|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x^{\prime \prime }+64 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.114 |
|
|
\[
{}x^{\prime \prime }+100 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.177 |
|
|
\[
{}x^{\prime \prime }+x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.874 |
|
|
\[
{}x^{\prime \prime }+4 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.117 |
|
|
\[
{}x^{\prime \prime }+16 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.087 |
|
|
\[
{}x^{\prime \prime }+256 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.271 |
|
|
\[
{}x^{\prime \prime }+9 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.820 |
|
|
\[
{}10 x^{\prime \prime }+\frac {x}{10} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.020 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+3 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.421 |
|
|
\[
{}\frac {x^{\prime \prime }}{32}+2 x^{\prime }+x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.392 |
|
|
\[
{}\frac {x^{\prime \prime }}{4}+2 x^{\prime }+x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.410 |
|
|
\[
{}4 x^{\prime \prime }+2 x^{\prime }+8 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.755 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+13 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.772 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+20 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.652 |
|
|
\[
{}x^{\prime \prime }+x = \left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.722 |
|
|
\[
{}x^{\prime \prime }+x = \left \{\begin {array}{cc} \cos \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
5.174 |
|
|
\[
{}x^{\prime \prime }+x = \left \{\begin {array}{cc} t & 0\le t <1 \\ -t +2 & 1\le t <2 \\ 0 & 2\le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
72.616 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+13 x = \left \{\begin {array}{cc} 1 & 0\le t <\pi \\ -t +1 & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
29.528 |
|
|
\[
{}x^{\prime \prime }+x = \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.439 |
|
|
\[
{}x^{\prime \prime }+x = \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.056 |
|
|
\[
{}x^{\prime \prime }+x = \cos \left (\frac {9 t}{10}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
10.432 |
|
|
\[
{}x^{\prime \prime }+x = \cos \left (\frac {7 t}{10}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
9.350 |
|
|
\[
{}x^{\prime \prime }+\frac {x^{\prime }}{10}+x = 3 \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
76.201 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=6 \\ y^{\prime }=\cos \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.264 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=1 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.373 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=0 \\ y^{\prime }=-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.295 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x^{2} \\ y^{\prime }={\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.022 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1} \\ x_{2}^{\prime }=1 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.516 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}+1 \\ x_{2}^{\prime }=x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.595 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+6 y \\ y^{\prime }=4 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.368 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=8 x-y \\ y^{\prime }=x+6 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.309 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x-2 y \\ y^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.402 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x+2 y \\ y^{\prime }=-x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.433 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x+1 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.573 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x+\sin \left (2 t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.607 |
|
|
\[
{}x^{\prime \prime }-3 x^{\prime }+4 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.314 |
|
|
\[
{}x^{\prime \prime }+6 x^{\prime }+9 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.904 |
|
|
\[
{}x^{\prime \prime }+16 x = t \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.487 |
|
|
\[
{}x^{\prime \prime }+x = {\mathrm e}^{t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.990 |
|
|
\[
{}y^{\prime } = y^{2}+x^{2}
\] |
[[_Riccati, _special]] |
✓ |
1.013 |
|
|
\[
{}y^{\prime } = \frac {x}{y}
\] |
[_separable] |
✓ |
2.958 |
|
|
\[
{}y^{\prime } = y+3 y^{{1}/{3}}
\] |
[_quadrature] |
✓ |
4.890 |
|
|
\[
{}y^{\prime } = \sqrt {x -y}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.941 |
