2.53 Problems 5201 to 5300

Table 2.53: Main lookup table

#

ODE

Mathematica result

Maple result

5201

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

5202

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

5203

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

5204

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

5205

\[ {}y^{\prime \prime }+\left (1+4 i\right ) y^{\prime }+y = 0 \]

5206

\[ {}y^{\prime \prime }+\left (-1+3 i\right ) y^{\prime }-3 i y = 0 \]

5207

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

5208

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

5209

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

5210

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

5211

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

5212

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

5213

\[ {}y^{\prime \prime }-7 y^{\prime }+6 y = \sin \relax (x ) \]

5214

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

5215

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

5216

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

5217

\[ {}6 y^{\prime \prime }+5 y^{\prime }-6 y = x \]

5218

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

5219

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

5220

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

5221

\[ {}y^{\prime \prime \prime }-5 y^{\prime \prime }+6 y^{\prime } = 0 \]

5222

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

5223

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

5224

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

5225

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

5226

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

5227

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

5228

\[ {}y^{\relax (5)}-y^{\prime \prime \prime \prime }-y^{\prime }+y = 0 \]

5229

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

5230

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

5231

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

5232

\[ {}y^{\relax (5)}+2 y = 0 \]

5233

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

5234

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

5235

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

5236

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

5237

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

5238

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

5239

\[ {}y^{\prime \prime \prime }-8 y = {\mathrm e}^{i x} \]

5240

\[ {}y^{\prime \prime \prime \prime }+16 y = \cos \relax (x ) \]

5241

\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y = {\mathrm e}^{x} \]

5242

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

5243

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

5244

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

5245

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

5246

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

5247

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

5248

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

5249

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

5250

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

5251

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

5252

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

5253

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

5254

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

5255

\[ {}\left (3 x -1\right )^{2} y^{\prime \prime }+\left (9 x -3\right ) y^{\prime }-9 y = 0 \]

5256

\[ {}x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = 0 \]

5257

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

5258

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

5259

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

5260

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

5261

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

5262

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

5263

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

5264

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

5265

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

5266

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

5267

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

5268

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

5269

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

5270

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

5271

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

5272

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

5273

\[ {}y^{\prime \prime }+y \,{\mathrm e}^{x} = 0 \]

5274

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

5275

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

5276

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

5277

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

5278

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

5279

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

5280

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

5281

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = x^{2} \]

5282

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

5283

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 1 \]

5284

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

5285

\[ {}x^{2} y^{\prime \prime }+\left (-2-i\right ) x y^{\prime }+3 i y = 0 \]

5286

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

5287

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

5288

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

5289

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

5290

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

5291

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

5292

\[ {}\left (x^{2}+x -2\right )^{2} y^{\prime \prime }+3 \left (2+x \right ) y^{\prime }+\left (x -1\right ) y = 0 \]

5293

\[ {}x^{2} y^{\prime \prime }+\sin \relax (x ) y^{\prime }+y \cos \relax (x ) = 0 \]

5294

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

5295

\[ {}4 x^{2} y^{\prime \prime }+\left (4 x^{4}-5 x \right ) y^{\prime }+\left (x^{2}+2\right ) y = 0 \]

5296

\[ {}x^{2} y^{\prime \prime }+\left (-3 x^{2}+x \right ) y^{\prime }+y \,{\mathrm e}^{x} = 0 \]

5297

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

5298

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

5299

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

5300

\[ {}2 x^{2} y^{\prime \prime }+\left (x^{2}+5 x \right ) y^{\prime }+\left (x^{2}-2\right ) y = 0 \]