|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}2 y^{\prime }+y \cot \left (x \right ) = \frac {8 \cos \left (x \right )^{3}}{y}
\] |
[_Bernoulli] |
✓ |
86.279 |
|
|
\[
{}\left (1-\sqrt {3}\right ) y^{\prime }+y \sec \left (x \right ) = y^{\sqrt {3}} \sec \left (x \right )
\] |
[_separable] |
✓ |
20.638 |
|
|
\[
{}y^{\prime }+\frac {2 x y}{x^{2}+1} = x y^{2}
\] |
[_rational, _Bernoulli] |
✓ |
5.362 |
|
|
\[
{}y^{\prime }+y \cot \left (x \right ) = y^{3} \sin \left (x \right )^{3}
\] |
[_Bernoulli] |
✓ |
5.472 |
|
|
\[
{}y^{\prime } = \left (9 x -y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
7.231 |
|
|
\[
{}y^{\prime } = \left (4 x +y+2\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
14.768 |
|
|
\[
{}y^{\prime } = \sin \left (3 x -3 y+1\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
31.562 |
|
|
\[
{}y^{\prime } = \frac {y \left (\ln \left (y x \right )-1\right )}{x}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
7.576 |
|
|
\[
{}y^{\prime } = 2 x \left (x +y\right )^{2}-1
\] |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
3.453 |
|
|
\[
{}y^{\prime } = \frac {x +2 y-1}{2 x -y+3}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
7.326 |
|
|
\[
{}y^{\prime }+p \left (x \right ) y+q \left (x \right ) y^{2} = r \left (x \right )
\] |
[_Riccati] |
✗ |
1.146 |
|
|
\[
{}y^{\prime }+\frac {2 y}{x}-y^{2} = -\frac {2}{x^{2}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
4.349 |
|
|
\[
{}y^{\prime }+\frac {7 y}{x}-3 y^{2} = \frac {3}{x^{2}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
1.985 |
|
|
\[
{}\frac {y^{\prime }}{y}+p \left (x \right ) \ln \left (y\right ) = q \left (x \right )
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
0.256 |
|
|
\[
{}\frac {y^{\prime }}{y}-\frac {2 \ln \left (y\right )}{x} = \frac {1-2 \ln \left (x \right )}{x}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
13.861 |
|
|
\[
{}\sec \left (y\right )^{2} y^{\prime }+\frac {\tan \left (y\right )}{2 \sqrt {x +1}} = \frac {1}{2 \sqrt {x +1}}
\] |
[_separable] |
✓ |
64.441 |
|
|
\[
{}y \,{\mathrm e}^{y x}+\left (2 y-x \,{\mathrm e}^{y x}\right ) y^{\prime } = 0
\] |
[‘x=_G(y,y’)‘] |
✗ |
1.743 |
|
|
\[
{}\cos \left (y x \right )-x y \sin \left (y x \right )-x^{2} \sin \left (y x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact] |
✓ |
0.335 |
|
|
\[
{}y+3 x^{2}+y^{\prime } x = 0
\] |
[_linear] |
✓ |
0.171 |
|
|
\[
{}2 x \,{\mathrm e}^{y}+\left (3 y^{2}+x^{2} {\mathrm e}^{y}\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
0.288 |
|
|
\[
{}2 y x +\left (x^{2}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
0.121 |
|
|
\[
{}y^{2}-2 x +2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
0.484 |
|
|
\[
{}4 \,{\mathrm e}^{2 x}+2 y x -y^{2}+\left (x -y\right )^{2} y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
1.290 |
|
|
\[
{}\frac {1}{x}-\frac {y}{x^{2}+y^{2}}+\frac {x y^{\prime }}{x^{2}+y^{2}} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _Riccati] |
✓ |
0.687 |
|
|
\[
{}y \cos \left (y x \right )-\sin \left (x \right )+x \cos \left (y x \right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
0.212 |
|
|
\[
{}2 y^{2} {\mathrm e}^{2 x}+3 x^{2}+2 y \,{\mathrm e}^{2 x} y^{\prime } = 0
\] |
[_exact, _Bernoulli] |
✓ |
0.625 |
|
|
\[
{}y^{2}+\cos \left (x \right )+\left (2 y x +\sin \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
0.236 |
|
|
\[
{}\sin \left (y\right )+y \cos \left (x \right )+\left (x \cos \left (y\right )+\sin \left (x \right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
0.280 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.257 |
|
|
\[
{}y^{\prime \prime }+7 y^{\prime }+10 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.475 |
|
|
\[
{}y^{\prime \prime }-36 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.808 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.659 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }-y^{\prime }+3 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.072 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y^{\prime }-12 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.067 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }-18 y^{\prime }-40 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.072 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }-2 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.079 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime }-10 y^{\prime }+8 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.088 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }-y^{\prime \prime }+2 y^{\prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.088 |
|
|
\[
{}y^{\prime \prime \prime \prime }-13 y^{\prime \prime }+36 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.086 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x -8 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.970 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+5 y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
4.217 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y = 0
\] |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
0.178 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-6 y^{\prime } x = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.174 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-6 y = 18 \,{\mathrm e}^{5 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.911 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = 4 x^{2}+5
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.837 |
|
|
\[
{}y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y = 4 \,{\mathrm e}^{2 x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.159 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime }-10 y^{\prime }+8 y = 24 \,{\mathrm e}^{-3 x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.148 |
|
|
\[
{}y^{\prime \prime \prime }+5 y^{\prime \prime }+6 y^{\prime } = 6 \,{\mathrm e}^{-x}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.137 |
|
|
\[
{}y^{\prime \prime }+y = 6 \,{\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.270 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = 5 x \,{\mathrm e}^{-2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.799 |
|
|
\[
{}y^{\prime \prime }+4 y = 8 \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
8.908 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 5 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.801 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 3 \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
