_{5}\relax (t )+2 x_{6}\relax (t ), x_{5}^{\prime }\relax (t ) = 6 x_{1}\relax (t )+9 x_{2}\relax (t )+6 x_{4}\relax (t )+5 x_{5}\relax (t )-15 x_{6}\relax (t ), x_{6}^{\prime }\relax (t ) = -14 x_{1}\relax (t )+23 x_{2}\relax (t )-10 x_{3}\relax (t )-20 x_{4}\relax (t )+10 x_{5}\relax (t )] \]

354

\[ {}[x_{1}^{\prime }\relax (t ) = 9 x_{1}\relax (t )+4 x_{2}\relax (t ), x_{2}^{\prime }\relax (t ) = -6 x_{1}\relax (t )-x_{2}\relax (t ), x_{3}^{\prime }\relax (t ) = 6 x_{1}\relax (t )+4 x_{2}\relax (t )+3 x_{3}\relax (t )] \]

355

\[ {}[x_{1}^{\prime }\relax (t ) = x_{1}\relax (t )-3 x_{2}\relax (t ), x_{2}^{\prime }\relax (t ) = 3 x_{1}\relax (t )+7 x_{2}\relax (t )] \]

356

\[ {}[x_{1}^{\prime }\relax (t ) = x_{2}\relax (t )+2 x_{3}\relax (t ), x_{2}^{\prime }\relax (t ) = -5 x_{1}\relax (t )-3 x_{2}\relax (t )-7 x_{3}\relax (t ), x_{3}^{\prime }\relax (t ) = x_{1}\relax (t )] \]

357

\[ {}[x_{1}^{\prime }\relax (t ) = x_{3}\relax (t ), x_{2}^{\prime }\relax (t ) = x_{4}\relax (t ), x_{3}^{\prime }\relax (t ) = -2 x_{1}\relax (t )+2 x_{2}\relax (t )-3 x_{3}\relax (t )+x_{4}\relax (t ), x_{4}^{\prime }\relax (t ) = 2 x_{1}\relax (t )-2 x_{2}\relax (t )+x_{3}\relax (t )-3 x_{4}\relax (t )] \]

358

\[ {}[x_{1}^{\prime }\relax (t ) = -2 x_{1}\relax (t )+x_{2}\relax (t ), x_{2}^{\prime }\relax (t ) = -x_{1}\relax (t )-4 x_{2}\relax (t )] \]

359

\[ {}[x_{1}^{\prime }\relax (t ) = 3 x_{1}\relax (t )-x_{2}\relax (t ), x_{2}^{\prime }\relax (t ) = x_{1}\relax (t )+x_{2}\relax (t )] \]

360

\[ {}[x_{1}^{\prime }\relax (t ) = x_{1}\relax (t )-2 x_{2}\relax (t ), x_{2}^{\prime }\relax (t ) = 2 x_{1}\relax (t )+5 x_{2}\relax (t )] \]

361

\[ {}[x_{1}^{\prime }\relax (t ) = 3 x_{1}\relax (t )-x_{2}\relax (t ), x_{2}^{\prime }\relax (t ) = x_{1}\relax (t )+5 x_{2}\relax (t )] \]

362

\[ {}[x_{1}^{\prime }\relax (t ) = 7 x_{1}\relax (t )+x_{2}\relax (t ), x_{2}^{\prime }\relax (t ) = -4 x_{1}\relax (t )+3 x_{2}\relax (t )] \]

363

\[ {}[x_{1}^{\prime }\relax (t ) = x_{1}\relax (t )-4 x_{2}\relax (t ), x_{2}^{\prime }\relax (t ) = 4 x_{1}\relax (t )+9 x_{2}\relax (t )] \]

364

\[ {}[x_{1}^{\prime }\relax (t ) = 2 x_{1}\relax (t ), x_{2}^{\prime }\relax (t ) = -7 x_{1}\relax (t )+9 x_{2}\relax (t )+7 x_{3}\relax (t ), x_{3}^{\prime }\relax (t ) = 2 x_{3}\relax (t )] \]

365

\[ {}[x_{1}^{\prime }\relax (t ) = 25 x_{1}\relax (t )+12 x_{2}\relax (t ), x_{2}^{\prime }\relax (t ) = -18 x_{1}\relax (t )-5 x_{2}\relax (t ), x_{3}^{\prime }\relax (t ) = 6 x_{1}\relax (t )+6 x_{2}\relax (t )+13 x_{3}\relax (t )] \]

