2.2.196 Problems 19501 to 19563

Table 2.393: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

19501

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

[[_3rd_order, _with_linear_symmetries]]

0.304

19502

\[ {}x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+4 x y^{\prime }-4 y = 0 \]

[[_3rd_order, _with_linear_symmetries]]

0.101

19503

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

[[_3rd_order, _exact, _linear, _homogeneous]]

0.115

19504

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

[[_2nd_order, _with_linear_symmetries]]

1.401

19505

\[ {}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+2 y = 10 x +\frac {10}{x} \]

[[_3rd_order, _exact, _linear, _nonhomogeneous]]

0.770

19506

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

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

1.921

19507

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

[[_3rd_order, _with_linear_symmetries]]

0.040

19508

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

[[_2nd_order, _with_linear_symmetries]]

1.191

19509

\[ {}16 \left (x +1\right )^{4} y^{\prime \prime \prime \prime }+96 \left (x +1\right )^{3} y^{\prime \prime \prime }+104 \left (x +1\right )^{2} y^{\prime \prime }+8 \left (x +1\right ) y^{\prime }+y = x^{2}+4 x +3 \]

[[_high_order, _with_linear_symmetries]]

0.053

19510

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

[[_2nd_order, _linear, _nonhomogeneous]]

5.056

19511

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

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]

0.139

19512

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

[[_2nd_order, _linear, _nonhomogeneous]]

57.691

19513

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

[[_2nd_order, _linear, _nonhomogeneous]]

8.834

19514

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

[[_3rd_order, _missing_y]]

0.163

19515

\[ {}\left (x^{3}-x \right ) y^{\prime \prime \prime }+\left (8 x^{2}-3\right ) y^{\prime \prime }+14 x y^{\prime }+4 y = \frac {2}{x^{3}} \]

[[_3rd_order, _fully, _exact, _linear]]

0.383

19516

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

[[_3rd_order, _fully, _exact, _linear]]

0.660

19517

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

[[_2nd_order, _with_linear_symmetries]]

0.840

19518

\[ {}2 x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (7 x +3\right ) y^{\prime }-3 y = x^{2} \]

[[_2nd_order, _with_linear_symmetries]]

0.969

19519

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

[[_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]

1.758

19520

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

[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]

0.922

19521

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

[[_2nd_order, _with_linear_symmetries]]

0.145

19522

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

[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_poly_yn]]

151.255

19523

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

[[_3rd_order, _quadrature]]

0.101

19524

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

[[_2nd_order, _quadrature]]

36.177

19525

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

[[_2nd_order, _quadrature]]

2.416

19526

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

[[_2nd_order, _missing_x]]

3.117

19527

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

[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]

0.798

19528

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

[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

0.526

19529

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

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]

2.030

19530

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

[[_2nd_order, _missing_x]]

21.150

19531

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

[[_2nd_order, _missing_y]]

0.715

19532

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

[[_high_order, _missing_x]]

0.056

19533

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

[[_2nd_order, _with_linear_symmetries]]

0.128

19534

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

[NONE]

0.139

19535

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

[[_2nd_order, _with_linear_symmetries]]

0.752

19536

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

[[_2nd_order, _with_linear_symmetries]]

0.862

19537

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

[[_2nd_order, _with_linear_symmetries]]

2.240

19538

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

[[_2nd_order, _with_linear_symmetries]]

1.414

19539

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

[[_2nd_order, _linear, _nonhomogeneous]]

2.196

19540

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

[[_2nd_order, _with_linear_symmetries]]

10.308

19541

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.566

19542

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

[[_2nd_order, _with_linear_symmetries]]

0.547

19543

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

[[_2nd_order, _with_linear_symmetries]]

1.264

19544

\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x^{{1}/{3}}}+\left (\frac {1}{4 x^{{2}/{3}}}-\frac {1}{6 x^{{4}/{3}}}-\frac {6}{x^{2}}\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.935

19545

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

[_Lienard]

4.830

19546

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

[[_2nd_order, _linear, _nonhomogeneous]]

3.763

19547

\[ {}y^{\prime \prime }-\left (8 \,{\mathrm e}^{2 x}+2\right ) y^{\prime }+4 \,{\mathrm e}^{4 x} y = {\mathrm e}^{6 x} \]

[[_2nd_order, _linear, _nonhomogeneous]]

4.021

19548

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

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

1.810

19549

\[ {}x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+a^{2} y = \frac {1}{x^{2}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

4.251

19550

\[ {}x y^{\prime \prime }-y^{\prime }-4 x^{3} y = 8 x^{3} \sin \left (x^{2}\right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

2.438

19551

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

[[_2nd_order, _linear, _nonhomogeneous]]

4.875

19552

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

[[_2nd_order, _linear, _nonhomogeneous]]

5.058

19553

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

[[_2nd_order, _with_linear_symmetries]]

1.124

19554

\[ {}3 x^{2} y^{\prime \prime }+\left (-6 x^{2}+6 x +2\right ) y^{\prime }-4 y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

1.234

19555

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

[[_2nd_order, _linear, _nonhomogeneous]]

2.972

19556

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

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

2.205

19557

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

[[_2nd_order, _with_linear_symmetries]]

1.450

19558

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

[[_2nd_order, _linear, _nonhomogeneous]]

2.536

19559

\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = {\mathrm e}^{2 x} \]

[[_3rd_order, _with_linear_symmetries]]

0.102

19560

\[ {}\left [\begin {array}{c} x^{\prime }-7 x+y=0 \\ y^{\prime }-2 x-5 y=0 \end {array}\right ] \]

system_of_ODEs

0.543

19561

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

system_of_ODEs

0.477

19562

\[ {}\left [\begin {array}{c} 4 x^{\prime }+9 y^{\prime }+11 x+31 y={\mathrm e}^{t} \\ 3 x^{\prime }+7 y^{\prime }+8 x+24 y={\mathrm e}^{2 t} \end {array}\right ] \]

system_of_ODEs

0.585

19563

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

system_of_ODEs

0.033