2.2.70 Problems 6901 to 7000

Table 2.141: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

6901

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

[_linear]

1.679

6902

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

[_linear]

1.494

6903

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

[_linear]

1.144

6904

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

[_separable]

2.135

6905

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

[_separable]

4.051

6906

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

[_quadrature]

1.701

6907

\[ {}5 y^{\prime } = 2 y \]

[_quadrature]

1.632

6908

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

[[_2nd_order, _missing_x]]

0.860

6909

\[ {}2 y^{\prime \prime }+7 y^{\prime }-4 y = 0 \]

[[_2nd_order, _missing_x]]

0.879

6910

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

[[_2nd_order, _missing_y]]

0.737

6911

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

[[_Emden, _Fowler]]

0.460

6912

\[ {}x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = 0 \]

[[_Emden, _Fowler]]

0.866

6913

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

[[_3rd_order, _missing_y]]

0.169

6914

\[ {}3 x y^{\prime }+5 y = 10 \]

[_separable]

2.297

6915

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

[_quadrature]

1.930

6916

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

[_quadrature]

1.740

6917

\[ {}y^{\prime \prime }+4 y^{\prime }+6 y = 10 \]

[[_2nd_order, _missing_x]]

5.478

6918

\[ {}{y^{\prime }}^{2} = 4 y \]

[_quadrature]

0.368

6919

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

[_quadrature]

0.712

6920

\[ {}y y^{\prime }+\sqrt {16-y^{2}} = 0 \]

[_quadrature]

2.693

6921

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

[[_homogeneous, ‘class C‘], _dAlembert]

0.404

6922

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

system_of_ODEs

0.469

6923

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

system_of_ODEs

0.027

6924

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

[_quadrature]

41.661

6925

\[ {}y^{\prime \prime }+2 y^{\prime }+4 y = 5 \sin \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

73.831

6926

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

[_quadrature]

0.175

6927

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

[[_2nd_order, _quadrature]]

0.495

6928

\[ {}x {y^{\prime }}^{2}-4 y^{\prime }-12 x^{3} = 0 \]

[_quadrature]

0.303

6929

\[ {}y^{\prime } = 5-y \]

[_quadrature]

1.421

6930

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

[_quadrature]

4.912

6931

\[ {}y^{\prime \prime \prime \prime }-20 y^{\prime \prime \prime }+158 y^{\prime \prime }-580 y^{\prime }+841 y = 0 \]

[[_high_order, _missing_x]]

0.075

6932

\[ {}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+20 x y^{\prime }-78 y = 0 \]

[[_3rd_order, _with_linear_symmetries]]

0.115

6933

\[ {}y^{\prime } = y-y^{2} \]
i.c.

[_quadrature]

2.739

6934

\[ {}y^{\prime } = y-y^{2} \]
i.c.

[_quadrature]

2.802

6935

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

[_separable]

2.456

6936

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

[_separable]

2.500

6937

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

[_separable]

2.487

6938

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

[_separable]

2.519

6939

\[ {}x^{\prime \prime }+x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

30.081

6940

\[ {}x^{\prime \prime }+x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2.020

6941

\[ {}x^{\prime \prime }+x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2.729

6942

\[ {}x^{\prime \prime }+x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

3.084

6943

\[ {}y^{\prime \prime }-y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2.542

6944

\[ {}y^{\prime \prime }-y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2.292

6945

\[ {}y^{\prime \prime }-y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

2.302

6946

\[ {}y^{\prime \prime }-y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1.593

6947

\[ {}y^{\prime } = 3 y^{{2}/{3}} \]
i.c.

[_quadrature]

2.029

6948

\[ {}x y^{\prime } = 2 y \]
i.c.

