| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime }&=4 x^{3}-x +2 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.463 |
|
| \begin{align*}
y^{\prime }&=\sin \left (2 t \right )-\cos \left (2 t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.586 |
|
| \begin{align*}
y^{\prime }&=\frac {\cos \left (\frac {1}{x}\right )}{x^{2}} \\
y \left (\frac {2}{\pi }\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.651 |
|
| \begin{align*}
y^{\prime }&=\frac {\ln \left (x \right )}{x} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.627 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (x -4\right ) y^{3}}{x^{3} \left (y-2\right )} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
19.333 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}+2 y x}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.557 |
|
| \begin{align*}
y^{\prime } x +y&=\cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.928 |
|
| \begin{align*}
16 y^{\prime \prime }+24 y^{\prime }+153 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
8.715 |
|
| \begin{align*}
x^{\prime }&=4 y \\
y^{\prime }&=-x-2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.671 |
|
| \begin{align*}
4 \left (x^{2}+y^{2}\right ) x -5 y+4 y \left (x^{2}+y^{2}-5 x \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
✗ |
24.788 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x \right )^{4} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.030 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+\frac {25 y^{\prime \prime }}{2}-5 y^{\prime }+\frac {629 y}{16}&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
y^{\prime \prime }\left (0\right ) &= -1 \\
y^{\prime \prime \prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.164 |
|
| \begin{align*}
x^{\prime }&=4 y \\
y^{\prime }&=-4 x \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 4 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.524 |
|
| \begin{align*}
x^{\prime }&=-5 x+4 y \\
y^{\prime }&=2 x+2 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 4 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.568 |
|
| \begin{align*}
y^{\prime }+\cos \left (x \right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.336 |
|
| \begin{align*}
y^{\prime }-y&=\sin \left (x \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.308 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }-5 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
5.348 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+45 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
8.229 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x -16 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
8.045 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
4.364 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
28.845 |
|
| \begin{align*}
12 y-7 y^{\prime }+y^{\prime \prime }&=2 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
29.275 |
|
| \begin{align*}
2 x -3 y+\left (-3 x +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.552 |
|
| \begin{align*}
y \cos \left (y x \right )+\sin \left (x \right )+x \cos \left (y x \right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
4.239 |
|
| \begin{align*}
y^{\prime }&=x \,{\mathrm e}^{-x^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.388 |
|
| \begin{align*}
y^{\prime }&=x^{2} \sin \left (x \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.441 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x^{2}-x +1}{\left (x -1\right ) \left (x^{2}+1\right )} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.425 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}}{\sqrt {x^{2}-1}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.394 |
|
| \begin{align*}
2 y+y^{\prime }&=x^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.921 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=t \\
y \left (\frac {\pi }{4}\right ) &= 1 \\
y^{\prime }\left (\frac {\pi }{4}\right ) &= \frac {\pi }{16} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
53.452 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
6.955 |
|
| \begin{align*}
y^{\prime }&=\cos \left (x \right )^{2} \sin \left (x \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.611 |
|
| \begin{align*}
y^{\prime }&=\frac {4 x -9}{3 \left (x -3\right )^{{2}/{3}}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.728 |
|
| \begin{align*}
y^{\prime }+t^{2}&=y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
21.512 |
|
| \begin{align*}
y^{\prime }+t^{2}&=\frac {1}{y^{2}} \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
✗ |
3.041 |
|
| \begin{align*}
y^{\prime }&=y+\frac {1}{1-t} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.408 |
|
| \begin{align*}
y^{\prime }&=y^{{1}/{5}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
18.277 |
|
| \begin{align*}
\frac {y^{\prime }}{t}&=\sqrt {y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
65.797 |
|
| \begin{align*}
y^{\prime }&=4 t^{2}-t y^{2} \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
15.439 |
|
| \begin{align*}
y^{\prime }&=y \sqrt {t} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.574 |
|
| \begin{align*}
y^{\prime }&=6 y^{{2}/{3}} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
6.023 |
|
| \begin{align*}
y^{\prime } t&=y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.615 |
|
| \begin{align*}
y^{\prime }&=\tan \left (t \right ) y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.421 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{t^{2}+1} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.412 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y^{2}-1} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
31.978 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y^{2}-1} \\
y \left (4\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
28.915 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y^{2}-1} \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
30.280 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y^{2}-1} \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
29.632 |
|
| \begin{align*}
y^{\prime }&=\sqrt {25-y^{2}} \\
y \left (-4\right ) &= 3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
279.732 |
|
| \begin{align*}
y^{\prime }&=\sqrt {25-y^{2}} \\
y \left (0\right ) &= 5 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.658 |
|
| \begin{align*}
y^{\prime }&=\sqrt {25-y^{2}} \\
y \left (3\right ) &= -6 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
21.367 |
|
| \begin{align*}
y^{\prime }&=\sqrt {25-y^{2}} \\
y \left (4\right ) &= -5 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
