2.5.10 second order ode flip role

Table 2.1155: second order ode flip role [20]

#

ODE

CAS classification

Solved

Maple

Mma

Sympy

time(sec)

6312

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

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

1.936

6342

\begin{align*} g \left (y\right )+f \left (y\right ) {y^{\prime }}^{2}+y^{\prime \prime }&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

3.491

6344

\begin{align*} f \left (y\right ) y^{\prime }+g \left (y\right ) {y^{\prime }}^{2}+y^{\prime \prime }&=0 \\ \end{align*}

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

1.017

6348

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

[[_2nd_order, _with_exponential_symmetries], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1]]

0.912

6352

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

[[_2nd_order, _with_exponential_symmetries], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]

1.021

8246

\begin{align*} 4 y+y^{\prime \prime }&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (\frac {\pi }{4}\right ) &= 3 \\ \end{align*}

[[_2nd_order, _missing_x]]

2.552

10417

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

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

12.122

13002

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

[[_2nd_order, _missing_x]]

2.626

13003

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

[[_2nd_order, _missing_x]]

2.584

13004

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

[[_2nd_order, _missing_x]]

2.864

13005

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

[[_2nd_order, _missing_x]]

5.194

13025

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

[[_2nd_order, _missing_x]]

3.028

13057

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

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

1.748

14432

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

[[_2nd_order, _missing_x]]

14.355

14433

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

[[_2nd_order, _missing_x]]

11.325

15094

\begin{align*} m x^{\prime \prime }&=f \left (x\right ) \\ \end{align*}

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

1.443

22287

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

[[_2nd_order, _missing_x]]

5.787

22805

\begin{align*} y^{\prime \prime }&={y^{\prime }}^{2} \left (2+y^{\prime } x -4 y^{2} y^{\prime }\right ) \\ \end{align*}

[[_2nd_order, _with_exponential_symmetries], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1]]

1.896

23354

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

[[_2nd_order, _missing_x]]

24.357

25724

\begin{align*} y^{\prime \prime }+9 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (\frac {\pi }{6}\right ) &= -1 \\ \end{align*}

[[_2nd_order, _missing_x]]

7.765