|
|
\[
{}y^{\prime } = \sqrt {x^{2}-y}-x
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
5.367 |
|
|
\[
{}y^{\prime } = \sqrt {1-y^{2}}
\] |
[_quadrature] |
✓ |
38.752 |
|
|
\[
{}y^{\prime } = \frac {y+1}{x -y}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.874 |
|
|
\[
{}y^{\prime } = \sin \left (y\right )-\cos \left (x \right )
\] |
[‘y=_G(x,y’)‘] |
✗ |
2.814 |
|
|
\[
{}y^{\prime } = 1-\cot \left (y\right )
\] |
[_quadrature] |
✓ |
1.789 |
|
|
\[
{}y^{\prime } = \left (3 x -y\right )^{{1}/{3}}-1
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.589 |
|
|
\[
{}y^{\prime } = \sin \left (x y\right )
\] |
[‘y=_G(x,y’)‘] |
✗ |
1.403 |
|
|
\[
{}x y^{\prime }+y = \cos \left (x \right )
\] |
[_linear] |
✓ |
1.141 |
|
|
\[
{}y^{\prime }+2 y = {\mathrm e}^{x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.066 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }+x y = 2 x
\] |
[_separable] |
✓ |
1.254 |
|
|
\[
{}y^{\prime } = x +1
\] |
[_quadrature] |
✓ |
0.255 |
|
|
\[
{}y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
0.962 |
|
|
\[
{}y^{\prime } = y-x
\] |
[[_linear, ‘class A‘]] |
✓ |
0.979 |
|
|
\[
{}y^{\prime } = \frac {x}{2}-y+\frac {3}{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.976 |
|
|
\[
{}y^{\prime } = \left (y-1\right )^{2}
\] |
[_quadrature] |
✓ |
0.870 |
|
|
\[
{}y^{\prime } = \left (y-1\right ) x
\] |
[_separable] |
✓ |
1.081 |
|
|
\[
{}y^{\prime } = x^{2}-y^{2}
\] |
[_Riccati] |
✓ |
1.002 |
|
|
\[
{}y^{\prime } = \cos \left (x -y\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.420 |
|
|
\[
{}y^{\prime } = y-x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.013 |
|
|
\[
{}y^{\prime } = x^{2}+2 x -y
\] |
[[_linear, ‘class A‘]] |
✓ |
0.986 |
|
|
\[
{}y^{\prime } = \frac {y+1}{x -1}
\] |
[_separable] |
✓ |
1.402 |
|
|
\[
{}y^{\prime } = \frac {x +y}{x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.645 |
|
|
\[
{}y^{\prime } = 1-x
\] |
[_quadrature] |
✓ |
0.260 |
|
|
\[
{}y^{\prime } = 2 x -y
\] |
[[_linear, ‘class A‘]] |
✓ |
0.956 |
|
|
\[
{}y^{\prime } = y+x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.974 |
|
|
\[
{}y^{\prime } = -\frac {y}{x}
\] |
[_separable] |
✓ |
1.584 |
|
|
\[
{}y^{\prime } = 1
\] |
[_quadrature] |
✓ |
0.447 |
|
|
\[
{}y^{\prime } = \frac {1}{x}
\] |
[_quadrature] |
✓ |
0.277 |
|
|
\[
{}y^{\prime } = y
\] |
[_quadrature] |
✓ |
0.966 |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
0.964 |
|
|
\[
{}y^{\prime } = x^{2}-y^{2}
\] |
[_Riccati] |
✓ |
1.378 |
|
|
\[
{}y^{\prime } = x +y^{2}
\] |
[[_Riccati, _special]] |
✓ |
15.266 |
|
|
\[
{}y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.274 |
|
|
\[
{}y^{\prime } = 2 y-2 x^{2}-3
\] |
[[_linear, ‘class A‘]] |
✓ |
1.270 |
|
|
\[
{}x y^{\prime } = 2 x -y
\] |
[_linear] |
✓ |
2.497 |
|
|
\[
{}1+y^{2}+\left (x^{2}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.814 |
|
|
\[
{}1+y^{2}+x y y^{\prime } = 0
\] |
[_separable] |
✓ |
2.125 |
|
|
\[
{}y^{\prime } \sin \left (x \right )-y \cos \left (x \right ) = 0
\] |
[_separable] |
✓ |
2.140 |
|
|
\[
{}1+y^{2} = x y^{\prime }
\] |
[_separable] |
✓ |
1.565 |
|
|
\[
{}x \sqrt {1+y^{2}}+y y^{\prime } \sqrt {x^{2}+1} = 0
\] |
[_separable] |
✓ |
2.751 |
|
|
\[
{}x \sqrt {1-y^{2}}+y \sqrt {-x^{2}+1}\, y^{\prime } = 0
\] |
[_separable] |
✓ |
3.413 |
|
|
\[
{}{\mathrm e}^{-y} y^{\prime } = 1
\] |
[_quadrature] |
✓ |
0.918 |
|
|
\[
{}y \ln \left (y\right )+x y^{\prime } = 1
\] |
[_separable] |
✓ |
2.701 |
|
|
\[
{}y^{\prime } = a^{x +y}
\] |
[_separable] |
✓ |
1.875 |
|
|
\[
{}{\mathrm e}^{y} \left (x^{2}+1\right ) y^{\prime }-2 x \left (1+{\mathrm e}^{y}\right ) = 0
\] |
[_separable] |
✓ |
2.872 |
|
|
\[
{}2 x \sqrt {1-y^{2}} = \left (x^{2}+1\right ) y^{\prime }
\] |
[_separable] |
✓ |
2.353 |
|
|
\[
{}{\mathrm e}^{x} \sin \left (y\right )^{3}+\left (1+{\mathrm e}^{2 x}\right ) \cos \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
3.618 |
|
|
\[
{}y^{2} \sin \left (x \right )+\cos \left (x \right )^{2} \ln \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
3.139 |
|
|
\[
{}y^{\prime } = \sin \left (x -y\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.373 |
|
|
\[
{}y^{\prime } = a x +b y+c
\] |
[[_linear, ‘class A‘]] |
✓ |
0.753 |
|
|
\[
{}\left (x +y\right )^{2} y^{\prime } = a^{2}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
4.360 |
|
|
\[
{}x y^{\prime }+y = a \left (x y+1\right )
\] |
[_linear] |
✓ |
1.084 |
|
|
\[
{}a^{2}+y^{2}+2 x \sqrt {a x -x^{2}}\, y^{\prime } = 0
\] |
[_separable] |
✓ |
3.432 |
|
|
\[
{}y^{\prime } = \frac {y}{x}
\] |
[_separable] |
✓ |
1.341 |
|
|
\[
{}\cos \left (y^{\prime }\right ) = 0
\] |
[_quadrature] |
✓ |
0.468 |
|
|
\[
{}{\mathrm e}^{y^{\prime }} = 1
\] |
[_quadrature] |
✓ |
0.397 |
|
|
\[
{}\sin \left (y^{\prime }\right ) = x
\] |
[_quadrature] |
✓ |
0.254 |
|