2.2.87 Problems 8601 to 8700

Table 2.175: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

8601

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

[[_2nd_order, _with_linear_symmetries]]

0.654

8602

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

[[_Emden, _Fowler]]

0.609

8603

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

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

0.611

8604

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

[[_Emden, _Fowler]]

0.592

8605

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

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

0.609

8606

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

[[_Emden, _Fowler]]

0.911

8607

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

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

0.885

8608

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

[[_Emden, _Fowler]]

0.440

8609

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

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

0.779

8610

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

[[_Emden, _Fowler]]

0.740

8611

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

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

0.811

8612

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

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

0.849

8613

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 0 \]

[[_Emden, _Fowler]]

0.863

8614

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

[[_Emden, _Fowler]]

3.397

8615

\[ {}x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-8 x y^{\prime }+8 y = 0 \]

[[_3rd_order, _with_linear_symmetries]]

0.107

8616

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

[[_2nd_order, _with_linear_symmetries]]

0.691

8617

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

[[_2nd_order, _with_linear_symmetries]]

0.730

8618

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

[[_2nd_order, _with_linear_symmetries]]

0.732

8619

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

[[_2nd_order, _with_linear_symmetries]]

0.621

8620

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

[[_2nd_order, _exact, _linear, _homogeneous]]

0.671

8621

\[ {}x^{2} y^{\prime \prime }-x \left (3 x +1\right ) y^{\prime }+\left (1-6 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.763

8622

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

[[_2nd_order, _with_linear_symmetries]]

0.731

8623

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

[[_2nd_order, _with_linear_symmetries]]

0.700

8624

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

[[_2nd_order, _with_linear_symmetries]]

0.727

8625

\[ {}4 \left (x -4\right )^{2} y^{\prime \prime }+\left (x -4\right ) \left (x -8\right ) y^{\prime }+x y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.781

8626

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

[[_2nd_order, _with_linear_symmetries]]

0.734

8627

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

[[_2nd_order, _with_linear_symmetries]]

0.480

8628

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

[[_2nd_order, _with_linear_symmetries]]

0.534

8629

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

[[_2nd_order, _with_linear_symmetries]]

0.815

8630

\[ {}4 x^{2} y^{\prime \prime }+8 x \left (x +1\right ) y^{\prime }+y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.801

8631

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

[[_2nd_order, _with_linear_symmetries]]

0.778

8632

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

[[_2nd_order, _exact, _linear, _homogeneous]]

0.645

8633

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

[[_2nd_order, _with_linear_symmetries]]

0.836

8634

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

[[_2nd_order, _with_linear_symmetries]]

0.924

8635

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

[[_2nd_order, _with_linear_symmetries]]

0.830

8636

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

[_Laguerre]

0.809

8637

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

[[_2nd_order, _with_linear_symmetries]]

0.888

8638

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

[[_2nd_order, _with_linear_symmetries]]

0.877

8639

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

[[_2nd_order, _with_linear_symmetries]]

0.842

8640

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

[[_2nd_order, _exact, _linear, _homogeneous]]

0.750

8641

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

[[_2nd_order, _exact, _linear, _homogeneous]]

0.861

8642

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

[[_2nd_order, _exact, _linear, _homogeneous]]

0.780

8643

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

[[_2nd_order, _with_linear_symmetries]]

0.842

8644

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

[[_2nd_order, _with_linear_symmetries]]

0.801

8645

\[ {}x \left (x +3\right ) y^{\prime \prime }-9 y^{\prime }-6 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.778

8646

\[ {}x \left (1-2 x \right ) y^{\prime \prime }-2 \left (x +2\right ) y^{\prime }+8 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.860

8647

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

[[_2nd_order, _with_linear_symmetries]]

0.646

8648

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

[[_2nd_order, _with_linear_symmetries]]

0.985

8649

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

[[_Emden, _Fowler]]

