2.7.2 higher order missing y

Table 2.1251: higher order missing y [70]

#

ODE

CAS classification

Solved

Maple

Mma

Sympy

time(sec)

4413

\begin{align*} y^{\prime \prime \prime }&=2 \left (y^{\prime \prime }-1\right ) \cot \left (x \right ) \\ \end{align*}

[[_3rd_order, _missing_y]]

0.628

6704

\begin{align*} \left (-a^{2}+1\right ) x y^{\prime }+3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}

[[_3rd_order, _missing_y]]

0.675

6712

\begin{align*} \left (-x^{3}+3 x^{2}-6 x +6\right ) y^{\prime \prime }+x \left (x^{2}-2 x +2\right ) y^{\prime \prime \prime }&=0 \\ \end{align*}

[[_3rd_order, _missing_y]]

1.019

6719

\begin{align*} 10 x^{2} y^{\prime }+8 x^{3} y^{\prime \prime }+x^{2} \left (x^{2}+1\right ) y^{\prime \prime \prime }&=-1+3 x^{2}+2 x^{2} \ln \left (x \right ) \\ \end{align*}

[[_3rd_order, _missing_y]]

2.224

6721

\begin{align*} 4 x^{2} y^{\prime }-4 x^{3} y^{\prime \prime }+4 x^{4} y^{\prime \prime \prime }&=1 \\ \end{align*}

[[_3rd_order, _missing_y]]

1.296

6790

\begin{align*} y^{\prime \prime \prime }&=y^{\prime } \left (y^{\prime }+1\right ) \\ \end{align*}

[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]

11.774

6801

\begin{align*} {y^{\prime }}^{2}+y^{\prime } y^{\prime \prime \prime }&=2 {y^{\prime \prime }}^{2} \\ \end{align*}

[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries]]

45.109

6803

\begin{align*} 2 y^{\prime } y^{\prime \prime \prime }&=2 {y^{\prime \prime }}^{2} \\ \end{align*}

[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]

4.744

6804

\begin{align*} \left (1+{y^{\prime }}^{2}\right ) y^{\prime \prime \prime }&=3 y^{\prime } {y^{\prime \prime }}^{2} \\ \end{align*}

[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]

3.439

6805

\begin{align*} \left (1+{y^{\prime }}^{2}\right ) y^{\prime \prime \prime }&=\left (a +3 y^{\prime }\right ) {y^{\prime \prime }}^{2} \\ \end{align*}

[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]

64.355

6806

\begin{align*} {y^{\prime }}^{3} y^{\prime \prime \prime }&=1 \\ \end{align*}

[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]

35.961

6807

\begin{align*} y^{\prime \prime } y^{\prime \prime \prime }&=2 \\ \end{align*}

[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]

3.760

6808

\begin{align*} y^{\prime \prime } y^{\prime \prime \prime }&=a \sqrt {1+b^{2} {y^{\prime \prime }}^{2}} \\ \end{align*}

[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]

68.554

6809

\begin{align*} 2 x y^{\prime \prime } y^{\prime \prime \prime }&=-a^{2}+{y^{\prime \prime }}^{2} \\ \end{align*}

[[_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]

10.500

6810

\begin{align*} 1-{y^{\prime \prime }}^{2}+2 x y^{\prime \prime } y^{\prime \prime \prime }+\left (-x^{2}+1\right ) {y^{\prime \prime \prime }}^{2}&=0 \\ \end{align*}

[[_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries]]

4.901

6811

\begin{align*} \sqrt {1+{y^{\prime \prime }}^{2}}\, \left (1-y^{\prime \prime \prime }\right )&=y^{\prime \prime } y^{\prime \prime \prime } \\ \end{align*}

[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]

19.484

6812

\begin{align*} 3 y^{\prime \prime } y^{\prime \prime \prime \prime }&=5 {y^{\prime \prime \prime }}^{2} \\ \end{align*}

[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries], [_high_order, _reducible, _mu_poly_yn]]

7.415

8055

\begin{align*} \left (2 x^{3}-1\right ) y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+6 x y^{\prime }&=0 \\ \end{align*}

[[_3rd_order, _missing_y]]

0.661

8801

\begin{align*} 3 {y^{\prime \prime }}^{2}-y^{\prime } y^{\prime \prime \prime }-y^{\prime \prime } {y^{\prime }}^{2}&=0 \\ \end{align*}

[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_exponential_symmetries], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]

11.147

8807

\begin{align*} y^{\left (5\right )}-\frac {y^{\prime \prime \prime \prime }}{t}&=0 \\ \end{align*}

[[_high_order, _missing_y]]

0.826

8828

\begin{align*} a y^{\prime \prime } y^{\prime \prime \prime }&=\sqrt {1+{y^{\prime \prime }}^{2}} \\ \end{align*}

[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]

