|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x^{\prime \prime }+x = \left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.472 |
|
|
\[
{}x^{\prime \prime }+x = \left \{\begin {array}{cc} \cos \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
3.480 |
|
|
\[
{}x^{\prime \prime }+x = \left \{\begin {array}{cc} t & 0\le t <1 \\ -t +2 & 1\le t <2 \\ 0 & 2\le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.152 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+13 x = \left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 1-t & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
53.443 |
|
|
\[
{}x^{\prime \prime }+x = \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.575 |
|
|
\[
{}x^{\prime \prime }+x = \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.669 |
|
|
\[
{}x^{\prime \prime }+x = \cos \left (\frac {9 t}{10}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
8.086 |
|
|
\[
{}x^{\prime \prime }+x = \cos \left (\frac {7 t}{10}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.826 |
|
|
\[
{}x^{\prime \prime }+\frac {x^{\prime }}{10}+x = 3 \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
36.904 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=6 \\ y^{\prime }=\cos \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.238 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=1 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.328 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=0 \\ y^{\prime }=-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.275 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x^{2} \\ y^{\prime }={\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.027 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1} \\ x_{2}^{\prime }=1 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.451 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}+1 \\ x_{2}^{\prime }=x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.451 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+6 y \\ y^{\prime }=4 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.326 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=8 x-y \\ y^{\prime }=x+6 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.270 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x-2 y \\ y^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.350 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x+2 y \\ y^{\prime }=-x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.386 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x+1 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.500 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x+\sin \left (2 t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.570 |
|
|
\[
{}x^{\prime \prime }-3 x^{\prime }+4 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.568 |
|
|
\[
{}x^{\prime \prime }+6 x^{\prime }+9 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.744 |
|
|
\[
{}x^{\prime \prime }+16 x = t \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.120 |
|
|
\[
{}x^{\prime \prime }+x = {\mathrm e}^{t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.589 |
|
|
\[
{}y^{\prime } = x^{2}+y^{2}
\] |
[[_Riccati, _special]] |
✓ |
0.996 |
|
|
\[
{}y^{\prime } = \frac {x}{y}
\] |
[_separable] |
✓ |
2.582 |
|
|
\[
{}y^{\prime } = y+3 y^{{1}/{3}}
\] |
[_quadrature] |
✓ |
1.475 |
|
|
\[
{}y^{\prime } = \sqrt {x -y}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.306 |
|
|
\[
{}y^{\prime } = \sqrt {x^{2}-y}-x
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
3.813 |
|
|
\[
{}y^{\prime } = \sqrt {1-y^{2}}
\] |
[_quadrature] |
✓ |
38.278 |
|
|
\[
{}y^{\prime } = \frac {1+y}{x -y}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.717 |
|
|
\[
{}y^{\prime } = \sin \left (y\right )-\cos \left (x \right )
\] |
[‘y=_G(x,y’)‘] |
✗ |
1.122 |
|
|
\[
{}y^{\prime } = 1-\cot \left (y\right )
\] |
[_quadrature] |
✓ |
0.805 |
|
|
\[
{}y^{\prime } = \left (3 x -y\right )^{{1}/{3}}-1
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.137 |
|
|
\[
{}y^{\prime } = \sin \left (y x \right )
\] |
[‘y=_G(x,y’)‘] |
✗ |
0.689 |
|
|
\[
{}y^{\prime } x +y = \cos \left (x \right )
\] |
[_linear] |
✓ |
1.066 |
|
|
\[
{}y^{\prime }+2 y = {\mathrm e}^{x}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.911 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }+y x = 2 x
\] |
[_separable] |
✓ |
1.176 |
|
|
\[
{}y^{\prime } = x +1
\] |
[_quadrature] |
✓ |
0.219 |
|
|
\[
{}y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
0.818 |
|
|
\[
{}y^{\prime } = -x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
0.838 |
|
|
\[
{}y^{\prime } = \frac {x}{2}-y+\frac {3}{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.966 |
|
|
\[
{}y^{\prime } = \left (-1+y\right )^{2}