1.177

8650

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

[[_2nd_order, _with_linear_symmetries]]

1.401

8651

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

[[_Emden, _Fowler]]

1.298

8652

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

[[_2nd_order, _with_linear_symmetries]]

1.437

8653

\[ {}x^{2} y^{\prime \prime }-x \left (6+x \right ) y^{\prime }+10 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

1.452

8654

\[ {}x y^{\prime \prime }+\left (2 x +3\right ) y^{\prime }+8 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

1.382

8655

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

[_Jacobi]

1.366

8656

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

[_Jacobi]

1.400

8657

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

[_Bessel]

0.701

8658

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

[_Bessel]

1.241

8659

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+\left (8+5 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

1.410

8660

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

[_Laguerre]

1.394

8661

\[ {}9 x^{2} y^{\prime \prime }-15 x y^{\prime }+7 \left (x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

1.457

8662

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

[[_2nd_order, _with_linear_symmetries]]

1.475

8663

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

[[_2nd_order, _with_linear_symmetries]]

0.829

8664

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

[_Jacobi]

1.000

8665

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

[[_2nd_order, _with_linear_symmetries]]

0.663

8666

\[ {}x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-\left (6 x^{2}-3 x +1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.911

8667

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

[[_2nd_order, _with_linear_symmetries]]

1.415

8668

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

[[_2nd_order, _with_linear_symmetries]]

0.825

8669

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

[[_2nd_order, _with_linear_symmetries]]

0.724

8670

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

[[_2nd_order, _with_linear_symmetries]]

0.882

8671

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

[[_2nd_order, _exact, _linear, _homogeneous]]

1.378

8672

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

[_Laguerre]

1.409

8673

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

[[_2nd_order, _with_linear_symmetries]]

0.862

8674

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

[[_2nd_order, _with_linear_symmetries]]

0.867

8675

\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+2 x \left (x^{2}+3\right ) y^{\prime }+6 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.798

8676

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-10 x y^{\prime }-18 y = 0 \]

[_Gegenbauer]

0.533

8677

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

[[_2nd_order, _with_linear_symmetries]]

0.864

8678

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

[_erf]

0.379

8679

\[ {}x \left (-x^{2}+1\right ) y^{\prime \prime }-\left (x^{2}+7\right ) y^{\prime }+4 x y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

0.776

8680

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

[[_2nd_order, _with_linear_symmetries]]

0.929

8681

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

[[_2nd_order, _with_linear_symmetries]]

0.898

8682

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

[[_2nd_order, _with_linear_symmetries]]

0.662

8683

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

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

0.826

8684

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

[[_2nd_order, _with_linear_symmetries]]

0.646

8685

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

[[_2nd_order, _with_linear_symmetries]]

0.806

8686

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

[[_2nd_order, _exact, _linear, _homogeneous]]

0.414

8687

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

[[_2nd_order, _with_linear_symmetries]]

0.908

8688

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

[[_2nd_order, _with_linear_symmetries]]

0.838

8689

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

[[_2nd_order, _with_linear_symmetries]]

0.611

8690

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

[[_2nd_order, _with_linear_symmetries]]

0.877

8691

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

[[_2nd_order, _exact, _linear, _homogeneous]]

0.721

8692

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

[[_2nd_order, _exact, _linear, _homogeneous]]

0.744

8693

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

[[_Bessel, _modified]]

1.330

8694

\[ {}x \left (1-2 x \right ) y^{\prime \prime }-2 \left (x +2\right ) y^{\prime }+18 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.898

8695

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

[[_2nd_order, _exact, _linear, _homogeneous]]

0.774

8696

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

[[_2nd_order, _with_linear_symmetries]]

0.750

8697

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

[_separable]

1.545

8698

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

[_separable]

2.938

8699

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

[_linear]

1.684

8700

\[ {}t x^{\prime }+2 x = 4 \,{\mathrm e}^{t} \]

[_linear]

1.371