2.2.150 Problems 14901 to 15000

Table 2.301: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

14901

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

[_quadrature]

37.606

14902

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

[[_linear, ‘class A‘]]

1.427

14903

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

[_quadrature]

43.776

14904

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

[_separable]

4.183

14905

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

[[_2nd_order, _quadrature]]

1.980

14906

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

[[_2nd_order, _quadrature]]

0.480

14907

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

[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]]

0.116

14908

\[ {}y^{\prime \prime }+3 y^{\prime }+8 y = {\mathrm e}^{-x^{2}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

27.324

14909

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

[[_2nd_order, _missing_y]]

0.548

14910

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

[_quadrature]

0.454

14911

\[ {}y^{\prime } = 20 \,{\mathrm e}^{-4 x} \]

[_quadrature]

0.541

14912

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

[_quadrature]

0.509

14913

\[ {}\sqrt {x +4}\, y^{\prime } = 1 \]

[_quadrature]

0.606

14914

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

[_quadrature]

0.590

14915

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

[_quadrature]

0.520

14916

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

[_quadrature]

0.624

14917

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

[_quadrature]

0.648

14918

\[ {}1 = x^{2}-9 y^{\prime } \]

[_quadrature]

0.460

14919

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

[[_2nd_order, _quadrature]]

2.169

14920

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

[[_2nd_order, _quadrature]]

1.877

14921

\[ {}y^{\prime \prime \prime \prime } = 1 \]

[[_high_order, _quadrature]]

0.090

14922

\[ {}y^{\prime } = 40 x \,{\mathrm e}^{2 x} \]
i.c.

[_quadrature]

0.769

14923

\[ {}\left (x +6\right )^{{1}/{3}} y^{\prime } = 1 \]
i.c.

[_quadrature]

0.682

14924

\[ {}y^{\prime } = \frac {-1+x}{x +1} \]
i.c.

[_quadrature]

0.767

14925

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

[_quadrature]

0.836

14926

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

[_quadrature]

2.224

14927

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

[_quadrature]

0.805

14928

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

[[_2nd_order, _quadrature]]

1.563

14929

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

[_quadrature]

0.612

14930

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

[_quadrature]

0.763

14931

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

[_quadrature]

0.791

14932

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

[_quadrature]

0.563

14933

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

[_quadrature]

0.537

14934

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

[_quadrature]

0.520

14935

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

[_quadrature]

0.514

14936

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

[_quadrature]

0.736

14937

\[ {}y^{\prime } = \frac {x}{\sqrt {x^{2}+5}} \]
i.c.

[_quadrature]

1.146

14938

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

[_quadrature]

0.769

14939

\[ {}y^{\prime } = {\mathrm e}^{-9 x^{2}} \]
i.c.

[_quadrature]

0.606

14940

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

[_quadrature]

0.881

14941

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

[_quadrature]

0.929

14942

\[ {}y^{\prime } = \left \{\begin {array}{cc} 0 & x <0 \\ 1 & 0\le x \end {array}\right . \]
i.c.

[_quadrature]

0.478

14943

\[ {}y^{\prime } = \left \{\begin {array}{cc} 0 & x <1 \\ 1 & 1\le x \end {array}\right . \]
i.c.

[_quadrature]

0.494

14944

\[ {}y^{\prime } = \left \{\begin {array}{cc} 0 & x <1 \\ 1 & 1\le x <2 \\ 0 & 2\le x \end {array}\right . \]
i.c.

[_quadrature]

0.528

14945

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

[_separable]

1.564

14946

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

[‘y=_G(x,y’)‘]

12.661

14947

\[ {}y^{\prime }-y^{3} = 8 \]

[_quadrature]

82.019

14948

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

[_separable]

1.944

14949

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

[[_Riccati, _special]]

1.077

14950

\[ {}y^{3}-25 y+y^{\prime } = 0 \]

[_quadrature]

3.625

14951

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

[_separable]

2.083

14952

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

[_separable]

3.553

14953

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

[_quadrature]

1.342

14954

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

[_Riccati]

1.655

14955

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

[_quadrature]

1.690

14956

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

[_separable]

2.406

14957

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

[_linear]

1.858

14958

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

[_rational, _Riccati]

1.960

14959

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

[_quadrature]

0.492

14960

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

[_quadrature]

1.681

14961

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

[_separable]

1.555

14962

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

[[_linear, ‘class A‘]]

1.358

14963

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

[_separable]

1.639

14964

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

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

2.327

14965

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

[_separable]

1.930

14966

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

[_separable]

4.642

14967

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

[_quadrature]

6.883

14968

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

[_separable]

3.699

14969

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

[_separable]

2.345

14970

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

[_separable]

2.183

14971

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

[_separable]

2.648

14972

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

[_separable]

4.807

14973

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

[_separable]

2.059

14974

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

[_separable]

3.099

14975

\[ {}y y^{\prime } = 3 \sqrt {x y^{2}+9 x} \]
i.c.

[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]

4.914

14976

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

[_separable]

1.554

14977

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

[_quadrature]

1.538

14978

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

[_separable]

2.220

14979

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

[_quadrature]

2.810

14980

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

[_separable]

1.437

14981

\[ {}y^{\prime } = 200 y-2 y^{2} \]

[_quadrature]

2.360

14982

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

[_separable]

1.566

14983

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

[_separable]

1.678

14984

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

[_separable]

2.434

14985

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

[_quadrature]

1.840

14986

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

[_separable]

1.723

14987

\[ {}y^{\prime } = \frac {6 x^{2}+4}{3 y^{2}-4 y} \]

[_separable]

1.694

14988

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

[_separable]

2.398

14989

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

[_separable]

11.540

14990

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

[_quadrature]

1.675

14991

\[ {}y^{\prime } = {\mathrm e}^{-y}+1 \]

[_quadrature]

2.156

14992

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

[_separable]

3.746

14993

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

[_separable]

1.684

14994

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

[_separable]

2.088

14995

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

[_separable]

2.204

14996

\[ {}y^{\prime } = 200 y-2 y^{2} \]

[_quadrature]

2.441

14997

\[ {}y^{\prime }-2 y = -10 \]
i.c.

[_quadrature]

2.062

14998

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

[_separable]

3.020

14999

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

[_separable]

1.839

15000

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

[_separable]

2.960