2.2.157 Problems 15601 to 15700

Table 2.315: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

15601

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

[_quadrature]

0.453

15602

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

[_separable]

0.535

15603

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

[_separable]

0.675

15604

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

[[_2nd_order, _with_linear_symmetries]]

11.536

15605

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

[[_2nd_order, _with_linear_symmetries]]

4.706

15606

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

[[_2nd_order, _with_linear_symmetries]]

52.899

15607

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

[[_2nd_order, _with_linear_symmetries]]

5.342

15608

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

[[_2nd_order, _with_linear_symmetries]]

1.393

15609

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

[[_2nd_order, _with_linear_symmetries]]

0.461

15610

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

[[_2nd_order, _with_linear_symmetries]]

0.679

15611

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

[[_2nd_order, _with_linear_symmetries]]

2.066

15612

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

[_separable]

0.564

15613

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

[_separable]

0.543

15614

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

[_separable]

0.571

15615

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

[_separable]

0.569

15616

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

[[_2nd_order, _with_linear_symmetries]]

0.620

15617

\[ {}y^{\prime \prime }+3 x y^{\prime }-y \,{\mathrm e}^{x} = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.674

15618

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

[[_2nd_order, _with_linear_symmetries]]

0.630

15619

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

[_Titchmarsh]

0.572

15620

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

[[_Emden, _Fowler]]

0.702

15621

\[ {}y^{\prime \prime }+\left (6 x^{2}+2 x +1\right ) y^{\prime }+\left (2+12 x \right ) y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

0.476

15622

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

[_separable]

0.805

15623

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

[_separable]

0.907

15624

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

[_separable]

1.162

15625

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

[_separable]

0.860

15626

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

[[_2nd_order, _with_linear_symmetries]]

0.636

15627

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

[[_2nd_order, _with_linear_symmetries]]

0.852

15628

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

[[_2nd_order, _exact, _linear, _homogeneous]]

0.858

15629

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

[[_2nd_order, _with_linear_symmetries]]

0.750

15630

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

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

0.358

15631

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

[[_2nd_order, _exact, _linear, _homogeneous]]

0.537

15632

\[ {}\left (-1+x \right )^{2} y^{\prime \prime }-5 \left (-1+x \right ) y^{\prime }+9 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.448

15633

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

[[_2nd_order, _missing_y]]

0.381

15634

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

[[_2nd_order, _with_linear_symmetries]]

0.510

15635

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

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

0.455

15636

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

[[_2nd_order, _with_linear_symmetries]]

1.026

15637

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

[[_Emden, _Fowler]]

0.586

15638

\[ {}\left (-x^{4}+x^{3}\right ) y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+827 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

2.259

15639

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

[[_2nd_order, _with_linear_symmetries]]

0.805

15640

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

[[_2nd_order, _with_linear_symmetries]]

1.036

15641

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

[[_2nd_order, _with_linear_symmetries]]

0.703

15642

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

[[_2nd_order, _with_linear_symmetries]]

1.702

15643

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

[[_Emden, _Fowler]]

0.402

15644

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

[[_2nd_order, _with_linear_symmetries]]

0.677

15645

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

[[_2nd_order, _with_linear_symmetries]]

0.635

15646

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

[[_2nd_order, _with_linear_symmetries]]

1.343

15647

\[ {}\left (-9 x^{4}+x^{2}\right ) y^{\prime \prime }-6 x y^{\prime }+10 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.773

15648

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

[[_2nd_order, _with_linear_symmetries]]

0.733

15649

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

[_Lienard]

0.453

15650

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

[_Bessel]

1.253

15651

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

[[_2nd_order, _with_linear_symmetries]]

0.717

15652

\[ {}x^{2} y^{\prime \prime }-\left (2 x^{2}+5 x \right ) y^{\prime }+\left (9+4 x \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.727

15653

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

[[_2nd_order, _with_linear_symmetries]]

0.780

15654

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

[_Laguerre]

1.419

15655

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

[[_2nd_order, _with_linear_symmetries]]

0.725

15656

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

[[_2nd_order, _with_linear_symmetries]]

0.471

15657

\[ {}\left (9 x^{3}+9 x^{2}\right ) y^{\prime \prime }+\left (27 x^{2}+9 x \right ) y^{\prime }+\left (8 x -1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.687

15658

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

[[_2nd_order, _exact, _linear, _homogeneous]]

1.303

15659

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

[[_2nd_order, _with_linear_symmetries]]

0.645

15660

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

[[_2nd_order, _with_linear_symmetries]]

0.722

15661

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

[[_2nd_order, _with_linear_symmetries]]

0.766

15662

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

[[_2nd_order, _with_linear_symmetries]]

0.679

15663

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

[[_2nd_order, _with_linear_symmetries]]

0.782

15664

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

[_Lienard]

0.446

15665

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

[[_2nd_order, _with_linear_symmetries]]

0.870

15666

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

[[_2nd_order, _with_linear_symmetries]]

0.706

15667

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

[[_2nd_order, _with_linear_symmetries]]

1.528

15668

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

[[_2nd_order, _with_linear_symmetries]]

0.737

15669

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

[[_2nd_order, _with_linear_symmetries]]