[_separable]

2.570

6949

\[ {}y^{\prime } = y^{{2}/{3}} \]

[_quadrature]

2.008

6950

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

[[_homogeneous, ‘class G‘]]

9.498

6951

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

[_separable]

1.603

6952

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

[[_linear, ‘class A‘]]

1.215

6953

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

[_separable]

1.320

6954

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

[_separable]

1.358

6955

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

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

3714.248

6956

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

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

4.999

6957

\[ {}y^{\prime } = \sqrt {y^{2}-9} \]
i.c.

[_quadrature]

168.398

6958

\[ {}y^{\prime } = \sqrt {y^{2}-9} \]
i.c.

[_quadrature]

3.195

6959

\[ {}y^{\prime } = \sqrt {y^{2}-9} \]
i.c.

[_quadrature]

3.083

6960

\[ {}y^{\prime } = \sqrt {y^{2}-9} \]
i.c.

[_quadrature]

21.756

6961

\[ {}x y^{\prime } = y \]
i.c.

[_separable]

1.267

6962

\[ {}y^{\prime } = 1+y^{2} \]
i.c.

[_quadrature]

3.071

6963

\[ {}y^{\prime } = y^{2} \]
i.c.

[_quadrature]

2.383

6964

\[ {}y^{\prime } = y^{2} \]
i.c.

[_quadrature]

2.771

6965

\[ {}y^{\prime } = y^{2} \]
i.c.

[_quadrature]

1.938

6966

\[ {}y^{\prime } = y^{2} \]
i.c.

[_quadrature]

2.181

6967

\[ {}y^{\prime } = y^{2} \]
i.c.

[_quadrature]

2.707

6968

\[ {}y y^{\prime } = 3 x \]
i.c.

[_separable]

4.698

6969

\[ {}y y^{\prime } = 3 x \]
i.c.

[_separable]

3.918

6970

\[ {}y y^{\prime } = 3 x \]
i.c.

[_separable]

7.868

6971

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

[[_2nd_order, _missing_x]]

1.786

6972

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

[[_2nd_order, _missing_x]]

1.574

6973

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

[[_2nd_order, _missing_x]]

1.812

6974

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

[[_2nd_order, _missing_x]]

2.559

6975

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

[[_2nd_order, _missing_x]]

1.673

6976

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

[[_2nd_order, _missing_x]]

1.736

6977

\[ {}y^{\prime } = x -2 y \]
i.c.

[[_linear, ‘class A‘]]

1.558

6978

\[ {}y^{\prime } = x^{2}+y^{2} \]
i.c.

[[_Riccati, _special]]

1.559

6979

\[ {}2 y^{\prime \prime }-3 y^{2} = 0 \]
i.c.

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

2.611

6980

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

[[_linear, ‘class A‘]]

1.299

6981

\[ {}y^{\prime } = x \sqrt {y} \]
i.c.

[_separable]

6.040

6982

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

[_quadrature]

0.821

6983

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

[_quadrature]

0.801

6984

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

[_quadrature]

1.469

6985

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

[_separable]

1.619

6986

\[ {}y^{\prime \prime }+9 y = 18 \]

[[_2nd_order, _missing_x]]

2.550

6987

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

[[_2nd_order, _missing_y]]

0.800

6988

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

[[_2nd_order, _missing_x]]

1.619

6989

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

[_quadrature]

1.940

6990

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

[_separable]

2.223

6991

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

[_separable]

3.845

6992

\[ {}x y^{\prime }+y = 2 x \]
i.c.

[_linear]

1.794

6993

\[ {}y^{\prime } = x^{2}+y^{2} \]
i.c.

[[_Riccati, _special]]

1.440

6994

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

[_quadrature]

0.460

6995

\[ {}y^{\prime } = 6 \sqrt {y}+5 x^{3} \]
i.c.

[_Chini]

1.235

6996

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

[[_2nd_order, _linear, _nonhomogeneous]]

3.699

6997

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

[[_2nd_order, _linear, _nonhomogeneous]]

2.816

6998

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

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

1.059

6999

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

[[_2nd_order, _linear, _nonhomogeneous]]

5.702

7000

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

[_linear]

1.671