| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
x^{\prime \prime }+4 x&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.797 |
|
| \begin{align*}
x^{\prime \prime }+16 x&=0 \\
x \left (0\right ) &= -2 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.681 |
|
| \begin{align*}
x^{\prime \prime }+256 x&=0 \\
x \left (0\right ) &= 2 \\
x^{\prime }\left (0\right ) &= 4 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.040 |
|
| \begin{align*}
x^{\prime \prime }+9 x&=0 \\
x \left (0\right ) &= {\frac {1}{3}} \\
x^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.249 |
|
| \begin{align*}
10 x^{\prime \prime }+\frac {x}{10}&=0 \\
x \left (0\right ) &= -5 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.694 |
|
| \begin{align*}
x^{\prime \prime }+4 x^{\prime }+3 x&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= -4 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.383 |
|
| \begin{align*}
\frac {x^{\prime \prime }}{32}+2 x^{\prime }+x&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.491 |
|
| \begin{align*}
\frac {x^{\prime \prime }}{4}+2 x^{\prime }+x&=0 \\
x \left (0\right ) &= -{\frac {1}{2}} \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.504 |
|
| \begin{align*}
4 x^{\prime \prime }+2 x^{\prime }+8 x&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.501 |
|
| \begin{align*}
x^{\prime \prime }+4 x^{\prime }+13 x&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.474 |
|
| \begin{align*}
x^{\prime \prime }+4 x^{\prime }+20 x&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.478 |
|
| \begin{align*}
x^{\prime \prime }+x&=\left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.859 |
|
| \begin{align*}
x^{\prime \prime }+x&=\left \{\begin {array}{cc} \cos \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✓ |
✓ |
6.937 |
|
| \begin{align*}
x^{\prime \prime }+x&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 2-t & 1\le t <2 \\ 0 & 2\le t \end {array}\right . \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.919 |
|
| \begin{align*}
x^{\prime \prime }+4 x^{\prime }+13 x&=\left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 1-t & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
8.148 |
|
| \begin{align*}
x^{\prime \prime }+x&=\cos \left (t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.605 |
|
| \begin{align*}
x^{\prime \prime }+x&=\cos \left (t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.527 |
|
| \begin{align*}
x^{\prime \prime }+x&=\cos \left (\frac {9 t}{10}\right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} | [[_2nd_order, _linear, _nonhomogeneous]] | ✓ | ✓ | ✓ | ✓ | 0.689 |
|
| \begin{align*}
x^{\prime \prime }+x&=\cos \left (\frac {7 t}{10}\right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.635 |
|
| \begin{align*}
x^{\prime \prime }+\frac {x^{\prime }}{10}+x&=3 \cos \left (2 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.780 |
|
| \begin{align*}
x^{\prime }&=6 \\
y^{\prime }&=\cos \left (t \right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.393 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.459 |
|
| \begin{align*}
x^{\prime }&=0 \\
y^{\prime }&=-2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.317 |
|
| \begin{align*}
x^{\prime }&=x^{2} \\
y^{\prime }&={\mathrm e}^{t} \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.039 |
|
| \begin{align*}
x_{1}^{\prime }&=-3 x_{1} \\
x_{2}^{\prime }&=1 \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= -1 \\
x_{2} \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.573 |
|
| \begin{align*}
x_{1}^{\prime }&=-x_{1}+1 \\
x_{2}^{\prime }&=x_{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 0 \\
x_{2} \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.550 |
|
| \begin{align*}
x^{\prime }&=-3 x+6 y \\
y^{\prime }&=4 x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.458 |
|
| \begin{align*}
x^{\prime }&=8 x-y \\
y^{\prime }&=x+6 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.364 |
|
| \begin{align*}
x^{\prime }&=-x-2 y \\
y^{\prime }&=x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| \begin{align*}
x^{\prime }&=4 x+2 y \\
y^{\prime }&=-x+2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.588 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=1-x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.615 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-x+\sin \left (2 t \right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.716 |
|
| \begin{align*}
x^{\prime \prime }-3 x^{\prime }+4 x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.364 |
|
| \begin{align*}
x^{\prime \prime }+6 x^{\prime }+9 x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.303 |
|
| \begin{align*}
x^{\prime \prime }+16 x&=t \sin \left (t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.635 |
|
| \begin{align*}
x^{\prime \prime }+x&={\mathrm e}^{t} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.368 |
|
| \begin{align*}
y^{\prime }&=y^{2}+x^{2} \\
\end{align*} | [[_Riccati, _special]] | ✓ | ✓ | ✓ | ✗ | 45.764 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.083 |
|
| \begin{align*}
y^{\prime }&=y+3 y^{{1}/{3}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.167 |
|
| \begin{align*}
y^{\prime }&=\sqrt {x -y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.220 |
|
| \begin{align*}
y^{\prime }&=\sqrt {x^{2}-y}-x \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
19.487 |
|
| \begin{align*}
y^{\prime }&=\sqrt {1-y^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.041 |
|
| \begin{align*}
y^{\prime }&=\frac {1+y}{x -y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.003 |
|
| \begin{align*}
y^{\prime }&=\sin \left (y\right )-\cos \left (x \right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
✗ |
2.570 |
|
| \begin{align*}
y^{\prime }&=1-\cot \left (y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.821 |
|
| \begin{align*}
y^{\prime }&=\left (3 x -y\right )^{{1}/{3}}-1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.611 |