\] |
[_quadrature] |
✓ |
0.336 |
|
|
\[
{}y^{\prime } = \left (-1+y\right ) x
\] |
[_separable] |
✓ |
0.988 |
|
|
\[
{}y^{\prime } = x^{2}-y^{2}
\] |
[_Riccati] |
✓ |
0.986 |
|
|
\[
{}y^{\prime } = \cos \left (x -y\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.080 |
|
|
\[
{}y^{\prime } = y-x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.906 |
|
|
\[
{}y^{\prime } = x^{2}+2 x -y
\] |
[[_linear, ‘class A‘]] |
✓ |
0.866 |
|
|
\[
{}y^{\prime } = \frac {1+y}{x -1}
\] |
[_separable] |
✓ |
1.387 |
|
|
\[
{}y^{\prime } = \frac {x +y}{x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.456 |
|
|
\[
{}y^{\prime } = 1-x
\] |
[_quadrature] |
✓ |
0.220 |
|
|
\[
{}y^{\prime } = 2 x -y
\] |
[[_linear, ‘class A‘]] |
✓ |
0.818 |
|
|
\[
{}y^{\prime } = y+x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.814 |
|
|
\[
{}y^{\prime } = -\frac {y}{x}
\] |
[_separable] |
✓ |
1.401 |
|
|
\[
{}y^{\prime } = 1
\] |
[_quadrature] |
✓ |
0.387 |
|
|
\[
{}y^{\prime } = \frac {1}{x}
\] |
[_quadrature] |
✓ |
0.233 |
|
|
\[
{}y^{\prime } = y
\] |
[_quadrature] |
✓ |
0.419 |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
0.385 |
|
|
\[
{}y^{\prime } = x^{2}-y^{2}
\] |
[_Riccati] |
✓ |
1.524 |
|
|
\[
{}y^{\prime } = x +y^{2}
\] |
[[_Riccati, _special]] |
✓ |
1.137 |
|
|
\[
{}y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.036 |
|
|
\[
{}y^{\prime } = 2 y-2 x^{2}-3
\] |
[[_linear, ‘class A‘]] |
✓ |
1.049 |
|
|
\[
{}y^{\prime } x = 2 x -y
\] |
[_linear] |
✓ |
2.005 |
|
|
\[
{}1+y^{2}+\left (x^{2}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.638 |
|
|
\[
{}1+y^{2}+x y y^{\prime } = 0
\] |
[_separable] |
✓ |
1.878 |
|
|
\[
{}\sin \left (x \right ) y^{\prime }-y \cos \left (x \right ) = 0
\] |
[_separable] |
✓ |
1.974 |
|
|
\[
{}1+y^{2} = y^{\prime } x
\] |
[_separable] |
✓ |
1.490 |
|
|
\[
{}x \sqrt {1+y^{2}}+y y^{\prime } \sqrt {x^{2}+1} = 0
\] |
[_separable] |
✓ |
2.651 |
|
|
\[
{}x \sqrt {1-y^{2}}+y \sqrt {-x^{2}+1}\, y^{\prime } = 0
\] |
[_separable] |
✓ |
2.164 |
|
|
\[
{}{\mathrm e}^{-y} y^{\prime } = 1
\] |
[_quadrature] |
✓ |
0.363 |
|
|
\[
{}y \ln \left (y\right )+y^{\prime } x = 1
\] |
[_separable] |
✓ |
2.398 |
|
|
\[
{}y^{\prime } = a^{x +y}
\] |
[_separable] |
✓ |
1.278 |
|
|
\[
{}{\mathrm e}^{y} \left (x^{2}+1\right ) y^{\prime }-2 x \left (1+{\mathrm e}^{y}\right ) = 0
\] |
[_separable] |
✓ |
5.028 |
|
|
\[
{}2 x \sqrt {1-y^{2}} = \left (x^{2}+1\right ) y^{\prime }
\] |
[_separable] |
✓ |
2.194 |
|
|
\[
{}{\mathrm e}^{x} \sin \left (y\right )^{3}+\left (1+{\mathrm e}^{2 x}\right ) \cos \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
3.558 |
|
|
\[
{}y^{2} \sin \left (x \right )+\cos \left (x \right )^{2} \ln \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
3.270 |
|
|
\[
{}y^{\prime } = \sin \left (x -y\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.997 |
|
|
\[
{}y^{\prime } = a x +b y+c
\] |
[[_linear, ‘class A‘]] |
✓ |
0.687 |
|
|
\[
{}\left (x +y\right )^{2} y^{\prime } = a^{2}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
3.114 |
|
|
\[
{}y^{\prime } x +y = a \left (1+y x \right )
\] |
[_linear] |
✓ |
1.030 |
|
|
\[
{}a^{2}+y^{2}+2 x \sqrt {a x -x^{2}}\, y^{\prime } = 0
\] |
[_separable] |
✓ |
3.409 |
|
|
\[
{}y^{\prime } = \frac {y}{x}
\] |
[_separable] |
✓ |
1.171 |
|
|
\[
{}\cos \left (y^{\prime }\right ) = 0
\] |
[_quadrature] |
✓ |
0.379 |
|
|
\[
{}{\mathrm e}^{y^{\prime }} = 1
\] |
[_quadrature] |
✓ |
0.331 |
|
|
\[
{}\sin \left (y^{\prime }\right ) = x
\] |
[_quadrature] |
✓ |
0.222 |
|
|
\[
{}\ln \left (y^{\prime }\right ) = x
\] |
[_quadrature] |
✓ |
0.252 |
|
|
\[
{}\tan \left (y^{\prime }\right ) = 0
\] |
[_quadrature] |
✓ |
0.348 |
|
|
\[
{}{\mathrm e}^{y^{\prime }} = x
\] |
[_quadrature] |
✓ |
0.240 |
|
|
\[
{}\tan \left (y^{\prime }\right ) = x
\] |
[_quadrature] |
✓ |
0.302 |
|
|
\[
{}x^{2} y^{\prime } \cos \left (y\right )+1 = 0
\] |
[_separable] |
✗ |
1.396 |
|
|
\[
{}x^{2} y^{\prime }+\cos \left (2 y\right ) = 1
\] |
[_separable] |
✗ |
2.473 |
|
|
\[
{}x^{3} y^{\prime }-\sin \left (y\right ) = 1
\] |
[_separable] |
✗ |
2.765 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }-\frac {\cos \left (2 y\right )^{2}}{2} = 0
\] |
[_separable] |
✓ |
6.750 |
|
|
\[
{}{\mathrm e}^{y} = {\mathrm e}^{4 y} y^{\prime }+1
\] |
[_quadrature] |
✓ |
0.595 |
|
|
\[
{}\left (x +1\right ) y^{\prime } = -1+y
\] |
[_separable] |
✓ |
1.292 |
|
|
\[
{}y^{\prime } = 2 x \left (\pi +y\right )
\] |
[_separable] |
✓ |
0.991 |
|
|
\[
{}x^{2} y^{\prime }+\sin \left (2 y\right ) = 1
\] |
[_separable] |
✗ |
9.854 |
|
|
\[
{}y^{\prime } x = y+x \cos \left (\frac {y}{x}\right )^{2}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.169 |
|
|
\[
{}x -y+y^{\prime } x = 0
\] |
[_linear] |
✓ |
1.094 |
|