| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
x^{\prime }&=5 x+y \\
y^{\prime }&=-2 x+3 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.793 |
|
| \begin{align*}
x^{\prime }&=4 x+5 y \\
y^{\prime }&=-2 x+6 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.822 |
|
| \begin{align*}
x^{\prime }&=4 x-5 y \\
y^{\prime }&=5 x-4 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.704 |
|
| \begin{align*}
x^{\prime }&=x-8 y \\
y^{\prime }&=x-3 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.796 |
|
| \begin{align*}
x^{\prime }&=z \\
y^{\prime }&=-z \\
z^{\prime }&=y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.865 |
|
| \begin{align*}
x^{\prime }&=2 x+y+2 z \\
y^{\prime }&=3 x+6 z \\
z^{\prime }&=-4 x-3 z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.546 |
|
| \begin{align*}
x^{\prime }&=x-12 y-14 z \\
y^{\prime }&=x+2 y-3 z \\
z^{\prime }&=x+y-2 z \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 4 \\
y \left (0\right ) &= 6 \\
z \left (0\right ) &= -7 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.340 |
|
| \begin{align*}
x^{\prime }&=2 x+3 y-7 \\
y^{\prime }&=-x-2 y+5 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.046 |
|
| \begin{align*}
x^{\prime }&=5 x+9 y+2 \\
y^{\prime }&=-x+11 y+6 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.881 |
|
| \begin{align*}
-y^{2}+{y^{\prime }}^{2} x^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.517 |
|
| \begin{align*}
{y^{\prime }}^{2} x -\left (2 x +3 y\right ) y^{\prime }+6 y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.436 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}-5 x y y^{\prime }+6 y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.491 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}+x y^{\prime }-y^{2}-y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.481 |
|
| \begin{align*}
{y^{\prime }}^{2} x +\left (1-x^{2} y\right ) y^{\prime }-y x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.620 |
|
| \begin{align*}
{y^{\prime }}^{2}-\left (x^{2} y+3\right ) y^{\prime }+3 x^{2} y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.471 |
|
| \begin{align*}
{y^{\prime }}^{2} x -\left (y x +1\right ) y^{\prime }+y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.508 |
|
| \begin{align*}
{y^{\prime }}^{2}-x^{2} y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.500 |
|
| \begin{align*}
\left (x +y\right )^{2} {y^{\prime }}^{2}&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.389 |
|
| \begin{align*}
y {y^{\prime }}^{2}+\left (x -y^{2}\right ) y^{\prime }-y x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.621 |
|
| \begin{align*}
{y^{\prime }}^{2}-y^{\prime } x y \left (x +y\right )+x^{3} y^{3}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| \begin{align*}
\left (4 x -y\right ) {y^{\prime }}^{2}+6 \left (x -y\right ) y^{\prime }+2 x -5 y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
17.516 |
|
| \begin{align*}
\left (x -y\right )^{2} {y^{\prime }}^{2}&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.101 |
|
| \begin{align*}
x y {y^{\prime }}^{2}+\left (x y^{2}-1\right ) y^{\prime }-y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.276 |
|
| \begin{align*}
\left (x^{2}+y^{2}\right )^{2} {y^{\prime }}^{2}&=4 x^{2} y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.128 |
|
| \begin{align*}
\left (x +y\right )^{2} {y^{\prime }}^{2}+\left (2 y^{2}+y x -x^{2}\right ) y^{\prime }+y \left (-x +y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.837 |
|
| \begin{align*}
x y \left (x^{2}+y^{2}\right ) \left (-1+{y^{\prime }}^{2}\right )&=y^{\prime } \left (x^{4}+x^{2} y^{2}+y^{4}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.998 |
|
| \begin{align*}
x {y^{\prime }}^{3}-\left (x +x^{2}+y\right ) {y^{\prime }}^{2}+\left (x^{2}+y+y x \right ) y^{\prime }-y x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.626 |
|
| \begin{align*}
x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.641 |
|
| \begin{align*}
4 x -2 y y^{\prime }+{y^{\prime }}^{2} x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.473 |
|
| \begin{align*}
3 x^{4} {y^{\prime }}^{2}-x y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
3.553 |
|
| \begin{align*}
{y^{\prime }}^{2}-x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.698 |
|
| \begin{align*}
{y^{\prime }}^{2}-x y^{\prime }+y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.552 |
|
| \begin{align*}
{y^{\prime }}^{2}+4 x^{5} y^{\prime }-12 x^{4} y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.212 |
|
| \begin{align*}
