2.65 Problems 6401 to 6500

Table 2.65: Main lookup table

#

ODE

Mathematica result

Maple result

6401

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

6402

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

6403

\[ {}y^{\prime \prime }-y^{\prime }-x y-x^{3}+1 = 0 \]

6404

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

6405

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

6406

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

6407

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

6408

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

6409

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

6410

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

6411

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

6412

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

6413

\[ {}y^{\prime \prime }-x y-x^{6}+64 = 0 \]

6414

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

6415

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

6416

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

6417

\[ {}y^{\prime \prime }-x y-x^{6}-x^{3}+42 = 0 \]

6418

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

6419

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

6420

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

6421

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

6422

\[ {}y^{\prime \prime }-2 x^{2} y-x^{4}+1 = 0 \]

6423

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

6424

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

6425

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

6426

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

6427

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

6428

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

6429

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

6430

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

6431

\[ {}y^{\prime \prime }-\frac {y^{\prime }}{x}-x y-x^{2}-\frac {1}{x} = 0 \]

6432

\[ {}y^{\prime \prime }-\frac {y^{\prime }}{x}-x^{2} y-x^{3}-\frac {1}{x} = 0 \]

6433

\[ {}y^{\prime \prime }-\frac {y^{\prime }}{x}-x^{3} y-x^{4}-\frac {1}{x} = 0 \]

6434

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

6435

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

6436

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

6437

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

6438

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

6439

\[ {}w^{\prime } = -\frac {1}{2}-\frac {\sqrt {1-12 w}}{2} \]

6440

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

6441

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

6442

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

6443

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

6444

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

6445

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

6446

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

6447

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

6448

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

6449

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

6450

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

6451

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

6452

\[ {}x^{4} y^{\prime \prime }+x^{3} y^{\prime }-4 x^{2} y = 1 \]

6453

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

6454

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

6455

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

6456

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

6457

\[ {}5 x^{5} y^{\prime \prime \prime \prime }+4 x^{4} y^{\prime \prime \prime }+x^{2} y^{\prime }+x y = 0 \]

6458

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

6459

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

6460

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

6461

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

6462

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

6463

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

6464

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

6465

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

6466

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

6467

\[ {}4 x^{2} y^{\prime \prime }+y = 8 \sqrt {x}\, \left (\ln \relax (x )+1\right ) \]

6468

\[ {}v v^{\prime } = \frac {2 v^{2}}{r^{3}}+\frac {\lambda r}{3} \]

6469

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

6470

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

6471

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

6472

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

6473

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

6474

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

6475

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

6476

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

6477

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

6478

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

6479

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

6480

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

6481

\[ {}x^{2} y^{\prime \prime }+\left (\cos \relax (x )-1\right ) y^{\prime }+y \,{\mathrm e}^{x} = 0 \]

6482

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

6483

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

6484

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

6485

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

6486

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

6487

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

6488

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

6489

\[ {}y^{\prime \prime }+\left (x -6\right ) y = 0 \]

6490

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

6491

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

6492

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

6493

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

6494

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

6495

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

6496

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

6497

\[ {}2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y = 0 \]

6498

\[ {}x^{2} \left (x +3\right ) y^{\prime \prime }+5 x \left (x +1\right ) y^{\prime }-\left (1-4 x \right ) y = 0 \]

6499

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

6500

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