2.3 Problems 201 to 300

Table 2.3: Main lookup table

#

ODE

Mathematica result

Maple result

201

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

202

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

203

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

204

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

205

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

206

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

207

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

208

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

209

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

210

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

211

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

212

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

213

\[ {}3 x^{\prime \prime }+30 x^{\prime }+63 x = 0 \]

214

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

215

\[ {}2 x^{\prime \prime }+12 x^{\prime }+50 x = 0 \]

216

\[ {}4 x^{\prime \prime }+20 x^{\prime }+169 x = 0 \]

217

\[ {}2 x^{\prime \prime }+16 x^{\prime }+40 x = 0 \]

218

\[ {}x^{\prime \prime }+10 x^{\prime }+125 x = 0 \]

219

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

220

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

221

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

222

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

223

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

224

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

225

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

226

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

227

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

228

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

229

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

230

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

231

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

232

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

233

\[ {}y^{\prime \prime }-6 y^{\prime }+13 y = x \,{\mathrm e}^{3 x} \sin \left (2 x \right ) \]

234

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

235

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

236

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

237

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

238

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

239

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

240

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

241

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

242

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 4 \,{\mathrm e}^{x} \]

243

\[ {}y^{\prime \prime }-2 y^{\prime }-8 y = 3 \,{\mathrm e}^{-2 x} \]

244

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 2 \,{\mathrm e}^{2 x} \]

245

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

246

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

247

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

248

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

249

\[ {}y^{\prime \prime }+y = \csc ^{2}\relax (x ) \]

250

\[ {}y^{\prime \prime }+4 y = \sin ^{2}\relax (x ) \]

251

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

252

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 72 x^{5} \]

253

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

254

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

255

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

256

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+y = \ln \relax (x ) \]

257

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

258

\[ {}x^{\prime \prime }+9 x = 10 \cos \left (2 t \right ) \]

259

\[ {}x^{\prime \prime }+4 x = 5 \sin \left (3 t \right ) \]

260

\[ {}x^{\prime \prime }+100 x = 225 \cos \left (5 t \right )+300 \sin \left (5 t \right ) \]

261

\[ {}x^{\prime \prime }+25 x = 90 \cos \left (4 t \right ) \]

262

\[ {}m x^{\prime \prime }+k x = F_{0} \cos \left (\omega t \right ) \]

263

\[ {}x^{\prime \prime }+4 x^{\prime }+4 x = 10 \cos \left (3 t \right ) \]

264

\[ {}x^{\prime \prime }+3 x^{\prime }+5 x = -4 \cos \left (5 t \right ) \]

265

\[ {}2 x^{\prime \prime }+2 x^{\prime }+x = 3 \sin \left (10 t \right ) \]

266

\[ {}x^{\prime \prime }+3 x^{\prime }+3 x = 8 \cos \left (10 t \right )+6 \sin \left (10 t \right ) \]

267

\[ {}x^{\prime \prime }+4 x^{\prime }+5 x = 10 \cos \left (3 t \right ) \]

268

\[ {}x^{\prime \prime }+6 x^{\prime }+13 x = 10 \sin \left (5 t \right ) \]

269

\[ {}x^{\prime \prime }+6 x^{\prime }+13 x = 10 \sin \left (5 t \right ) \]

270

\[ {}x^{\prime \prime }+2 x^{\prime }+26 x = 600 \cos \left (10 t \right ) \]

271

\[ {}x^{\prime \prime }+8 x^{\prime }+25 x = 200 \cos \relax (t )+520 \sin \relax (t ) \]

272

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

273

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

274

\[ {}[x^{\prime }\relax (t ) = 2 x \relax (t )+4 y \relax (t )+3 \,{\mathrm e}^{t}, y^{\prime }\relax (t ) = 5 x \relax (t )-y \relax (t )-t^{2}] \]

275

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

276

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

277

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

278

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

279

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

280

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

281

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

282

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

283

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

284

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

285

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

286

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

287

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

288

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

289

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

290

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

291

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

292

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

293

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

294

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

295

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

296

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

297

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

298

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

299

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

300

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