|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{t} \ln \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.447 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{t} \ln \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.074 |
|
|
\[
{}y^{\prime \prime }-2 t y^{\prime }+t^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.360 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.066 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.186 |
|
|
\[
{}t^{2} y^{\prime \prime }-5 t y^{\prime }+5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.195 |
|
|
\[
{}x^{2} y^{\prime \prime }+7 y^{\prime } x +8 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.109 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.127 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.215 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+5 y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
2.016 |
|
|
\[
{}5 x^{2} y^{\prime \prime }-y^{\prime } x +2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.004 |
|
|
\[
{}x^{2} y^{\prime \prime }-7 y^{\prime } x +25 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.470 |
|
|
\[
{}x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y = 8 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.453 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.658 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-3 y = x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.720 |
|
|
\[
{}\left (2 x^{2}-1\right ) y^{\prime \prime }+2 y^{\prime } x -3 y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.586 |
|
|
\[
{}3 x y^{\prime \prime }+11 y^{\prime }-y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.798 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+5 y^{\prime } x -2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.710 |
|
|
\[
{}x^{2} y^{\prime \prime }-7 y^{\prime } x +\left (-2 x^{2}+7\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.252 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+10 y = 0
\] |
[_Jacobi] |
✓ |
0.789 |
|
|
\[
{}x \left (x +1\right ) y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }-10 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.794 |
|
|
\[
{}t \left (y y^{\prime \prime }+{y^{\prime }}^{2}\right )+y^{\prime } y = 1
\] |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.604 |
|
|
\[
{}4 x^{\prime \prime }+9 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.333 |
|
|
\[
{}9 x^{\prime \prime }+4 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.274 |
|
|
\[
{}x^{\prime \prime }+64 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.341 |
|
|
\[
{}x^{\prime \prime }+100 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.408 |
|
|
\[
{}x^{\prime \prime }+x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.080 |
|
|
\[
{}x^{\prime \prime }+4 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.378 |
|
|
\[
{}x^{\prime \prime }+16 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.338 |
|
|
\[
{}x^{\prime \prime }+256 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.510 |
|
|
\[
{}x^{\prime \prime }+9 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.056 |
|
|
\[
{}10 x^{\prime \prime }+\frac {x}{10} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.298 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+3 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.651 |
|
|
\[
{}\frac {x^{\prime \prime }}{32}+2 x^{\prime }+x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.355 |
|
|
\[
{}\frac {x^{\prime \prime }}{4}+2 x^{\prime }+x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.701 |
|
|
\[
{}4 x^{\prime \prime }+2 x^{\prime }+8 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.868 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+13 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.826 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+20 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.701 |
|
|
\[
{}x^{\prime \prime }+x = \left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.501 |
|
|
\[
{}x^{\prime \prime }+x = \left \{\begin {array}{cc} \cos \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
5.094 |
|
|
\[
{}x^{\prime \prime }+x = \left \{\begin {array}{cc} t & 0\le t <1 \\ 2-t & 1\le t <2 \\ 0 & 2\le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.906 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+13 x = \left \{\begin {array}{cc} 1 & 0\le t <\pi \\ -t +1 & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
26.544 |
|
|
\[
{}x^{\prime \prime }+x = \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.042 |
|
|
\[
{}x^{\prime \prime }+x = \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.372 |
|
|
\[
{}x^{\prime \prime }+x = \cos \left (\frac {9 t}{10}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
9.082 |
|
|
\[
{}x^{\prime \prime }+x = \cos \left (\frac {7 t}{10}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
8.026 |
|
|
\[
{}x^{\prime \prime }+\frac {x^{\prime }}{10}+x = 3 \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
