2.2.160 Problems 15901 to 16000

Table 2.321: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

15901

\[ {}y^{\prime }-\frac {9 x y}{9 x^{2}+49} = x \]

[_linear]

3.486

15902

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

[_linear]

2.058

15903

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

[_linear]

1.609

15904

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

[_separable]

1.516

15905

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

[[_1st_order, _with_exponential_symmetries]]

1.177

15906

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

[[_linear, ‘class A‘]]

1.264

15907

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

[[_homogeneous, ‘class G‘], _rational]

2.402

15908

\[ {}x^{\prime } = \frac {3 x t^{2}}{-t^{3}+1} \]

[_separable]

1.751

15909

\[ {}p^{\prime } = t^{3}+\frac {p}{t} \]

[_linear]

1.608

15910

\[ {}v^{\prime }+v = {\mathrm e}^{-s} \]

[[_linear, ‘class A‘]]

1.313

15911

\[ {}y^{\prime }-y = 4 \,{\mathrm e}^{t} \]
i.c.

[[_linear, ‘class A‘]]

1.605

15912

\[ {}y^{\prime }+y = {\mathrm e}^{-t} \]
i.c.

[[_linear, ‘class A‘]]

1.606

15913

\[ {}y^{\prime }+3 t^{2} y = {\mathrm e}^{-t^{3}} \]
i.c.

[_linear]

2.371

15914

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

[_separable]

2.029

15915

\[ {}t y^{\prime }+y = \cos \left (t \right ) \]
i.c.

[_linear]

1.660

15916

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

[_linear]

1.636

15917

\[ {}\left (1+{\mathrm e}^{t}\right ) y^{\prime }+{\mathrm e}^{t} y = t \]
i.c.

[_linear]

2.101

15918

\[ {}\left (t^{2}+4\right ) y^{\prime }+2 t y = 2 t \]
i.c.

[_separable]

2.311

15919

\[ {}x^{\prime } = x+t +1 \]
i.c.

[[_linear, ‘class A‘]]

1.658

15920

\[ {}y^{\prime } = {\mathrm e}^{2 t}+2 y \]
i.c.

[[_linear, ‘class A‘]]

1.621

15921

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

[_linear]

1.323

15922

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

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

1.799

15923

\[ {}y^{\prime }+y = \left \{\begin {array}{cc} 4 & 0\le t <2 \\ 0 & 2\le t \end {array}\right . \]
i.c.

[[_linear, ‘class A‘]]

0.865

15924

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

[[_linear, ‘class A‘]]

0.854

15925

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

[[_linear, ‘class A‘]]

1.651

15926

\[ {}y^{\prime }+y = 5 \,{\mathrm e}^{2 t} \]

[[_linear, ‘class A‘]]

1.456

15927

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

[[_linear, ‘class A‘]]

1.309

15928

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

[[_linear, ‘class A‘]]

1.452

15929

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

[[_linear, ‘class A‘]]

1.329

15930

\[ {}y^{\prime }+3 y = 27 t^{2}+9 \]

[[_linear, ‘class A‘]]

1.457

15931

\[ {}y^{\prime }-\frac {y}{2} = 5 \cos \left (t \right )+2 \,{\mathrm e}^{t} \]

[[_linear, ‘class A‘]]

2.220

15932

\[ {}y^{\prime }+4 y = 8 \cos \left (4 t \right ) \]

[[_linear, ‘class A‘]]

1.784

15933

\[ {}y^{\prime }+10 y = 2 \,{\mathrm e}^{t} \]

[[_linear, ‘class A‘]]

1.461

15934

\[ {}y^{\prime }-3 y = 27 t^{2} \]

[[_linear, ‘class A‘]]

1.428

15935

\[ {}y^{\prime }-y = 2 \,{\mathrm e}^{t} \]

[[_linear, ‘class A‘]]

1.352

15936

\[ {}y^{\prime }+y = 4+3 \,{\mathrm e}^{t} \]

[[_linear, ‘class A‘]]

1.489

15937

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

[[_linear, ‘class A‘]]

1.856

15938

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

[[_linear, ‘class A‘]]

1.746

15939

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

[[_linear, ‘class A‘]]

1.730

15940

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

[_linear]

1.502

15941

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

[[_linear, ‘class A‘]]

1.554

15942

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

[[_linear, ‘class A‘]]

1.827

15943

\[ {}y^{\prime }+y = \cos \left (t \right ) \]
i.c.

[[_linear, ‘class A‘]]

1.806

15944

\[ {}y^{\prime }+y = {\mathrm e}^{t} \]
i.c.