4 y^{3} {y^{\prime }}^{2}-4 x y^{\prime }+y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✗ |
1.616 |
|
| \begin{align*}
4 y^{3} {y^{\prime }}^{2}+4 x y^{\prime }+y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✗ |
2.527 |
|
| \begin{align*}
{y^{\prime }}^{3}+{y^{\prime }}^{2} x -y&=0 \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
73.093 |
|
| \begin{align*}
y^{4} {y^{\prime }}^{3}-6 x y^{\prime }+2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.984 |
|
| \begin{align*}
{y^{\prime }}^{2}+x^{3} y^{\prime }-2 x^{2} y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.652 |
|
| \begin{align*}
{y^{\prime }}^{2}+4 x^{5} y^{\prime }-12 x^{4} y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.168 |
|
| \begin{align*}
2 x {y^{\prime }}^{3}-6 y {y^{\prime }}^{2}+x^{4}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.057 |
|
| \begin{align*}
{y^{\prime }}^{2}-x y^{\prime }+y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| \begin{align*}
y&=x y^{\prime }+k {y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.727 |
|
| \begin{align*}
x^{8} {y^{\prime }}^{2}+3 x y^{\prime }+9 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
3.678 |
|
| \begin{align*}
x^{4} {y^{\prime }}^{2}+2 x^{3} y y^{\prime }-4&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
1.766 |
|
| \begin{align*}
4 x -2 y y^{\prime }+{y^{\prime }}^{2} x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.419 |
|
| \begin{align*}
3 x^{4} {y^{\prime }}^{2}-x y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
2.872 |
|
| \begin{align*}
{y^{\prime }}^{2} x +\left (x -y\right ) y^{\prime }+1-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
0.814 |
|
| \begin{align*}
y^{\prime } \left (x y^{\prime }-y+k \right )+a&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.747 |
|
| \begin{align*}
x^{6} {y^{\prime }}^{3}-3 x y^{\prime }-3 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.135 |
|
| \begin{align*}
y&=x^{6} {y^{\prime }}^{3}-x y^{\prime } \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
✗ |
1.169 |
|
| \begin{align*}
x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+1&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
2.398 |
|
| \begin{align*}
{y^{\prime }}^{2}-x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.613 |
|
| \begin{align*}
2 {y^{\prime }}^{3}+x y^{\prime }-2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
9.645 |
|
| \begin{align*}
2 {y^{\prime }}^{2}+x y^{\prime }-2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.442 |
|
| \begin{align*}
{y^{\prime }}^{3}+2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
2.511 |
|
| \begin{align*}
4 {y^{\prime }}^{2} x -3 y y^{\prime }+3&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
45.684 |
|
| \begin{align*}
{y^{\prime }}^{3}-x y^{\prime }+2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.448 |
|
| \begin{align*}
5 {y^{\prime }}^{2}+6 x y^{\prime }-2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.716 |
|
| \begin{align*}
2 {y^{\prime }}^{2} x +\left (2 x -y\right ) y^{\prime }+1-y&=0 \\
\end{align*} |
[_rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
7.642 |
|
| \begin{align*}
5 {y^{\prime }}^{2}+3 x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.637 |
|
| \begin{align*}
{y^{\prime }}^{2}+3 x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.641 |
|
| \begin{align*}
y&=x y^{\prime }+x^{3} {y^{\prime }}^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
22.909 |
|
| \begin{align*}
y^{\prime \prime }&=x {y^{\prime }}^{3} \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
3.511 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+{y^{\prime }}^{2}-2 x y^{\prime }&=0 \\
y \left (2\right ) &= 5 \\
y^{\prime }\left (2\right ) &= -4 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.801 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+{y^{\prime }}^{2}-2 x y^{\prime }&=0 \\
y \left (2\right ) &= 5 \\
y^{\prime }\left (2\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.589 |
|
| \begin{align*}
y y^{\prime \prime }+{y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
1.214 |
|
| \begin{align*}
y^{2} y^{\prime \prime }+{y^{\prime }}^{3}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✗ |
1.368 |
|
| \begin{align*}
\left (y+1\right ) y^{\prime \prime }&={y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
1.593 |
|
| \begin{align*}
2 a y^{\prime \prime }+{y^{\prime }}^{3}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
6.004 |
|
| \begin{align*}
x y^{\prime \prime }&=y^{\prime }+x^{5} \\
y \left (1\right ) &= {\frac {1}{2}} \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.891 |