366

\[ {}[x_{1}^{\prime }\relax (t ) = -19 x_{1}\relax (t )+12 x_{2}\relax (t )+84 x_{3}\relax (t ), x_{2}^{\prime }\relax (t ) = 5 x_{2}\relax (t ), x_{3}^{\prime }\relax (t ) = -8 x_{1}\relax (t )+4 x_{2}\relax (t )+33 x_{3}\relax (t )] \]

367

\[ {}[x_{1}^{\prime }\relax (t ) = -13 x_{1}\relax (t )+40 x_{2}\relax (t )-48 x_{3}\relax (t ), x_{2}^{\prime }\relax (t ) = -8 x_{1}\relax (t )+23 x_{2}\relax (t )-24 x_{3}\relax (t ), x_{3}^{\prime }\relax (t ) = 3 x_{3}\relax (t )] \]

368

\[ {}[x_{1}^{\prime }\relax (t ) = -3 x_{1}\relax (t )-4 x_{3}\relax (t ), x_{2}^{\prime }\relax (t ) = -x_{1}\relax (t )-x_{2}\relax (t )-x_{3}\relax (t ), x_{3}^{\prime }\relax (t ) = x_{1}\relax (t )+x_{3}\relax (t )] \]

369

\[ {}[x_{1}^{\prime }\relax (t ) = -x_{1}\relax (t )+x_{3}\relax (t ), x_{2}^{\prime }\relax (t ) = -x_{2}\relax (t )+x_{3}\relax (t ), x_{3}^{\prime }\relax (t ) = x_{1}\relax (t )-x_{2}\relax (t )-x_{3}\relax (t )] \]

370

\[ {}[x_{1}^{\prime }\relax (t ) = -x_{1}\relax (t )+x_{3}\relax (t ), x_{2}^{\prime }\relax (t ) = x_{2}\relax (t )-4 x_{3}\relax (t ), x_{3}^{\prime }\relax (t ) = x_{2}\relax (t )-3 x_{3}\relax (t )] \]

371

\[ {}[x_{1}^{\prime }\relax (t ) = x_{3}\relax (t ), x_{2}^{\prime }\relax (t ) = -5 x_{1}\relax (t )-x_{2}\relax (t )-5 x_{3}\relax (t ), x_{3}^{\prime }\relax (t ) = 4 x_{1}\relax (t )+x_{2}\relax (t )-2 x_{3}\relax (t )] \]

372

\[ {}[x_{1}^{\prime }\relax (t ) = -2 x_{1}\relax (t )-9 x_{2}\relax (t ), x_{2}^{\prime }\relax (t ) = x_{1}\relax (t )+4 x_{2}\relax (t ), x_{3}^{\prime }\relax (t ) = x_{1}\relax (t )+3 x_{2}\relax (t )+x_{3}\relax (t )] \]

373

\[ {}[x_{1}^{\prime }\relax (t ) = x_{1}\relax (t ), x_{2}^{\prime }\relax (t ) = -2 x_{1}\relax (t )-2 x_{2}\relax (t )-3 x_{3}\relax (t ), x_{3}^{\prime }\relax (t ) = 2 x_{1}\relax (t )+3 x_{2}\relax (t )+4 x_{3}\relax (t )] \]

374

\[ {}[x_{1}^{\prime }\relax (t ) = x_{1}\relax (t ), x_{2}^{\prime }\relax (t ) = 18 x_{1}\relax (t )+7 x_{2}\relax (t )+4 x_{3}\relax (t ), x_{3}^{\prime }\relax (t ) = -27 x_{1}\relax (t )-9 x_{2}\relax (t )-5 x_{3}\relax (t )] \]

375

\[ {}[x_{1}^{\prime }\relax (t ) = x_{1}\relax (t ), x_{2}^{\prime }\relax (t ) = x_{1}\relax (t )+3 x_{2}\relax (t )+x_{3}\relax (t ), x_{3}^{\prime }\relax (t ) = -2 x_{1}\relax (t )-4 x_{2}\relax (t )-x_{3}\relax (t )] \]

376

\[ {}[x_{1}^{\prime }\relax (t ) = x_{1}\relax (t )-4 x_{2}\relax (t )-2 x_{4}\relax (t ), x_{2}^{\prime }\relax (t ) = x_{2}\relax (t ), x_{3}^{\prime }\relax (t ) = 6 x_{1}\relax (t )-12 x_{2}\relax (t )-x_{3}\relax (t )-6 x_{4}\relax (t ), x_{4}^{\prime }\relax (t ) = -4 x_{2}\relax (t )-x_{4}\relax (t )] \]