[[_linear, ‘class A‘]]

1.699

15945

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

[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

55.004

15946

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

[_separable]

4.398

15947

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

[_separable]

2.283

15948

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

[_linear]

12.042

15949

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

[_separable]

4.334

15950

\[ {}t -\sin \left (t \right ) y+\left (y^{6}+\cos \left (t \right )\right ) y^{\prime } = 0 \]

[_exact]

3.550

15951

\[ {}y \sin \left (2 t \right )+\left (\sqrt {y}+\cos \left (2 t \right )\right ) y^{\prime } = 0 \]

[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]

6.809

15952

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

[[_homogeneous, ‘class G‘], _exact]

3.098

15953

\[ {}{\mathrm e}^{t y}+\frac {t \,{\mathrm e}^{t y} y^{\prime }}{y} = 0 \]

[_separable]

2.338

15954

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

[_quadrature]

0.474

15955

\[ {}-1+3 y^{2} y^{\prime } = 0 \]

[_quadrature]

1.837

15956

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

[_separable]

2.414

15957

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

[_separable]

2.316

15958

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

[_exact, _rational]

1.513

15959

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

[[_homogeneous, ‘class G‘], _exact, _rational]

1.906

15960

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

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

18.844

15961

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

[[_homogeneous, ‘class G‘], _exact, _rational]

2.261

15962

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

[_separable]

7.431

15963

\[ {}3 t^{2}+3 y^{2}+6 t y y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli]

60.826

15964

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

[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]

2.197

15965

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

[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

1.926

15966

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

[_separable]

3.241

15967

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

[_exact]

41.040

15968

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

[‘y=_G(x,y’)‘]

60.929

15969

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

[_exact]

36.896

15970

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

[[_1st_order, _with_linear_symmetries], _exact]

20.934

15971

\[ {}\frac {2 t^{2} y \cos \left (t^{2}\right )-y \sin \left (t^{2}\right )}{t^{2}}+\frac {\left (2 t y+\sin \left (t^{2}\right )\right ) y^{\prime }}{t} = 0 \]

[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]]

10.270

15972

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

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

5.135

15973

\[ {}2 t \sin \left (\frac {y}{t}\right )-y \cos \left (\frac {y}{t}\right )+t \cos \left (\frac {y}{t}\right ) y^{\prime } = 0 \]

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

4.500

15974

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

[_separable]

2.730

15975

\[ {}1+\frac {y}{t^{2}}-\frac {y^{\prime }}{t} = 0 \]
i.c.

[_linear]

1.893

15976

\[ {}2 t y+3 t^{2}+\left (t^{2}-1\right ) y^{\prime } = 0 \]
i.c.

[_linear]

1.587

15977

\[ {}1+5 t -y-\left (t +2 y\right ) y^{\prime } = 0 \]
i.c.

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

5.228

15978

\[ {}{\mathrm e}^{y}-2 t y+\left (t \,{\mathrm e}^{y}-t^{2}\right ) y^{\prime } = 0 \]
i.c.

[_exact]

2.133

15979

\[ {}2 t y \,{\mathrm e}^{t^{2}}+2 t \,{\mathrm e}^{-y}+\left ({\mathrm e}^{t^{2}}-t^{2} {\mathrm e}^{-y}+1\right ) y^{\prime } = 0 \]
i.c.

[_exact]

37.009

15980

\[ {}y^{2}-2 \sin \left (2 t \right )+\left (1+2 t y\right ) y^{\prime } = 0 \]
i.c.

[_exact, [_Abel, ‘2nd type‘, ‘class B‘]]

38.071

15981

\[ {}\cos \left (t \right )^{2}-\sin \left (t \right )^{2}+y+\left (\sec \left (y\right ) \tan \left (y\right )+t \right ) y^{\prime } = 0 \]
i.c.

[_exact]

41.970

15982

\[ {}\frac {1}{t^{2}+1}-y^{2}-2 t y y^{\prime } = 0 \]
i.c.

[_exact, _rational, _Bernoulli]

6.608

15983

\[ {}\frac {2 t}{t^{2}+1}+y+\left ({\mathrm e}^{y}+t \right ) y^{\prime } = 0 \]
i.c.

[_exact]

3.921

15984

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

[_exact]

13.452

15985

\[ {}-4 x^{3}+6 y \sin \left (6 x y\right )+\left (4 y^{3}+6 x \sin \left (6 x y\right )\right ) y^{\prime } = 0 \]
i.c.

[_exact]

43.849

15986

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

[_separable]

2.276

15987

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

[_separable]

2.214

15988

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

[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]

1.369

15989

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

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

3.048

15990

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

[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]]

1.519

15991

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

[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]

1.852

15992

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

[[_homogeneous, ‘class D‘], _rational, _Bernoulli]

3.821

15993

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

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]

2.720

15994

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

[_exact]

39.712

15995

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

[_exact]

37.973

15996

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

[_quadrature]

0.967

15997

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

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

4.051

15998

\[ {}2 t +\frac {19 y}{10}+\left (\frac {19 t}{10}+2 y\right ) y^{\prime } = 0 \]

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

4.152

15999

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

[_rational, _Bernoulli]

1.586

16000

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

[_Bernoulli]

1.852