2.5.4 higher order ode exact

Table 2.509: higher order ode exact

#

ODE

CAS classification

Solved?

1466

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

[[_3rd_order, _missing_y]]

3499

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

[[_3rd_order, _missing_y]]

6913

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

[[_3rd_order, _missing_y]]

8038

\[ {}x^{3} y^{\prime \prime \prime \prime }+8 x^{2} y^{\prime \prime \prime }+8 x y^{\prime \prime }-8 y^{\prime } = 0 \]

[[_high_order, _missing_y]]

8572

\[ {}y^{\prime \prime \prime }+x^{2} y^{\prime \prime }+5 x y^{\prime }+3 y = 0 \]

[[_3rd_order, _exact, _linear, _homogeneous]]

11440

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

[[_3rd_order, _fully, _exact, _linear]]

11448

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

[[_3rd_order, _fully, _exact, _linear]]

11452

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

[[_3rd_order, _exact, _linear, _homogeneous]]

11454

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

[[_3rd_order, _missing_y]]

11461

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

[[_3rd_order, _missing_y]]

11462

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

[[_3rd_order, _missing_y]]

11470

\[ {}\left (x^{2}+1\right ) y^{\prime \prime \prime }+8 x y^{\prime \prime }+10 y^{\prime }-3+\frac {1}{x^{2}}-2 \ln \left (x \right ) = 0 \]

[[_3rd_order, _missing_y]]

11493

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

[[_3rd_order, _missing_y]]

11494

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

[[_3rd_order, _fully, _exact, _linear]]

11509

\[ {}y^{\prime \prime \prime \prime } x +5 y^{\prime \prime \prime }-24 = 0 \]

[[_high_order, _missing_y]]

11513

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

[[_high_order, _missing_y]]

11514

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

[[_high_order, _missing_y]]

11516

\[ {}x^{2} y^{\prime \prime \prime \prime }+8 x y^{\prime \prime \prime }+12 y^{\prime \prime } = 0 \]

[[_high_order, _missing_y]]

11520

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

[[_high_order, _missing_y]]

11533

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

[[_high_order, _fully, _exact, _linear]]

12920

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

[[_3rd_order, _missing_y]]

12923

\[ {}\left (x^{3}-x \right ) y^{\prime \prime \prime }+\left (8 x^{2}-3\right ) y^{\prime \prime }+14 x y^{\prime }+4 y = 0 \]

[[_3rd_order, _fully, _exact, _linear]]

12936

\[ {}\left (x^{3}+1\right ) y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+18 x y^{\prime }+6 y = 0 \]

[[_3rd_order, _fully, _exact, _linear]]

12943

\[ {}4 x^{2} y^{\prime \prime \prime }+8 x y^{\prime \prime }+y^{\prime } = 0 \]

[[_3rd_order, _missing_y]]

14148

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

[[_3rd_order, _quadrature]]

15146

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

[[_3rd_order, _missing_y]]

15169

\[ {}x y^{\prime \prime \prime }+2 y^{\prime \prime } = 6 x \]
i.c.

[[_3rd_order, _missing_y]]

16360

\[ {}t y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime } = \frac {45}{8 t^{{7}/{2}}} \]
i.c.

[[_high_order, _missing_y]]

16380

\[ {}x^{3} y^{\prime \prime \prime \prime }+6 x^{2} y^{\prime \prime \prime }+7 x y^{\prime \prime }+y^{\prime } = 0 \]

[[_high_order, _missing_y]]

16828

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

[[_3rd_order, _quadrature]]

16849

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

[[_3rd_order, _missing_y]]

17044

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

[[_3rd_order, _missing_y]]

17045

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

[[_3rd_order, _missing_y]]

17046

\[ {}\left (x +1\right )^{2} y^{\prime \prime \prime }-12 y^{\prime } = 0 \]

[[_3rd_order, _missing_y]]

17047

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

[[_3rd_order, _missing_y]]

17117

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

[[_high_order, _missing_y]]

17118

\[ {}x^{3} y^{\prime \prime \prime \prime }+6 x^{2} y^{\prime \prime \prime }+6 x y^{\prime \prime } = 0 \]
i.c.

[[_high_order, _missing_y]]

17733

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

[[_3rd_order, _missing_y]]

17921

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

[[_3rd_order, _missing_y]]

18300

\[ {}x^{3} y^{\prime \prime \prime \prime }+8 x^{2} y^{\prime \prime \prime }+8 x y^{\prime \prime }-8 y^{\prime } = 0 \]

[[_high_order, _missing_y]]

18617

\[ {}\left (x^{3}+x^{2}-3 x +1\right ) y^{\prime \prime \prime }+\left (9 x^{2}+6 x -9\right ) y^{\prime \prime }+\left (18 x +6\right ) y^{\prime }+6 y = x^{3} \]

[[_3rd_order, _fully, _exact, _linear]]

18618

\[ {}x^{2} y^{\prime \prime \prime }+5 x y^{\prime \prime }+4 y^{\prime } = -\frac {1}{x^{2}} \]

[[_3rd_order, _missing_y]]

18868

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

[[_3rd_order, _fully, _exact, _linear]]

18876

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

[[_high_order, _quadrature]]

18882

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

[[_3rd_order, _missing_y]]

18892

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

[[_high_order, _missing_y]]

18906

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

[[_3rd_order, _exact, _linear, _nonhomogeneous]]

18909

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

[[_3rd_order, _fully, _exact, _linear]]

18913

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

[[_3rd_order, _missing_y]]

18918

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

[[_3rd_order, _fully, _exact, _linear]]

19239

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

[[_3rd_order, _missing_y]]

19242

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

[[_3rd_order, _missing_y]]

19245

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

[[_3rd_order, _missing_y]]

19256

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

[[_3rd_order, _missing_y]]

19272

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

[[_3rd_order, _fully, _exact, _linear]]

19283

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

[[_3rd_order, _exact, _linear, _nonhomogeneous]]

19305

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

[[_3rd_order, _missing_y]]

19310

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

[[_3rd_order, _missing_y]]

19333

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

[[_high_order, _missing_y]]

19334

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

[[_high_order, _missing_y]]

19345

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

[[_high_order, _quadrature]]

19355

\[ {}\left (x^{3}-4 x \right ) y^{\prime \prime \prime }+\left (9 x^{2}-4\right ) y^{\prime \prime }+18 x y^{\prime }+6 y = 6 \]

[[_3rd_order, _fully, _exact, _linear]]

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]]

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]]

19516

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

[[_3rd_order, _fully, _exact, _linear]]