2.2.191 Problems 19001 to 19100

Table 2.383: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

19001

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

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

1.910

19002

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

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

2.012

19003

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

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

7.398

19004

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

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

5.743

19005

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

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

15.869

19006

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

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

3.541

19007

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

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

3.421

19008

\[ {}\left (6 x -5 y+4\right ) y^{\prime }+y-2 x -1 = 0 \]

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

81.902

19009

\[ {}\left (x -3 y+4\right ) y^{\prime }+7 y-5 x = 0 \]

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

7.069

19010

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

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

1.948

19011

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

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

8.435

19012

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

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

26.245

19013

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

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

7.155

19014

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

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

3.276

19015

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

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

37.393

19016

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

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

1.937

19017

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

[_linear]

1.995

19018

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

[_linear]

4.470

19019

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

[_linear]

6.336

19020

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

[_linear]

1.689

19021

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

[_linear]

1.174

19022

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

[_linear]

3.543

19023

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

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

1.408

19024

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

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

2.123

19025

\[ {}y^{\prime }+3 x^{2} y = x^{5} {\mathrm e}^{x^{3}} \]

[_linear]

1.522

19026

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

[‘y=_G(x,y’)‘]

46.418

19027

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

[_linear]

1.864

19028

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

[_linear]

1.584

19029

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

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

6.056

19030

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

[_linear]

1.403

19031

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

[_linear]

1.428

19032

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

[‘y=_G(x,y’)‘]

46.005

19033

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

[‘x=_G(y,y’)‘]

1.824

19034

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

[_separable]

1.889

19035

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

[_Bernoulli]

2.752

19036

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

[_Bernoulli]

12.716

19037

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

[_Bernoulli]

6.137

19038

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

[[_1st_order, _with_linear_symmetries], _exact, _rational]

1.571

19039

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

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

1.729

19040

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

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

36.149

19041

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

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

2.923

19042

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

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

2.092

19043

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

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

2.510

19044

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

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

7.693

19045

\[ {}\left (20 x^{2}+8 x y+4 y^{2}+3 y^{3}\right ) y+4 \left (x^{2}+x y+y^{2}+y^{3}\right ) x y^{\prime } = 0 \]

[_rational]

1.822

19046

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

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

2.089

19047

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

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

4.057

19048

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

[[_1st_order, _with_linear_symmetries]]

508.325

19049

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

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

4.338

19050

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

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

2.962

19051

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

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

4.146

19052

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

[[_homogeneous, ‘class C‘], _Riccati]

6.028

19053

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

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

3.707

19054

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

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

1.593

19055

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

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

8.220

19056

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

[_exact, _rational]

1.897

19057

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

[_rational, _Bernoulli]

2.351

19058

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

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

4.201

19059

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

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

1.638

19060

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

[‘y=_G(x,y’)‘]

1.918

19061

\[ {}{x^{\prime }}^{2} = k^{2} \left (1-{\mathrm e}^{-\frac {2 g x}{k^{2}}}\right ) \]
i.c.

[_quadrature]

1.048

19062

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

[_Bernoulli]

2.931

19063

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

[_separable]

1.572

19064

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

[_rational]

1.483

19065

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

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

4.025

19066

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

[_exact]

38.715

19067

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

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

1.994

19068

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

[_separable]

35.228

19069

\[ {}s^{\prime }+x^{2} = x^{2} {\mathrm e}^{3 s} \]

[_separable]

2.046

19070

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

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

2.497

19071

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

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

74.459

19072

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

[‘y=_G(x,y’)‘]

45.026

19073

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

[_exact, _rational]

1.110

19074

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

[_Bernoulli]

2.704

19075

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

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

72.090

19076

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

[_linear]

4.029

19077

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

[‘x=_G(y,y’)‘]

2.126

19078

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

[‘y=_G(x,y’)‘]

3.744

19079

\[ {}y^{\prime }+\frac {a x +b y+c}{b x +f y+e} = 0 \]

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

4.094

19080

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

[[_2nd_order, _missing_x]]

1.637

19081

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

[[_3rd_order, _missing_x]]

0.051

19082

\[ {}2 x^{\prime \prime }+5 x^{\prime }-12 x = 0 \]

[[_2nd_order, _missing_x]]

0.873

19083

\[ {}y^{\prime \prime }+3 y^{\prime }-54 y = 0 \]

[[_2nd_order, _missing_x]]

0.842

19084

\[ {}9 x^{\prime \prime }+18 x^{\prime }-16 x = 0 \]

[[_2nd_order, _missing_x]]

0.862

19085

\[ {}y^{\prime \prime \prime }+y^{\prime \prime }-5 y^{\prime }+3 y = 0 \]

[[_3rd_order, _missing_x]]

0.054

19086

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

[[_2nd_order, _missing_x]]

0.953

19087

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

[[_3rd_order, _missing_x]]

0.052

19088

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

[[_high_order, _missing_x]]

0.053

19089

\[ {}y^{\prime \prime \prime \prime }+8 y^{\prime \prime }+16 y = 0 \]

[[_high_order, _missing_x]]

0.068

19090

\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }+y^{\prime }-5 y = 0 \]

[[_3rd_order, _missing_x]]

0.059

19091

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

[[_3rd_order, _missing_x]]

0.057

19092

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

[[_high_order, _missing_x]]

0.055

19093

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

[[_high_order, _missing_x]]

0.066

19094

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{4 x} \]

[[_2nd_order, _with_linear_symmetries]]

1.000

19095

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

[[_2nd_order, _with_linear_symmetries]]

1.125

19096

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

[[_2nd_order, _with_linear_symmetries]]

1.198

19097

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

[[_2nd_order, _linear, _nonhomogeneous]]

2.967

19098

\[ {}y^{\prime \prime }-2 y^{\prime }+y = 2 \,{\mathrm e}^{\frac {5 x}{2}} \]

[[_2nd_order, _with_linear_symmetries]]

1.237

19099

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

[[_2nd_order, _with_linear_symmetries]]

21.846

19100

\[ {}y^{\prime \prime }+2 p y^{\prime }+\left (p^{2}+q^{2}\right ) y = {\mathrm e}^{k x} \]

[[_2nd_order, _with_linear_symmetries]]

44.007