|
| \begin{align*}
x y^{\prime \prime }+y^{\prime }+x&=0 \\
y \left (2\right ) &= -1 \\
y^{\prime }\left (2\right ) &= -{\frac {1}{2}} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
2.123 |
|
| \begin{align*}
y^{\prime \prime }&=2 y {y^{\prime }}^{3} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✗ |
0.671 |
|
| \begin{align*}
-{y^{\prime }}^{2}+{y^{\prime }}^{3}+y y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✗ |
6.293 |
|
| \begin{align*}
y^{\prime \prime }+\beta ^{2} y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
4.782 |
|
| \begin{align*}
{y^{\prime }}^{3}+y y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✗ |
1.839 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime \prime }&=y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
2.363 |
|
| \begin{align*}
y^{\prime \prime }&={y^{\prime }}^{2} x \\
y \left (2\right ) &= \frac {\pi }{4} \\
y^{\prime }\left (2\right ) &= -{\frac {1}{4}} \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
0.685 |
|
| \begin{align*}
y^{\prime \prime }&={y^{\prime }}^{2} x \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
0.780 |
|
| \begin{align*}
y^{\prime \prime }&=-{\mathrm e}^{-2 y} \\
y \left (3\right ) &= 0 \\
y^{\prime }\left (3\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
0.857 |
|
| \begin{align*}
y^{\prime \prime }&=-{\mathrm e}^{-2 y} \\
y \left (3\right ) &= 0 \\
y^{\prime }\left (3\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
0.679 |
|
| \begin{align*}
2 y^{\prime \prime }&=\sin \left (2 y\right ) \\
y \left (0\right ) &= \frac {\pi }{2} \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✗ |
✗ |
✗ |
10.392 |
|
| \begin{align*}
2 y^{\prime \prime }&=\sin \left (2 y\right ) \\
y \left (0\right ) &= -\frac {\pi }{2} \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✗ |
✗ |
✗ |
6.903 |
|
| \begin{align*}
-x^{2} y^{\prime }+x^{3} y^{\prime \prime }&=-x^{2}+3 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.217 |
|
| \begin{align*}
y^{\prime \prime }&={y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
1.271 |
|
| \begin{align*}
y^{\prime \prime }&={\mathrm e}^{x} {y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.852 |
|
| \begin{align*}
2 y^{\prime \prime }&={y^{\prime }}^{3} \sin \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✗ |
3.979 |
|
| \begin{align*}
{y^{\prime }}^{2}+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
0.898 |
|
| \begin{align*}
y^{\prime \prime }&=1+{y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
5.970 |
|
| \begin{align*}
y^{\prime \prime }&=\left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
11.810 |
|
| \begin{align*}
y y^{\prime \prime }&={y^{\prime }}^{2} \left (1-y^{\prime } \sin \left (y\right )-\cos \left (y\right ) y y^{\prime }\right ) \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✗ |
3.124 |
|
| \begin{align*}
\left (1+y^{2}\right ) y^{\prime \prime }+{y^{\prime }}^{3}+y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
13.582 |
|
| \begin{align*}
\left (1+{y^{\prime }}^{2}+y y^{\prime \prime }\right )^{2}&=\left (1+{y^{\prime }}^{2}\right )^{3} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
115.139 |
|
| \begin{align*}
x^{2} y^{\prime \prime }&=y^{\prime } \left (2 x -y^{\prime }\right ) \\
y \left (-1\right ) &= 5 \\
y^{\prime }\left (-1\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.850 |
|
| \begin{align*}
x^{2} y^{\prime \prime }&=\left (3 x -2 y^{\prime }\right ) y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.925 |
|
| \begin{align*}
x y^{\prime \prime }&=y^{\prime } \left (2-3 x y^{\prime }\right ) \\
\end{align*} |
[[_2nd_order, _missing_y], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
1.306 |
|
| \begin{align*}
x^{4} y^{\prime \prime }&=y^{\prime } \left (y^{\prime }+x^{3}\right ) \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.830 |
|
| \begin{align*}
y^{\prime \prime }&=2 x +\left (x^{2}-y^{\prime }\right )^{2} \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
2.786 |
|
| \begin{align*}
{y^{\prime \prime }}^{2}-2 y^{\prime \prime }+{y^{\prime }}^{2}-2 x y^{\prime }+x^{2}&=0 \\
y \left (0\right ) &= {\frac {1}{2}} \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✗ |
✗ |
13.796 |
|
| \begin{align*}
y^{\prime }-x y^{\prime \prime }+{y^{\prime \prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.694 |
|
| \begin{align*}
{y^{\prime \prime }}^{3}&=12 y^{\prime } \left (-2 y^{\prime }+x y^{\prime \prime }\right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✗ |
✗ |
1.320 |
|