60.801 |
|
| \begin{align*}
y^{\prime } t +y&=t^{3} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.954 |
|
| \begin{align*}
t^{3} y^{\prime }+t^{4} y&=2 t^{3} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.329 |
|
| \begin{align*}
2 y^{\prime }+t y&=\ln \left (t \right ) \\
y \left ({\mathrm e}\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.926 |
|
| \begin{align*}
y^{\prime }+y \sec \left (t \right )&=t \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.311 |
|
| \begin{align*}
y^{\prime }+\frac {y}{t -3}&=\frac {1}{t -1} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.773 |
|
| \begin{align*}
\left (-2+t \right ) y^{\prime }+\left (t^{2}-4\right ) y&=\frac {1}{t +2} \\
y \left (0\right ) &= 3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
3.240 |
|
| \begin{align*}
y^{\prime }+\frac {y}{\sqrt {-t^{2}+4}}&=t \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.035 |
|
| \begin{align*}
y^{\prime }+\frac {y}{\sqrt {-t^{2}+4}}&=t \\
y \left (3\right ) &= -1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
14.361 |
|
| \begin{align*}
y^{\prime } t +y&=t \sin \left (t \right ) \\
y \left (\pi \right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.544 |
|
| \begin{align*}
\tan \left (t \right ) y+y^{\prime }&=\sin \left (t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.168 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
14.023 |
|
| \begin{align*}
y^{\prime }&=t y^{2} \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
28.949 |
|
| \begin{align*}
y^{\prime }&=-\frac {t}{y} \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
30.177 |
|
| \begin{align*}
y^{\prime }&=-y^{3} \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
45.346 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.944 |
|
| \begin{align*}
\frac {1}{2 \sqrt {t}}+y^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.021 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {y}}{x^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
20.288 |
|
| \begin{align*}
y^{\prime }&=\frac {1+y^{2}}{y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.561 |
|
| \begin{align*}
6+4 t^{3}+\left (5+\frac {9}{y^{8}}\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.441 |
|
| \begin{align*}
\frac {6}{t^{9}}-\frac {6}{t^{3}}+t^{7}+\left (9+\frac {1}{s^{2}}-4 s^{8}\right ) s^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.120 |
|
| \begin{align*}
4 \sinh \left (4 y\right ) y^{\prime }&=6 \cosh \left (3 x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
4.231 |
|
| \begin{align*}
y^{\prime }&=\frac {1+y}{1+t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.162 |
|
| \begin{align*}
y^{\prime }&=\frac {2+y}{2 t +1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
15.417 |
|
| \begin{align*}
\frac {3}{t^{2}}&=\left (\frac {1}{\sqrt {y}}+\sqrt {y}\right ) y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
6.840 |
|
| \begin{align*}
3 \sin \left (x \right )-4 y^{\prime } \cos \left (y\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.031 |
|
| \begin{align*}
\cos \left (y\right ) y^{\prime }&=8 \sin \left (8 t \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.947 |
|
| \begin{align*}
y^{\prime }+k y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.126 |
|
| \begin{align*}
\left (5 x^{5}-4 \cos \left (x\right )\right ) x^{\prime }+2 \cos \left (9 t \right )+2 \sin \left (7 t \right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.171 |
|
| \begin{align*}
\cosh \left (6 t \right )+5 \sinh \left (4 t \right )+20 \sinh \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.154 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{2 y+10 t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.815 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{3 y+2 t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.735 |
|
| \begin{align*}
\sin \left (t \right )^{2}&=\cos \left (y\right )^{2} y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.696 |
|
| \begin{align*}
3 \sin \left (t \right )-\sin \left (3 t \right )&=\left (\cos \left (4 y\right )-4 \cos \left (y\right )\right ) y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
24.710 |
|
| \begin{align*}
x^{\prime }&=\frac {\sec \left (t \right )^{2}}{\sec \left (x\right ) \tan \left (x\right )} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
36.617 |
|
| \begin{align*}
\left (2-\frac {5}{y^{2}}\right ) y^{\prime }+4 \cos \left (x \right )^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.193 |
|
| \begin{align*}
y^{\prime }&=\frac {t^{3}}{y \sqrt {\left (1-y^{2}\right ) \left (t^{4}+9\right )}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
15.449 |
|
| \begin{align*}
\tan \left (y\right ) \sec \left (y\right )^{2} y^{\prime }+\cos \left (2 x \right )^{3} \sin \left (2 x \right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.093 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (1+2 \,{\mathrm e}^{y}\right ) {\mathrm e}^{-y}}{t \ln \left (t \right )} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.999 |
|
| \begin{align*}
x \sin \left (x^{2}\right )&=\frac {\cos \left (\sqrt {y}\right ) y^{\prime }}{\sqrt {y}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
22.202 |
|
| \begin{align*}
\frac {x -2}{x^{2}-4 x +3}&=\frac {\left (1-\frac {1}{y}\right )^{2} y^{\prime }}{y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
5.403 |
|
| \begin{align*}
\frac {\cos \left (y\right ) y^{\prime }}{\left (1-\sin \left (y\right )\right )^{2}}&=\sin \left (x \right )^{3} \cos \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.650 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (5-2 \cos \left (x \right )\right )^{3} \sin \left (x \right ) \cos \left (y\right )^{4}}{\sin \left (y\right )} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
18.872 |
|
| \begin{align*}
\frac {\sqrt {\ln \left (x \right )}}{x}&=\frac {{\mathrm e}^{\frac {3}{y}} y^{\prime }}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.413 |
|
| \begin{align*}
y^{\prime }&=\frac {5^{-t}}{y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.200 |
|
| \begin{align*}
y^{\prime }&=t^{2} y^{2}+y^{2}-t^{2}-1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
5.867 |
|
| \begin{align*}
y^{\prime }&=y^{2}-3 y+2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.185 |
|
| \begin{align*}
4 \left (x -1\right )^{2} y^{\prime }-3 \left (3+y\right )^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
16.830 |
|
| \begin{align*}
y^{\prime }&=\sin \left (t -y\right )+\sin \left (y+t \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
15.998 |
|