4.56 Problems 5501 to 5600

Table 4.111: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

5501

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

5502

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

5503

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

5504

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

5505

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

5506

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

5507

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

5508

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

5509

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

5510

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

5511

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

5512

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

5513

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

5514

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

5515

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

5516

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

5517

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

5518

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

5519

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

5520

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

5521

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

5522

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

5523

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

5524

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

5525

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

5526

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

5527

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

5528

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

5529

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

5530

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

5531

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

5532

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

5533

\[ {}\left (x^{2}-25\right ) y^{\prime \prime }+2 x y^{\prime }+y = 0 \]

5534

\[ {}\left (x^{2}-25\right ) y^{\prime \prime }+2 x y^{\prime }+y = 0 \]

5535

\[ {}\left (x^{2}-2 x +10\right ) y^{\prime \prime }+x y^{\prime }-4 y = 0 \]

5536

\[ {}\left (x^{2}-2 x +10\right ) y^{\prime \prime }+x y^{\prime }-4 y = 0 \]

5537

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

5538

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

5539

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

5540

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

5541

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

5542

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

5543

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

5544

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

5545

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

5546

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-6 y = 0 \]

5547

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

5548

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

5549

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

5550

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

5551

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

5552

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

5553

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

5554

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

5555

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

5556

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

5557

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

5558

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

5559

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

5560

\[ {}\left (x^{3}+4 x \right ) y^{\prime \prime }-2 x y^{\prime }+6 y = 0 \]

5561

\[ {}x^{2} \left (x -5\right )^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}-25\right ) y = 0 \]

5562

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

5563

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

5564

\[ {}x^{3} \left (x^{2}-25\right ) \left (-2+x \right )^{2} y^{\prime \prime }+3 x \left (-2+x \right ) y^{\prime }+7 \left (5+x \right ) y = 0 \]

5565

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

5566

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

5567

\[ {}x y^{\prime \prime }+\left (x +3\right ) y^{\prime }+7 x^{2} y = 0 \]

5568

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

5569

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

5570

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

5571

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

5572

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

5573

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

5574

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

5575

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

5576

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

5577

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {4}{9}\right ) y = 0 \]

5578

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

5579

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

5580

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

5581

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

5582

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

5583

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

5584

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

5585

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

5586

\[ {}x y^{\prime \prime }+\left (x -6\right ) y^{\prime }-3 y = 0 \]

5587

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

5588

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

5589

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

5590

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

5591

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

5592

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

5593

\[ {}4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-25\right ) y = 0 \]

5594

\[ {}16 x^{2} y^{\prime \prime }+16 x y^{\prime }+\left (16 x^{2}-1\right ) y = 0 \]

5595

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

5596

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

5597

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (9 x^{2}-4\right ) y = 0 \]

5598

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (36 x^{2}-\frac {1}{4}\right ) y = 0 \]

5599

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (25 x^{2}-\frac {4}{9}\right ) y = 0 \]

5600

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (2 x^{2}-64\right ) y = 0 \]