75.966 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=6 \\ y^{\prime }=\cos \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.230 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=1 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.424 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=0 \\ y^{\prime }=-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.344 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x^{2} \\ y^{\prime }={\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.025 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1} \\ x_{2}^{\prime }=1 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.556 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}+1 \\ x_{2}^{\prime }=x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.633 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+6 y \\ y^{\prime }=4 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.417 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=8 x-y \\ y^{\prime }=x+6 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.378 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x-2 y \\ y^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.486 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x+2 y \\ y^{\prime }=-x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.489 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x+1 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.586 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x+\sin \left (2 t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.530 |
|
|
\[
{}x^{\prime \prime }-3 x^{\prime }+4 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.354 |
|
|
\[
{}x^{\prime \prime }+6 x^{\prime }+9 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.181 |
|
|
\[
{}x^{\prime \prime }+16 x = t \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.202 |
|
|
\[
{}x^{\prime \prime }+x = {\mathrm e}^{t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.069 |
|
|
\[
{}y^{\prime } = x^{2}+y^{2}
\] |
[[_Riccati, _special]] |
✓ |
1.030 |
|
|
\[
{}y^{\prime } = \frac {x}{y}
\] |
[_separable] |
✓ |
3.474 |
|
|
\[
{}y^{\prime } = y+3 y^{{1}/{3}}
\] |
[_quadrature] |
✓ |
4.760 |
|
|
\[
{}y^{\prime } = \sqrt {x -y}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.752 |
|
|
\[
{}y^{\prime } = \sqrt {x^{2}-y}-x
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
4.941 |
|
|
\[
{}y^{\prime } = \sqrt {1-y^{2}}
\] |
[_quadrature] |
✓ |
39.059 |
|
|
\[
{}y^{\prime } = \frac {1+y}{x -y}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.105 |
|
|
\[
{}y^{\prime } = \sin \left (y\right )-\cos \left (x \right )
\] |
[‘y=_G(x,y’)‘] |
✗ |
2.749 |
|
|
\[
{}y^{\prime } = 1-\cot \left (y\right )
\] |
[_quadrature] |
✓ |
1.928 |
|
|
\[
{}y^{\prime } = \left (3 x -y\right )^{{1}/{3}}-1
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.507 |
|
|
\[
{}y^{\prime } = \sin \left (x y\right )
\] |
[‘y=_G(x,y’)‘] |
✗ |
1.434 |
|
|
\[
{}y^{\prime } x +y = \cos \left (x \right )
\] |
[_linear] |
✓ |
1.257 |
|
|
\[
{}y^{\prime }+2 y = {\mathrm e}^{x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.243 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }+x y = 2 x
\] |
[_separable] |
✓ |
1.573 |
|
|
\[
{}y^{\prime } = x +1
\] |
[_quadrature] |
✓ |
0.458 |
|
|
\[
{}y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.192 |
|
|
\[
{}y^{\prime } = y-x
\] |
[[_linear, ‘class A‘]] |
✓ |
1.191 |
|
|
\[
{}y^{\prime } = \frac {x}{2}-y+\frac {3}{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.238 |
|
|
\[
{}y^{\prime } = \left (-1+y\right )^{2}
\] |
[_quadrature] |
✓ |
1.117 |
|
|
\[
{}y^{\prime } = \left (-1+y\right ) x
\] |
[_separable] |
✓ |
1.418 |
|
|
\[
{}y^{\prime } = x^{2}-y^{2}
\] |
[_Riccati] |
✓ |
1.030 |
|
|
\[
{}y^{\prime } = \cos \left (x -y\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.559 |
|
|
\[
{}y^{\prime } = y-x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.219 |
|
|
\[
{}y^{\prime } = x^{2}+2 x -y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.247 |
|
|
\[
{}y^{\prime } = \frac {1+y}{x -1}
\] |
[_separable] |
✓ |
1.826 |
|
|
\[
{}y^{\prime } = \frac {x +y}{x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.508 |
|
|
\[
{}y^{\prime } = 1-x
\] |
[_quadrature] |
✓ |
0.438 |
|
|
\[
{}y^{\prime } = 2 x -y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.225 |
|
|
\[
{}y^{\prime } = y+x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.221 |
|
|
\[
{}y^{\prime } = -\frac {y}{x}
\] |
[_separable] |
✓ |
2.123 |
|
|
\[
{}y^{\prime } = 1
\] |
[_quadrature] |
✓ |
0.735 |
|
|
\[
{}y^{\prime } = \frac {1}{x}
\] |
[_quadrature] |
✓ |
0.445 |
|
|
\[
{}y^{\prime } = y
\] |
[_quadrature] |
✓ |
1.325 |
|
|
\[
{}y^{\prime } = y^{2}
\] |
[_quadrature] |
✓ |
1.270 |
|
|
\[
{}y^{\prime } = x^{2}-y^{2}
\] |
[_Riccati] |
✓ |
1.419 |
|
|
\[
{}y^{\prime } = x +y^{2}
\] |
[[_Riccati, _special]] |
✓ |
15.283 |
|
|
\[
{}y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.477 |
|