2.64 Problems 6301 to 6400

Table 2.127: Main lookup table

#

ODE

Mathematica result

Maple result

6301

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

6302

\[ {}y^{\prime \prime }+3 y^{\prime }-10 y = 6 \,{\mathrm e}^{4 x} \]

6303

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

6304

\[ {}y^{\prime \prime }+10 y^{\prime }+25 y = 14 \,{\mathrm e}^{-5 x} \]

6305

\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 25 x^{2}+12 \]

6306

\[ {}y^{\prime \prime }-y^{\prime }-6 y = 20 \,{\mathrm e}^{-2 x} \]

6307

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 14 \sin \left (2 x \right )-18 \cos \left (2 x \right ) \]

6308

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

6309

\[ {}y^{\prime \prime }-2 y^{\prime } = 12 x -10 \]

6310

\[ {}y^{\prime \prime }-2 y^{\prime }+y = 6 \,{\mathrm e}^{x} \]

6311

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

6312

\[ {}y^{\prime \prime }+y^{\prime } = 10 x^{4}+2 \]

6313

\[ {}y^{\prime \prime }+4 y = 4 \cos \left (2 x \right )+6 \cos \left (x \right )+8 x^{2}-4 x \]

6314

\[ {}y^{\prime \prime }+9 y = 2 \sin \left (3 x \right )+4 \sin \left (x \right )-26 \,{\mathrm e}^{-2 x}+27 x^{3} \]

6315

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

6316

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

6317

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

6318

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

6319

\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 64 x \,{\mathrm e}^{-x} \]

6320

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

6321

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

6322

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

6323

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

6324

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

6325

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

6326

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

6327

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

6328

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

6329

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

6330

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

6331

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

6332

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

6333

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

6334

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

6335

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

6336

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

6337

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

6338

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

6339

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

6340

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

6341

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

6342

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

6343

\[ {}y^{\prime \prime }-\frac {x y^{\prime }}{x -1}+\frac {y}{x -1} = 0 \]

6344

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

6345

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

6346

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

6347

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

6348

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

6349

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

6350

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

6351

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

6352

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

6353

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

6354

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

6355

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

6356

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

6357

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

6358

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

6359

\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-2 y^{\prime \prime }-6 y^{\prime }+5 y = 0 \]

6360

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

6361

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

6362

\[ {}y^{\left (5\right )}-6 y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+48 y^{\prime \prime }+16 y^{\prime }-96 y = 0 \]

6363

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

6364

\[ {}y^{\prime \prime \prime \prime } = \sin \left (x \right )+24 \]

6365

\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = 10+42 \,{\mathrm e}^{3 x} \]

6366

\[ {}y^{\prime \prime \prime }-y^{\prime } = 1 \]

6367

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

6368

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

6369

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

6370

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

6371

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

6372

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

6373

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

6374

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

6375

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

6376

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

6377

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

6378

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

6379

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

6380

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

6381

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

6382

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

6383

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

6384

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

6385

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

6386

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

6387

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

6388

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

6389

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

6390

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

6391

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

6392

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

6393

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

6394

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

6395

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

6396

\[ {}y^{\prime \prime }+y = -8 \sin \left (3 x \right ) \]

6397

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

6398

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

6399

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

6400

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