|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime }-y \tan \left (x \right ) = x
\] |
[_linear] |
✓ |
1.742 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x -2 y}
\] |
[_separable] |
✓ |
3.414 |
|
|
\[
{}y^{\prime } = \frac {x^{2}+y^{2}}{2 x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
2.232 |
|
|
\[
{}x y^{\prime } = x +y
\] |
[_linear] |
✓ |
1.717 |
|
|
\[
{}{\mathrm e}^{-y}+\left (x^{2}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.770 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x} \sin \left (x \right )
\] |
[_quadrature] |
✓ |
0.906 |
|
|
\[
{}y^{\prime }-3 y = {\mathrm e}^{3 x}+{\mathrm e}^{-3 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.888 |
|
|
\[
{}y^{\prime } = x +\frac {1}{x}
\] |
[_quadrature] |
✓ |
0.667 |
|
|
\[
{}x y^{\prime }+2 y = \left (3 x +2\right ) {\mathrm e}^{3 x}
\] |
[_linear] |
✓ |
1.988 |
|
|
\[
{}2 \sin \left (3 x \right ) \sin \left (2 y\right ) y^{\prime }-3 \cos \left (3 x \right ) \cos \left (2 y\right ) = 0
\] |
[_separable] |
✓ |
5.327 |
|
|
\[
{}x y y^{\prime } = \left (x +1\right ) \left (y+1\right )
\] |
[_separable] |
✓ |
2.067 |
|
|
\[
{}y^{\prime } = \frac {2 x -y}{y+2 x}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
27.632 |
|
|
\[
{}y^{\prime } = \frac {3 x -y+1}{3 y-x +5}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
11.283 |
|
|
\[
{}3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1441.016 |
|
|
\[
{}x +\left (2-x +2 y\right ) y^{\prime } = x y \left (y^{\prime }-1\right )
\] |
[_quadrature] |
✓ |
0.708 |
|
|
\[
{}\cos \left (x \right ) y^{\prime }+y \sin \left (x \right ) = 1
\] |
[_linear] |
✓ |
2.305 |
|
|
\[
{}\left (x +y^{2}\right ) y^{\prime }+y-x^{2} = 0
\] |
[_exact, _rational] |
✓ |
2.751 |
|
|
\[
{}y^{\prime \prime }+8 y^{\prime }+15 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.912 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-15 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.889 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.987 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.985 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.855 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+13 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.855 |
|
|
\[
{}2 y^{\prime \prime }+3 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.022 |
|
|
\[
{}y^{\prime \prime }+25 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.308 |
|
|
\[
{}4 y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.102 |
|
|
\[
{}y^{\prime \prime } = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.956 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.452 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+3 y = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.038 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = -2 x^{2}+2 x +2
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.185 |
|
|
\[
{}y^{\prime \prime }+y = x^{3}+x
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.958 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.125 |
|
|
\[
{}y^{\prime \prime }+2 y = x +{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.283 |
|
|
\[
{}y^{\prime \prime }+2 y = {\mathrm e}^{x}+2
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.727 |
|
|
\[
{}y^{\prime \prime }-y = 2 \,{\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.199 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.021 |
|
|
\[
{}y^{\prime \prime }-y = 4 x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.230 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+3 y = x^{3}+\sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
77.747 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }-4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.417 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = x^{2}+2
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.056 |
|
|
\[
{}y^{\prime \prime }+2 n y^{\prime }+n^{2} y = A \cos \left (x p \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.336 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.049 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }-12 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.101 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.056 |
|
|
\[
{}y^{\prime \prime \prime }+2 y^{\prime \prime }-5 y^{\prime }-6 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.053 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.060 |
|
|
\[
{}y^{\prime \prime \prime }+4 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.051 |
|
|
\[
{}y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.061 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-9 y^{\prime \prime }-11 y^{\prime }-4 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.059 |
|
|
\[
{}y^{\left (6\right )}+9 y^{\prime \prime \prime \prime }+24 y^{\prime \prime }+16 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.079 |
|
|
\[
{}y^{\prime \prime \prime }-y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.059 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.371 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-2 y = x^{2}+1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.405 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{2}+\frac {y}{8} = \frac {\sin \left (x \right )}{8}-\frac {\cos \left (x \right )}{4}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
