4.2.1 Problems 1 to 100

Table 4.207: Second order linear ODE

#

ODE

Mathematica

Maple

Sympy

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

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

147

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

149

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

150

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

152

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

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

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

227

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

228

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

229

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

230

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

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

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

244

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

245

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

246

\[ {} 4 x^{2} y^{\prime \prime }+8 x y^{\prime }-3 y = 0 \]

247

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

248

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

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

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

262

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

263

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

264

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 0 \]

265

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

266

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

267

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

268

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

269

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

270

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

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

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

291

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

292

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

293

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

309

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

310

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

311

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

315

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+9 y = 0 \]

316

\[ {} x^{2} y^{\prime \prime }+7 x y^{\prime }+25 y = 0 \]

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

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

334

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

337

\[ {} y^{\prime \prime }+9 y = 2 x^{2} {\mathrm e}^{3 x}+5 \]

338

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

342

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

344

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

346

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

347

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

351

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

352

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

353

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

354

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

355

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

358

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

363

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

364

\[ {} y^{\prime \prime }+9 y = \sin \left (x \right )^{4} \]

365

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