377

\[ {}[x_{1}^{\prime }\relax (t ) = 2 x_{1}\relax (t )+x_{2}\relax (t )+x_{4}\relax (t ), x_{2}^{\prime }\relax (t ) = 2 x_{2}\relax (t )+x_{3}\relax (t ), x_{3}^{\prime }\relax (t ) = 2 x_{3}\relax (t )+x_{4}\relax (t ), x_{4}^{\prime }\relax (t ) = 2 x_{4}\relax (t )] \]

378

\[ {}[x_{1}^{\prime }\relax (t ) = -x_{1}\relax (t )-4 x_{2}\relax (t ), x_{2}^{\prime }\relax (t ) = x_{1}\relax (t )+3 x_{2}\relax (t ), x_{3}^{\prime }\relax (t ) = x_{1}\relax (t )+2 x_{2}\relax (t )+x_{3}\relax (t ), x_{4}^{\prime }\relax (t ) = x_{2}\relax (t )+x_{4}\relax (t )] \]

379

\[ {}[x_{1}^{\prime }\relax (t ) = x_{1}\relax (t )+3 x_{2}\relax (t )+7 x_{3}\relax (t ), x_{2}^{\prime }\relax (t ) = -x_{2}\relax (t )-4 x_{3}\relax (t ), x_{3}^{\prime }\relax (t ) = x_{2}\relax (t )+3 x_{3}\relax (t ), x_{4}^{\prime }\relax (t ) = -6 x_{2}\relax (t )-14 x_{3}\relax (t )+x_{4}\relax (t )] \]

380

\[ {}[x_{1}^{\prime }\relax (t ) = 39 x_{1}\relax (t )+8 x_{2}\relax (t )-16 x_{3}\relax (t ), x_{2}^{\prime }\relax (t ) = -36 x_{1}\relax (t )-5 x_{2}\relax (t )+16 x_{3}\relax (t ), x_{3}^{\prime }\relax (t ) = 72 x_{1}\relax (t )+16 x_{2}\relax (t )-29 x_{3}\relax (t )] \]

381

\[ {}[x_{1}^{\prime }\relax (t ) = 28 x_{1}\relax (t )+50 x_{2}\relax (t )+100 x_{3}\relax (t ), x_{2}^{\prime }\relax (t ) = 15 x_{1}\relax (t )+33 x_{2}\relax (t )+60 x_{3}\relax (t ), x_{3}^{\prime }\relax (t ) = -15 x_{1}\relax (t )-30 x_{2}\relax (t )-57 x_{3}\relax (t )] \]

382

\[ {}[x_{1}^{\prime }\relax (t ) = -2 x_{1}\relax (t )+17 x_{2}\relax (t )+4 x_{3}\relax (t ), x_{2}^{\prime }\relax (t ) = -x_{1}\relax (t )+6 x_{2}\relax (t )+x_{3}\relax (t ), x_{3}^{\prime }\relax (t ) = x_{2}\relax (t )+2 x_{3}\relax (t )] \]

383

\[ {}[x_{1}^{\prime }\relax (t ) = 5 x_{1}\relax (t )-x_{2}\relax (t )+x_{3}\relax (t ), x_{2}^{\prime }\relax (t ) = x_{1}\relax (t )+3 x_{2}\relax (t ), x_{3}^{\prime }\relax (t ) = -3 x_{1}\relax (t )+2 x_{2}\relax (t )+x_{3}\relax (t )] \]

384

\[ {}[x_{1}^{\prime }\relax (t ) = -3 x_{1}\relax (t )+5 x_{2}\relax (t )-5 x_{3}\relax (t ), x_{2}^{\prime }\relax (t ) = 3 x_{1}\relax (t )-x_{2}\relax (t )+3 x_{3}\relax (t ), x_{3}^{\prime }\relax (t ) = 8 x_{1}\relax (t )-8 x_{2}\relax (t )+10 x_{3}\relax (t )] \]

385

\[ {}[x_{1}^{\prime }\relax (t ) = -15 x_{1}\relax (t )-7 x_{2}\relax (t )+4 x_{3}\relax (t ), x_{2}^{\prime }\relax (t ) = 34 x_{1}\relax (t )+16 x_{2}\relax (t )-11 x_{3}\relax (t ), x_{3}^{\prime }\relax (t ) = 17 x_{1}\relax (t )+7 x_{2}\relax (t )+5 x_{3}\relax (t )] \]