42.944 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{x}-2 \,{\mathrm e}^{2 x}+\sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.063 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = x^{3} {\mathrm e}^{2 x}+x \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.328 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = x \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.687 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.614 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }-4 y^{\prime }+4 y = 2 x^{2}-4 x -1+2 x^{2} {\mathrm e}^{2 x}+5 x \,{\mathrm e}^{2 x}+{\mathrm e}^{2 x}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.171 |
|
|
\[
{}y^{\prime \prime \prime \prime }+10 y^{\prime \prime }+9 y = \cos \left (2 x +3\right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.192 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.151 |
|
|
\[
{}y^{\prime \prime }+9 y = 8 \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.584 |
|
|
\[
{}25 y^{\prime \prime }-30 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.398 |
|
|
\[
{}9 y^{\prime \prime }-6 y^{\prime }+y = \left (4 x^{2}+24 x +18\right ) {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.747 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\] |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
0.109 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{2} \\ y_{2}^{\prime }=3 y_{2}-2 y_{1} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.449 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{1}+y_{2} \\ y_{2}^{\prime }=3 y_{2}-y_{1} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.431 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{1}-y_{2} \\ y_{2}^{\prime }=2 y_{1}+3 y_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.573 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=4 y_{2} \\ y_{2}^{\prime }=4 y_{2}-y_{1} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.460 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{1}+y_{2} \\ y_{2}^{\prime }=y_{1}-y_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.577 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{2} \\ y_{2}^{\prime }=y_{1} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.441 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{2}-y_{1} \\ y_{2}^{\prime }=3 y_{1}-4 y_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.640 |
|
|
\[
{}\left [\begin {array}{c} 2 y_{1}^{\prime }=y_{1}+y_{2} \\ 2 y_{2}^{\prime }=5 y_{2}-3 y_{1} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.595 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-2 y_{2} \\ y_{2}^{\prime }=y_{1}+2 y_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.606 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=1 \\ y_{2}^{\prime }=2 y_{1} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.464 |
|
|
\[
{}\left [\begin {array}{c} 2 y_{1}^{\prime }+y_{2}^{\prime }-4 y_{1}-y_{2}={\mathrm e}^{x} \\ y_{1}^{\prime }+3 y_{1}+y_{2}=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.694 |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{2} \\ y_{2}^{\prime }=-y_{1}+y_{3} \\ y_{3}^{\prime }=-y_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.555 |
|
|
\[
{}y^{\prime \prime }+\frac {y}{x^{2}} = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.421 |
|
|
\[
{}y^{\prime \prime }-\frac {\left (-3 x^{2}+x \right ) y^{\prime }}{2 x^{3}+2 x^{2}}+\frac {y}{2 x^{3}+2 x^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.679 |
|
|
\[
{}y^{\prime \prime }+\left (1-\frac {1}{x}\right ) y^{\prime }-\frac {y}{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.669 |
|
|
\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{x}+y = 0
\] |
[_Lienard] |
✓ |
0.595 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+\left (\frac {1}{4 x^{2}}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.717 |
|
|
\[
{}y^{\prime \prime }-\frac {\left (x^{2}+4 x +2\right ) \left (\left (1-x \right ) y^{\prime }+y\right )}{x \left (-x^{2}+2\right )} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.812 |
|
|
\[
{}y^{\prime \prime }-\frac {3 y^{\prime }}{x \left (1-x \right )}+\frac {2 y}{x \left (1-x \right )} = 0
\] |
[_Jacobi, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.661 |
|
|
\[
{}y^{\prime \prime }+\frac {\left (1-x \right ) y^{\prime }}{2 x}-\frac {y}{4 x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.647 |
|
|
\[
{}y^{\prime \prime }-\frac {y^{\prime }}{2 x}+\frac {y}{4 x} = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.676 |
|
|
\[
{}y^{\prime \prime }-\frac {y^{\prime }}{x}+\left (1+\frac {1}{x^{2}}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.528 |
|
|
\[
{}y^{\prime \prime }+\frac {\left (1-5 x \right ) y^{\prime }}{-x^{2}+x}-\frac {4 y}{-x^{2}+x} = 0
\] |
[_Jacobi] |
✓ |
0.640 |
|
|
\[
{}y^{\prime \prime }+\frac {\left (-1+x \right ) y^{\prime }}{x \left (x +1\right )}-\frac {y}{x \left (x +1\right )} = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.641 |
|
|
\[
{}y y^{\prime } = x
\] |
[_separable] |
✓ |
4.459 |
|
|
\[
{}y^{\prime }-y = x^{3}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.554 |
|
|
\[
{}y^{\prime }+y \cot \left (x \right ) = x
\] |
[_linear] |
✓ |
1.548 |
|
|
\[
{}y^{\prime }+y \cot \left (x \right ) = \tan \left (x \right )
\] |
[_linear] |
✓ |
1.831 |
|
|
\[
{}y^{\prime }+y \tan \left (x \right ) = \cot \left (x \right )
\] |
[_linear] |
✓ |
1.797 |
|
|
\[
{}y^{\prime }+y \ln \left (x \right ) = x^{-x}
\] |
[_linear] |
✓ |
1.333 |
|
|
\[
{}x y^{\prime }+y = x
\] |
[_linear] |
✓ |
2.796 |
|
|
\[
{}x y^{\prime }-y = x^{3}
\] |
[_linear] |
✓ |
1.722 |
|
|
\[
{}x y^{\prime }+n y = x^{n}
\] |
[_linear] |
✓ |
1.043 |
|
|
\[
{}x y^{\prime }-n y = x^{n}
\] |
[_linear] |
✓ |
0.828 |
|
|
\[
{}\left (x^{3}+x \right ) y^{\prime }+y = x
\] |
[_linear] |
✓ |
3.155 |
|