4.46 Problems 4501 to 4600

Table 4.91: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

4501

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

4502

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

4503

\[ {}\tan \left (\theta \right ) r^{\prime }-r = \tan \left (\theta \right )^{2} \]

4504

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

4505

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

4506

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

4507

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

4508

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

4509

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

4510

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

4511

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

4512

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

4513

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

4514

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

4515

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

4516

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

4517

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

4518

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

4519

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

4520

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

4521

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

4522

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

4523

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

4524

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

4525

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

4526

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

4527

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

4528

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

4529

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

4530

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

4531

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

4532

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

4533

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

4534

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

4535

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

4536

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

4537

\[ {}y^{\prime }+a y = k \,{\mathrm e}^{b x} \]

4538

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

4539

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

4540

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

4541

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

4542

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

4543

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

4544

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

4545

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

4546

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

4547

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

4548

\[ {}x y^{\prime }+a y+b \,x^{n} = 0 \]

4549

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

4550

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

4551

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

4552

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

4553

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

4554

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

4555

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

4556

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

4557

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

4558

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

4559

\[ {}y^{2}+12 x^{2} y+\left (2 x y+4 x^{3}\right ) y^{\prime } = 0 \]

4560

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

4561

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

4562

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

4563

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

4564

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

4565

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

4566

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

4567

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

4568

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

4569

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

4570

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

4571

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

4572

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

4573

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

4574

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

4575

\[ {}6 y^{\prime \prime }-11 y^{\prime }+4 y = 0 \]

4576

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

4577

\[ {}y^{\prime \prime \prime }+y^{\prime \prime }-10 y^{\prime }-6 y = 0 \]

4578

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

4579

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

4580

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

4581

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

4582

\[ {}y^{\prime \prime }+4 k y^{\prime }-12 k^{2} y = 0 \]

4583

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

4584

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

4585

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

4586

\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = 0 \]

4587

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

4588

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

4589

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

4590

\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-11 y^{\prime \prime }-12 y^{\prime }+36 y = 0 \]

4591

\[ {}36 y^{\prime \prime \prime \prime }-37 y^{\prime \prime }+4 y^{\prime }+5 y = 0 \]

4592

\[ {}y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+36 y = 0 \]

4593

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

4594

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

4595

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

4596

\[ {}y^{\prime \prime }-4 y^{\prime }+20 y = 0 \]

4597

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

4598

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

4599

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

4600

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