386

\[ {}[x_{1}^{\prime }\relax (t ) = -x_{1}\relax (t )+x_{2}\relax (t )+x_{3}\relax (t )-2 x_{4}\relax (t ), x_{2}^{\prime }\relax (t ) = 7 x_{1}\relax (t )-4 x_{2}\relax (t )-6 x_{3}\relax (t )+11 x_{4}\relax (t ), x_{3}^{\prime }\relax (t ) = 5 x_{1}\relax (t )-x_{2}\relax (t )+x_{3}\relax (t )+3 x_{4}\relax (t ), x_{4}^{\prime }\relax (t ) = 6 x_{1}\relax (t )-2 x_{2}\relax (t )-2 x_{3}\relax (t )+6 x_{4}\relax (t )] \]

387

\[ {}[x_{1}^{\prime }\relax (t ) = 2 x_{1}\relax (t )+x_{2}\relax (t )-2 x_{3}\relax (t )+x_{4}\relax (t ), x_{2}^{\prime }\relax (t ) = 3 x_{2}\relax (t )-5 x_{3}\relax (t )+3 x_{4}\relax (t ), x_{3}^{\prime }\relax (t ) = -13 x_{2}\relax (t )+22 x_{3}\relax (t )-12 x_{4}\relax (t ), x_{4}^{\prime }\relax (t ) = -27 x_{2}\relax (t )+45 x_{3}\relax (t )-25 x_{4}\relax (t )] \]

388

\[ {}[x_{1}^{\prime }\relax (t ) = 35 x_{1}\relax (t )-12 x_{2}\relax (t )+4 x_{3}\relax (t )+30 x_{4}\relax (t ), x_{2}^{\prime }\relax (t ) = 22 x_{1}\relax (t )-8 x_{2}\relax (t )+3 x_{3}\relax (t )+19 x_{4}\relax (t ), x_{3}^{\prime }\relax (t ) = -10 x_{1}\relax (t )+3 x_{2}\relax (t )-9 x_{4}\relax (t ), x_{4}^{\prime }\relax (t ) = -27 x_{1}\relax (t )+9 x_{2}\relax (t )-3 x_{3}\relax (t )-23 x_{4}\relax (t )] \]

389

\[ {}[x_{1}^{\prime }\relax (t ) = 11 x_{1}\relax (t )-x_{2}\relax (t )+26 x_{3}\relax (t )+6 x_{4}\relax (t )-3 x_{5}\relax (t ), x_{2}^{\prime }\relax (t ) = 3 x_{2}\relax (t ), x_{3}^{\prime }\relax (t ) = -9 x_{1}\relax (t )-24 x_{3}\relax (t )-6 x_{4}\relax (t )+3 x_{5}\relax (t ), x_{4}^{\prime }\relax (t ) = 3 x_{1}\relax (t )+9 x_{3}\relax (t )+5 x_{4}\relax (t )-x_{5}\relax (t ), x_{5}^{\prime }\relax (t ) = -48 x_{1}\relax (t )-3 x_{2}\relax (t )-138 x_{3}\relax (t )-30 x_{4}\relax (t )+18 x_{5}\relax (t )] \]

390

\[ {}[x_{1}^{\prime }\relax (t ) = 3 x_{1}\relax (t )-4 x_{2}\relax (t )+x_{3}\relax (t ), x_{2}^{\prime }\relax (t ) = 4 x_{1}\relax (t )+3 x_{2}\relax (t )+x_{4}\relax (t ), x_{3}^{\prime }\relax (t ) = 3 x_{3}\relax (t )-4 x_{4}\relax (t ), x_{4}^{\prime }\relax (t ) = 4 x_{3}\relax (t )+3 x_{4}\relax (t )] \]

391

\[ {}[x_{1}^{\prime }\relax (t ) = 2 x_{1}\relax (t )-8 x_{3}\relax (t )-3 x_{4}\relax (t ), x_{2}^{\prime }\relax (t ) = -18 x_{1}\relax (t )-x_{2}\relax (t ), x_{3}^{\prime }\relax (t ) = -9 x_{1}\relax (t )-3 x_{2}\relax (t )-25 x_{3}\relax (t )-9 x_{4}\relax (t ), x_{4}^{\prime }\relax (t ) = 33 x_{1}\relax (t )+10 x_{2}\relax (t )+90 x_{3}\relax (t )+32 x_{4}\relax (t )] \]

392

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

393

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

394

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

395

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

396

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

397

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

398

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

399

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

400

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