6.796

12741

\begin{align*} x^{2} y^{\prime \prime \prime }-x y^{\prime \prime }+\left (x^{2}+1\right ) y^{\prime }&=0 \\ \end{align*}

[[_3rd_order, _missing_y]]

0.226

12761

\begin{align*} \left (-a^{2}+1\right ) x y^{\prime }+3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}

[[_3rd_order, _missing_y]]

0.148

12771

\begin{align*} 4 x^{4} y^{\prime \prime \prime }-4 x^{3} y^{\prime \prime }+4 x^{2} y^{\prime }-1&=0 \\ \end{align*}

[[_3rd_order, _missing_y]]

0.298

13041

\begin{align*} y^{\prime \prime \prime }-a^{2} \left ({y^{\prime }}^{5}+2 {y^{\prime }}^{3}+y^{\prime }\right )&=0 \\ \end{align*}

[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]

2.403

13051

\begin{align*} \left (1+{y^{\prime }}^{2}\right ) y^{\prime \prime \prime }-3 y^{\prime } {y^{\prime \prime }}^{2}&=0 \\ \end{align*}

[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]

1.018

13052

\begin{align*} \left (1+{y^{\prime }}^{2}\right ) y^{\prime \prime \prime }-\left (a +3 y^{\prime }\right ) {y^{\prime \prime }}^{2}&=0 \\ \end{align*}

[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]

17.279

13053

\begin{align*} y^{\prime \prime } y^{\prime \prime \prime }-a \sqrt {1+b^{2} {y^{\prime \prime }}^{2}}&=0 \\ \end{align*}

[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]

18.752

13055

\begin{align*} 3 y^{\prime \prime } y^{\prime \prime \prime \prime }-5 {y^{\prime \prime \prime }}^{2}&=0 \\ \end{align*}

[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries], [_high_order, _reducible, _mu_poly_yn]]

1.669

14157

\begin{align*} \left (x y^{\prime \prime \prime }-y^{\prime \prime }\right )^{2}&={y^{\prime \prime \prime }}^{2}+1 \\ \end{align*}

[[_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries]]

2.864

15078

\begin{align*} {y^{\prime \prime \prime }}^{2}+{y^{\prime \prime }}^{2}&=1 \\ \end{align*}

[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]

4.273

15106

\begin{align*} 6 y^{\prime \prime } y^{\prime \prime \prime \prime }-5 {y^{\prime \prime \prime }}^{2}&=0 \\ \end{align*}

[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries], [_high_order, _reducible, _mu_poly_yn]]

2.971

15331

\begin{align*} y^{\prime \prime \prime }+\frac {3 y^{\prime \prime }}{x}&=0 \\ \end{align*}

[[_3rd_order, _missing_y]]

0.885

15408

\begin{align*} y^{\prime \prime \prime }&={y^{\prime \prime }}^{2} \\ \end{align*}

[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]

1.969

15409

\begin{align*} y^{\prime } y^{\prime \prime \prime }-3 {y^{\prime \prime }}^{2}&=0 \\ \end{align*}

[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]

3.973

15654

\begin{align*} x y^{\prime \prime \prime }+x y^{\prime }&=4 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 1 \\ y^{\prime \prime }\left (1\right ) &= -1 \\ \end{align*}

[[_3rd_order, _missing_y]]

0.779

16399

\begin{align*} y^{\prime \prime \prime }&=2 \sqrt {y^{\prime \prime }} \\ \end{align*}

[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]

1.621

17609

\begin{align*} t^{2} \ln \left (t \right ) y^{\prime \prime \prime }-t y^{\prime \prime }+y^{\prime }&=1 \\ \end{align*}

[[_3rd_order, _missing_y]]

1.171

17610

\begin{align*} \left (t^{2}+t \right ) y^{\prime \prime \prime }+\left (-t^{2}+2\right ) y^{\prime \prime }-\left (t +2\right ) y^{\prime }&=-2-t \\ \end{align*}

[[_3rd_order, _missing_y]]

1.126

18100

\begin{align*} y^{\prime \prime \prime }&=\sqrt {1-{y^{\prime \prime }}^{2}} \\ \end{align*}

[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]

5.945

18111

\begin{align*} y^{\prime \prime \prime }+{y^{\prime \prime }}^{2}&=0 \\ \end{align*}

[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]

1.671

19142

\begin{align*} {y^{\prime \prime \prime }}^{2}+x^{2}&=1 \\ \end{align*}

[[_3rd_order, _quadrature]]

2.902

19144

\begin{align*} a^{3} y^{\prime \prime \prime } y^{\prime \prime }&=\sqrt {1+c^{2} {y^{\prime \prime }}^{2}} \\ \end{align*}

[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]

24.574

19145

\begin{align*} y^{\prime \prime \prime }&=\sqrt {1+{y^{\prime \prime }}^{2}} \\ \end{align*}

[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]