|
| \begin{align*}
y^{\prime }&=\sin \left (y x \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✓ |
✗ |
1.350 |
|
| \begin{align*}
y^{\prime } x +y&=\cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.257 |
|
| \begin{align*}
2 y+y^{\prime }&={\mathrm e}^{x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.523 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+y x&=2 x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.634 |
|
| \begin{align*}
y^{\prime }&=x +1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.266 |
|
| \begin{align*}
y^{\prime }&=x +y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.108 |
|
| \begin{align*}
y^{\prime }&=y-x \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.950 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{2}-y+\frac {3}{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.305 |
|
| \begin{align*}
y^{\prime }&=\left (y-1\right )^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.306 |
|
| \begin{align*}
y^{\prime }&=\left (y-1\right ) x \\
\end{align*} | [_separable] | ✓ | ✓ | ✓ | ✓ | 2.473 |
|
| \begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
7.887 |
|
| \begin{align*}
y^{\prime }&=\cos \left (x -y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.338 |
|
| \begin{align*}
y^{\prime }&=y-x^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.980 |
|
| \begin{align*}
y^{\prime }&=x^{2}+2 x -y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.491 |
|
| \begin{align*}
y^{\prime }&=\frac {1+y}{x -1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.644 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y}{x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.539 |
|
| \begin{align*}
y^{\prime }&=1-x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.270 |
|
| \begin{align*}
y^{\prime }&=2 x -y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.216 |
|
| \begin{align*}
y^{\prime }&=y+x^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.944 |
|
| \begin{align*}
y^{\prime }&=-\frac {y}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.033 |
|
| \begin{align*}
y^{\prime }&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.575 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.361 |
|
| \begin{align*}
y^{\prime }&=y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.601 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.975 |
|
| \begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
8.106 |
|
| \begin{align*}
y^{\prime }&=x +y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
128.487 |
|
| \begin{align*}
y^{\prime }&=x +y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.294 |
|
| \begin{align*}
y^{\prime }&=2 y-2 x^{2}-3 \\
y \left (0\right ) &= 2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.420 |
|
| \begin{align*}
y^{\prime } x&=2 x -y \\
y \left (1\right ) &= 2 \\
\end{align*} | [_linear] | ✓ | ✓ | ✓ | ✓ | 4.572 |
|
| \begin{align*}
1+y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.691 |
|
| \begin{align*}
x y^{\prime } y+1+y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.978 |
|
| \begin{align*}
\sin \left (x \right ) y^{\prime }-y \cos \left (x \right )&=0 \\
y \left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.645 |
|
| \begin{align*}
1+y^{2}&=y^{\prime } x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.924 |
|
| \begin{align*}
y y^{\prime } \sqrt {x^{2}+1}+x \sqrt {1+y^{2}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.747 |
|
| \begin{align*}
x \sqrt {1-y^{2}}+y \sqrt {-x^{2}+1}\, y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.059 |
|
| \begin{align*}
{\mathrm e}^{-y} y^{\prime }&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.662 |
|
| \begin{align*}
y \ln \left (y\right )+y^{\prime } x&=1 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✓ |
7.550 |
|
| \begin{align*}
y^{\prime }&=a^{x +y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.168 |
|
| \begin{align*}
{\mathrm e}^{y} \left (x^{2}+1\right ) y^{\prime }-2 x \left (1+{\mathrm e}^{y}\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.132 |
|
| \begin{align*}
2 x \sqrt {1-y^{2}}&=\left (x^{2}+1\right ) y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.039 |
|
| \begin{align*}
{\mathrm e}^{x} \sin \left (y\right )^{3}+\left ({\mathrm e}^{2 x}+1\right ) \cos \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.646 |
|
| \begin{align*}
\sin \left (x \right ) y^{2}+\cos \left (x \right )^{2} \ln \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.369 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x -y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.352 |
|
| \begin{align*}
y^{\prime }&=a x +b y+c \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.692 |
|
| \begin{align*}
\left (x +y\right )^{2} y^{\prime }&=a^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
9.485 |
|
| \begin{align*}
y^{\prime } x +y&=a \left (y x +1\right ) \\
y \left (\frac {1}{a}\right ) &= -a \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.834 |
|
| \begin{align*}
a^{2}+y^{2}+2 x \sqrt {a x -x^{2}}\, y^{\prime }&=0 \\
y \left (a \right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✗ |
10.022 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x} \\
y \left (0\right ) &= 0 \\
\end{align*} | [_separable] | ✓ | ✓ | ✓ | ✗ | 5.754 |
|
| \begin{align*}
\cos \left (y^{\prime }\right )&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.632 |
|
| \begin{align*}
{\mathrm e}^{y^{\prime }}&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.417 |
|
| \begin{align*}
\sin \left (y^{\prime }\right )&=x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.329 |
|
| \begin{align*}
\ln \left (y^{\prime }\right )&=x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.441 |
|
| \begin{align*}
\tan \left (y^{\prime }\right )&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.428 |
|
| \begin{align*}
{\mathrm e}^{y^{\prime }}&=x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.296 |
|