3.20.1 Problems 1 to 100

Table 3.729: Second or higher order ODE with constant coefficients

#

ODE

Mathematica

Maple

157

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

158

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

159

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

160

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

161

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

162

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

163

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

164

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

165

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

166

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

167

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

168

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

173

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

174

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

175

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

176

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

177

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

178

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

179

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

180

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

181

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

182

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

188

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

189

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

190

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

191

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

192

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

193

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

194

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

195

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

196

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

197

\[ {}y^{\prime \prime }+3 y^{\prime }-10 y = 0 \]

198

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

199

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

200

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

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

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

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

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

224

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

225

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

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

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

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

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

238

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

239

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

240

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

241

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

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

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

250

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

251

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

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

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

279

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

285

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