1.358

15670

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

[[_2nd_order, _with_linear_symmetries]]

0.858

15671

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

[[_2nd_order, _with_linear_symmetries]]

0.828

15672

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

[[_2nd_order, _exact, _linear, _homogeneous]]

1.351

15673

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

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

0.829

15674

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

[[_2nd_order, _with_linear_symmetries]]

0.694

15675

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

[_Lienard]

0.446

15676

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

[_Laguerre]

1.444

15677

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

[[_2nd_order, _with_linear_symmetries]]

1.452

15678

\[ {}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=1-2 x \end {array}\right ] \]

system_of_ODEs

0.684

15679

\[ {}\left [\begin {array}{c} x^{\prime }=4 x-3 y \\ y^{\prime }=6 x-7 y \end {array}\right ] \]

system_of_ODEs

0.495

15680

\[ {}\left [\begin {array}{c} t x^{\prime }+2 x=15 y \\ t y^{\prime }=x \end {array}\right ] \]

system_of_ODEs

0.032

15681

\[ {}\left [\begin {array}{c} x^{\prime }=x+2 y \\ y^{\prime }=5 x-2 y \end {array}\right ] \]
i.c.

system_of_ODEs

0.634

15682

\[ {}\left [\begin {array}{c} x^{\prime }=5 x+4 y \\ y^{\prime }=8 x+y \end {array}\right ] \]
i.c.

system_of_ODEs

0.607

15683

\[ {}\left [\begin {array}{c} x^{\prime }=4 x+2 y \\ y^{\prime }=3 x-y \end {array}\right ] \]
i.c.

system_of_ODEs

0.637

15684

\[ {}\left [\begin {array}{c} x^{\prime }=x+2 y \\ y^{\prime }=5 x-2 y \end {array}\right ] \]
i.c.

system_of_ODEs

0.635

15685

\[ {}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=2 x \end {array}\right ] \]

system_of_ODEs

0.464

15686

\[ {}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=-2 x \end {array}\right ] \]

system_of_ODEs

0.556

15687

\[ {}\left [\begin {array}{c} x^{\prime }=-2 y \\ y^{\prime }=8 x \end {array}\right ] \]

system_of_ODEs

0.542

15688

\[ {}\left [\begin {array}{c} x^{\prime }=4 x-13 y \\ y^{\prime }=x \end {array}\right ] \]
i.c.

system_of_ODEs

0.638

15689

\[ {}\left [\begin {array}{c} x^{\prime }=3 x+2 y \\ y^{\prime }=-2 x+3 y \end {array}\right ] \]
i.c.

system_of_ODEs

0.564

15690

\[ {}\left [\begin {array}{c} x^{\prime }=8 x+2 y-17 \\ y^{\prime }=4 x+y-13 \end {array}\right ] \]
i.c.

system_of_ODEs

0.784

15691

\[ {}\left [\begin {array}{c} x^{\prime }=8 x+2 y+7 \,{\mathrm e}^{2 t} \\ y^{\prime }=4 x+y-7 \,{\mathrm e}^{2 t} \end {array}\right ] \]
i.c.

system_of_ODEs

0.600

15692

\[ {}\left [\begin {array}{c} x^{\prime }=4 x+3 y-6 \,{\mathrm e}^{3 t} \\ y^{\prime }=x+6 y+2 \,{\mathrm e}^{3 t} \end {array}\right ] \]
i.c.

system_of_ODEs

0.625

15693

\[ {}\left [\begin {array}{c} x^{\prime }=-y \\ y^{\prime }=4 x+24 t \end {array}\right ] \]
i.c.

system_of_ODEs

0.683

15694

\[ {}\left [\begin {array}{c} x^{\prime }=4 x-13 y \\ y^{\prime }=x+19 \cos \left (4 t \right )-13 \sin \left (4 t \right ) \end {array}\right ] \]
i.c.

system_of_ODEs

1.774

15695

\[ {}\left [\begin {array}{c} x^{\prime }=4 x+3 y+5 \operatorname {Heaviside}\left (t -2\right ) \\ y^{\prime }=x+6 y+17 \operatorname {Heaviside}\left (t -2\right ) \end {array}\right ] \]
i.c.

system_of_ODEs

0.766

15696

\[ {}\left [\begin {array}{c} x^{\prime }=5 x+4 y \\ y^{\prime }=8 x+y \end {array}\right ] \]

system_of_ODEs

0.486

15697

\[ {}\left [\begin {array}{c} x^{\prime }=2 x-5 y \\ y^{\prime }=3 x-7 y \end {array}\right ] \]

system_of_ODEs

0.622

15698

\[ {}\left [\begin {array}{c} x^{\prime }=2 x-5 y+4 \\ y^{\prime }=3 x-7 y+5 \end {array}\right ] \]

system_of_ODEs

1.037

15699

\[ {}\left [\begin {array}{c} x^{\prime }=3 x+y \\ y^{\prime }=6 x+2 y \end {array}\right ] \]

system_of_ODEs

0.481

15700

\[ {}\left [\begin {array}{c} x^{\prime }=x y-6 y \\ y^{\prime }=x-y-5 \end {array}\right ] \]

system_of_ODEs

0.033