35.321 |
|
|
\[
{}y^{\prime \prime \prime }+2 y^{\prime \prime }-5 y^{\prime }-6 y = 4 x^{2}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.155 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 9 \,{\mathrm e}^{-x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.160 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y = 2 \,{\mathrm e}^{-x}+3 \,{\mathrm e}^{2 x}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.263 |
|
|
\[
{}y^{\prime \prime }+9 y = 5 \cos \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
7.694 |
|
|
\[
{}y^{\prime \prime }-y = 9 x \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.950 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = -10 \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.717 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = 4 \cos \left (x \right )-2 \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.579 |
|
|
\[
{}y^{\prime \prime }+\omega ^{2} y = \frac {F_{0} \cos \left (\omega t \right )}{m}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.484 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+6 y = 7 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
13.515 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y = 4 x \,{\mathrm e}^{x}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.170 |
|
|
\[
{}y^{\prime \prime \prime \prime }+104 y^{\prime \prime \prime }+2740 y^{\prime \prime } = 5 \,{\mathrm e}^{-2 x} \cos \left (3 x \right )
\] |
[[_high_order, _missing_y]] |
✓ |
0.203 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-3 y = \sin \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.388 |
|
|
\[
{}y^{\prime \prime }+6 y = \sin \left (x \right )^{2} \cos \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
11.596 |
|
|
\[
{}y^{\prime \prime }-16 y = 20 \cos \left (4 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.355 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 50 \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.450 |
|
|
\[
{}y^{\prime \prime }-y = 10 \,{\mathrm e}^{2 x} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.484 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = 169 \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.107 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 40 \sin \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.220 |
|
|
\[
{}y^{\prime \prime }+y = 3 \,{\mathrm e}^{x} \cos \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.527 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = 2 \,{\mathrm e}^{-x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
8.186 |
|
|
\[
{}y^{\prime \prime }-4 y = 100 x \,{\mathrm e}^{x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.948 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 4 \,{\mathrm e}^{-x} \cos \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
39.604 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+10 y = 24 \,{\mathrm e}^{x} \cos \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
38.168 |
|
|
\[
{}y^{\prime \prime }+16 y = 34 \,{\mathrm e}^{x}+16 \cos \left (4 x \right )-8 \sin \left (4 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
13.635 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 4 \,{\mathrm e}^{3 x} \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.007 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = \frac {{\mathrm e}^{-2 x}}{x^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.804 |
|
|
\[
{}y^{\prime \prime }+9 y = 18 \sec \left (3 x \right )^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.197 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = \frac {2 \,{\mathrm e}^{-3 x}}{x^{2}+1}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
7.748 |
|
|
\[
{}y^{\prime \prime }-4 y = \frac {8}{{\mathrm e}^{2 x}+1}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.197 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = {\mathrm e}^{2 x} \tan \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
35.232 |
|
|
\[
{}y^{\prime \prime }+9 y = \frac {36}{4-\cos \left (3 x \right )^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
49.714 |
|
|
\[
{}y^{\prime \prime }-10 y^{\prime }+25 y = \frac {2 \,{\mathrm e}^{5 x}}{x^{2}+4}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.017 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+13 y = 4 \,{\mathrm e}^{3 x} \sec \left (2 x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
30.532 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (x \right )+4 \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.123 |
|
|
\[
{}y^{\prime \prime }+y = \csc \left (x \right )+2 x^{2}+5 x +1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.132 |
|
|
\[
{}y^{\prime \prime }-y = 2 \tanh \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.763 |
|
|
\[
{}y^{\prime \prime }-2 m y^{\prime }+m^{2} y = \frac {{\mathrm e}^{m x}}{x^{2}+1}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.904 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = \frac {4 \,{\mathrm e}^{x} \ln \left (x \right )}{x^{3}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.885 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = \frac {{\mathrm e}^{-x}}{\sqrt {-x^{2}+4}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.908 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+17 y = \frac {64 \,{\mathrm e}^{-x}}{3+\sin \left (4 x \right )^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
76.901 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = \frac {4 \,{\mathrm e}^{-2 x}}{x^{2}+1}+2 x^{2}-1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.571 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = 15 \,{\mathrm e}^{-2 x} \ln \left (x \right )+25 \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.332 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = \frac {2 \,{\mathrm e}^{x}}{x^{2}}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.267 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = 36 \,{\mathrm e}^{2 x} \ln \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.326 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y = \frac {2 \,{\mathrm e}^{-x}}{x^{2}+1}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.309 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+9 y^{\prime } = 12 \,{\mathrm e}^{3 x}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.139 |
|
|
\[
{}y^{\prime \prime }-9 y = F \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.734 |
|