5.20.1 Problems 1 to 100

Table 5.907: Second or higher order ODE with constant coefficients

#

ODE

Mathematica

Maple

11

\[ {}x^{\prime \prime } = 50 \]

12

\[ {}x^{\prime \prime } = -20 \]

13

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

14

\[ {}x^{\prime \prime } = 2 t +1 \]

15

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

16

\[ {}x^{\prime \prime } = \frac {1}{\sqrt {t +4}} \]

17

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

18

\[ {}x^{\prime \prime } = 50 \sin \left (5 t \right ) \]

149

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

215

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

216

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

217

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

218

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

219

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

220

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

221

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

222

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

223

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

224

\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = 0 \]

225

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

226

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

234

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

235

\[ {}y^{\prime \prime }+2 y^{\prime }-15 y = 0 \]

236

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

237

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

238

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

239

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

240

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

241

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

242

\[ {}6 y^{\prime \prime }-7 y^{\prime }-20 y = 0 \]

243

\[ {}35 y^{\prime \prime }-y^{\prime }-12 y = 0 \]

249

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

250

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

251

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

252

\[ {}y^{\prime \prime \prime }-5 y^{\prime \prime }+8 y^{\prime }-4 y = 0 \]

253

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

254

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

257

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

258

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

259

\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 6 \]

260

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

261

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

263

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

265

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

271

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

272

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

273

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

274

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

275

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

276

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

277

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

278

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

279

\[ {}y^{\prime \prime }+8 y^{\prime }+25 y = 0 \]

280

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

281

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

282

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

283

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

284

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

285

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

286

\[ {}y^{\prime \prime \prime \prime }+18 y^{\prime \prime }+81 y = 0 \]

287

\[ {}6 y^{\prime \prime \prime \prime }+11 y^{\prime \prime }+4 y = 0 \]

288

\[ {}y^{\prime \prime \prime \prime } = 16 y \]

289

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

290

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

291

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

292

\[ {}9 y^{\prime \prime }+6 y^{\prime }+4 y = 0 \]

293

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

294

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

295

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

296

\[ {}y^{\prime \prime \prime }+10 y^{\prime \prime }+25 y^{\prime } = 0 \]

297

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

298

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

299

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

300

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

301

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

302

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

303

\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }-54 y = 0 \]

304

\[ {}3 y^{\prime \prime \prime }-2 y^{\prime \prime }+12 y^{\prime }-8 y = 0 \]

305

\[ {}6 y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }+25 y^{\prime \prime }+20 y^{\prime }+4 y = 0 \]

306

\[ {}9 y^{\prime \prime \prime }+11 y^{\prime \prime }+4 y^{\prime }-14 y = 0 \]

307

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

308

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

309

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

310

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

311

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

312

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

313

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

322

\[ {}y^{\prime \prime }+16 y = {\mathrm e}^{3 x} \]

323

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

324

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

325

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

326

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

327

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

328

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

329

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

330

\[ {}y^{\prime \prime }+2 y^{\prime }-3 y = 1+x \,{\mathrm e}^{x} \]

331

\[ {}2 y^{\prime \prime }+9 y = 2 \cos \left (3 x \right )+3 \sin \left (3 x \right ) \]

332

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

333

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

334

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