3.593

19147

\begin{align*} y^{\prime \prime }-x y^{\prime \prime \prime }+{y^{\prime \prime \prime }}^{3}&=0 \\ \end{align*}

[[_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries]]

0.774

19160

\begin{align*} 5 {y^{\prime \prime \prime }}^{2}-3 y^{\prime \prime } y^{\prime \prime \prime \prime }&=0 \\ \end{align*}

[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries], [_high_order, _reducible, _mu_poly_yn]]

1.511

19775

\begin{align*} y^{\prime \prime \prime }+\frac {3 y^{\prime \prime }}{x}&=0 \\ \end{align*}

[[_3rd_order, _missing_y]]

0.355

20133

\begin{align*} 2 x y^{\prime \prime } y^{\prime \prime \prime }&=-a^{2}+{y^{\prime \prime }}^{2} \\ \end{align*}

[[_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]

1.539

20144

\begin{align*} y^{\prime \prime } y^{\prime \prime \prime }&=2 \\ \end{align*}

[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]

0.605

20540

\begin{align*} y^{\prime \prime \prime } \csc \left (x \right )^{2}&=1 \\ \end{align*}

[[_3rd_order, _quadrature]]

0.245

20571

\begin{align*} y^{\prime \prime } y^{\prime \prime \prime }&=2 \\ \end{align*}

[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]

1.030

20600

\begin{align*} 2 x y^{\prime \prime } y^{\prime \prime \prime }&=-a^{2}+{y^{\prime \prime }}^{2} \\ \end{align*}

[[_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]

2.034

21949

\begin{align*} y^{\prime \prime \prime }-5 x y^{\prime }&=1+{\mathrm e}^{x} \\ \end{align*}

[[_3rd_order, _missing_y]]

1.585

21955

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+x y^{\prime \prime \prime }&={\mathrm e}^{x} \\ \end{align*}

[[_high_order, _missing_y]]

0.893

22495

\begin{align*} {y^{\prime \prime \prime }}^{2}&={y^{\prime \prime }}^{3} \\ \end{align*}

[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]

2.356

22579

\begin{align*} x^{4} y^{\prime \prime \prime }+1&=0 \\ \end{align*}

[[_3rd_order, _quadrature]]

0.464

23231

\begin{align*} y^{\left (5\right )}-\frac {y^{\prime \prime \prime \prime }}{x}&=0 \\ \end{align*}

[[_high_order, _missing_y]]

0.477

26418

\begin{align*} y^{\prime } y^{\prime \prime \prime }&=3 {y^{\prime \prime }}^{2} \\ \end{align*}

[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]

1.206

26450

\begin{align*} {y^{\prime \prime \prime }}^{2}+{y^{\prime \prime }}^{2}&=1 \\ \end{align*}

[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]

1.775

26458

\begin{align*} y^{\prime } y^{\prime \prime \prime }-3 {y^{\prime \prime }}^{2}&=0 \\ \end{align*}

[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]

1.212

26460

\begin{align*} x^{4} y^{\prime \prime \prime }+2 x^{3} y^{\prime \prime }&=1 \\ \end{align*}

[[_3rd_order, _missing_y]]

0.374

27533

\begin{align*} y^{\prime \prime \prime }&={y^{\prime \prime }}^{2} \\ \end{align*}

[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]

0.375

27535

\begin{align*} y^{\prime \prime \prime }&=2 \left (y^{\prime \prime }-1\right ) \cot \left (x \right ) \\ \end{align*}

[[_3rd_order, _missing_y]]

0.329

27540

\begin{align*} x^{2} y^{\prime \prime \prime }&={y^{\prime \prime }}^{2} \\ \end{align*}

[[_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]

0.369

27543

\begin{align*} y^{\prime \prime }-x y^{\prime \prime \prime }+{y^{\prime \prime \prime }}^{3}&=0 \\ \end{align*}

[[_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries]]

0.560

27548

\begin{align*} {y^{\prime \prime }}^{2}-2 y^{\prime } y^{\prime \prime \prime }+1&=0 \\ \end{align*}

[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]

1.620

27561

\begin{align*} y^{\prime } y^{\prime \prime \prime }&=2 {y^{\prime \prime }}^{2} \\ \end{align*}

[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]

0.294

27563

\begin{align*} 5 {y^{\prime \prime \prime }}^{2}-3 y^{\prime \prime } y^{\prime \prime \prime \prime }&=0 \\ \end{align*}

[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries], [_high_order, _reducible, _mu_poly_yn]]

0.681

27595

\begin{align*} y^{\prime } y^{\prime \prime \prime }&={y^{\prime \prime }}^{2}+y^{\prime \prime } {y^{\prime }}^{2} \\ \end{align*}

[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_exponential_symmetries], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]

0.466

27599

\begin{align*} y^{\prime \prime \prime } {y^{\prime }}^{2}&=1 \\ \end{align*}

[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]

337.752