|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } x +y = x \,{\mathrm e}^{x}
\] |
[_linear] |
✓ |
1.075 |
|
|
\[
{}y^{\prime } x +y = {\mathrm e}^{-x}
\] |
[_linear] |
✓ |
1.127 |
|
|
\[
{}y^{\prime }-\frac {2 t y}{t^{2}+1} = 2
\] |
[_linear] |
✓ |
1.434 |
|
|
\[
{}y^{\prime }-\frac {4 t y}{4 t^{2}+1} = 4 t
\] |
[_linear] |
✓ |
1.866 |
|
|
\[
{}y^{\prime } = 2 x +\frac {x y}{x^{2}-1}
\] |
[_linear] |
✓ |
3.628 |
|
|
\[
{}y^{\prime }+\cot \left (t \right ) y = \cos \left (t \right )
\] |
[_linear] |
✓ |
1.958 |
|
|
\[
{}y^{\prime }-\frac {3 t y}{t^{2}-4} = t
\] |
[_linear] |
✓ |
1.868 |
|
|
\[
{}y^{\prime }-\frac {4 t y}{4 t^{2}-9} = t
\] |
[_linear] |
✓ |
4.909 |
|
|
\[
{}y^{\prime }-\frac {9 x y}{9 x^{2}+49} = x
\] |
[_linear] |
✓ |
3.925 |
|
|
\[
{}y^{\prime }+2 \cot \left (x \right ) y = \cos \left (x \right )
\] |
[_linear] |
✓ |
1.751 |
|
|
\[
{}y^{\prime }+x y = x^{3}
\] |
[_linear] |
✓ |
1.328 |
|
|
\[
{}y^{\prime }-x y = x
\] |
[_separable] |
✓ |
1.137 |
|
|
\[
{}y^{\prime } = \frac {1}{x +y^{2}}
\] |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
0.994 |
|
|
\[
{}y^{\prime }-x = y
\] |
[[_linear, ‘class A‘]] |
✓ |
0.925 |
|
|
\[
{}y-\left (x +3 y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.017 |
|
|
\[
{}x^{\prime } = \frac {3 x t^{2}}{-t^{3}+1}
\] |
[_separable] |
✓ |
1.228 |
|
|
\[
{}p^{\prime } = t^{3}+\frac {p}{t}
\] |
[_linear] |
✓ |
1.157 |
|
|
\[
{}v^{\prime }+v = {\mathrm e}^{-s}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.921 |
|
|
\[
{}-y+y^{\prime } = 4 \,{\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.294 |
|
|
\[
{}y+y^{\prime } = {\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.186 |
|
|
\[
{}y^{\prime }+3 t^{2} y = {\mathrm e}^{-t^{3}}
\] |
[_linear] |
✓ |
2.353 |
|
|
\[
{}2 t y+y^{\prime } = 2 t
\] |
[_separable] |
✓ |
1.429 |
|
|
\[
{}y^{\prime } t +y = \cos \left (t \right )
\] |
[_linear] |
✓ |
1.470 |
|
|
\[
{}y^{\prime } t +y = 2 \,{\mathrm e}^{t} t
\] |
[_linear] |
✓ |
1.402 |
|
|
\[
{}\left (1+{\mathrm e}^{t}\right ) y^{\prime }+{\mathrm e}^{t} y = t
\] |
[_linear] |
✓ |
2.059 |
|
|
\[
{}\left (t^{2}+4\right ) y^{\prime }+2 t y = 2 t
\] |
[_separable] |
✓ |
1.576 |
|
|
\[
{}x^{\prime } = x+t +1
\] |
[[_linear, ‘class A‘]] |
✓ |
1.266 |
|
|
\[
{}y^{\prime } = 2 y+{\mathrm e}^{2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.231 |
|
|
\[
{}y^{\prime }-\frac {y}{t} = \ln \left (t \right )
\] |
[_linear] |
✓ |
0.968 |
|
|
\[
{}y^{\prime \prime }-\frac {y^{\prime }}{t}+\frac {y}{t^{2}} = \frac {1}{t}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.462 |
|
|
\[
{}y+y^{\prime } = \left \{\begin {array}{cc} 4 & 0\le t <2 \\ 0 & 2\le t \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
0.960 |
|
|
\[
{}y+y^{\prime } = \left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
0.894 |
|
|
\[
{}-y+y^{\prime } = \sin \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.397 |
|
|
\[
{}y+y^{\prime } = 5 \,{\mathrm e}^{2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.131 |
|
|
\[
{}y+y^{\prime } = {\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.896 |
|
|
\[
{}y+y^{\prime } = 2-{\mathrm e}^{2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.081 |
|
|
\[
{}y^{\prime }-5 y = t
\] |
[[_linear, ‘class A‘]] |
✓ |
0.973 |
|
|
\[
{}3 y+y^{\prime } = 27 t^{2}+9
\] |
[[_linear, ‘class A‘]] |
✓ |
1.023 |
|
|
\[
{}-\frac {y}{2}+y^{\prime } = 5 \cos \left (t \right )+2 \,{\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.961 |
|
|
\[
{}y^{\prime }+4 y = 8 \cos \left (4 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.574 |
|
|
\[
{}y^{\prime }+10 y = 2 \,{\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.160 |
|
|
\[
{}y^{\prime }-3 y = 27 t^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.070 |
|
|
\[
{}-y+y^{\prime } = 2 \,{\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.970 |
|
|
\[
{}y+y^{\prime } = 4+3 \,{\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.066 |
|
|
\[
{}y+y^{\prime } = 2 \cos \left (t \right )+t
\] |
[[_linear, ‘class A‘]] |
✓ |
1.681 |
|
|
\[
{}\frac {y}{2}+y^{\prime } = \sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.634 |
|
|
\[
{}-\frac {y}{2}+y^{\prime } = \sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.524 |
|
|
\[
{}y^{\prime } t +y = t \cos \left (t \right )
\] |
[_linear] |
✓ |
1.233 |
|
|
\[
{}y+y^{\prime } = t
\] |
[[_linear, ‘class A‘]] |
✓ |
1.215 |
|
|
\[
{}y+y^{\prime } = \sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.572 |
|
|
\[
{}y+y^{\prime } = \cos \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.465 |
|
|
\[
{}y+y^{\prime } = {\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.319 |
|
|
\[
{}y^{2}-\frac {y}{2 \sqrt {t}}+\left (2 t y-\sqrt {t}+1\right ) y^{\prime } = 0
\] |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
91.976 |
|
|
\[
{}\frac {t}{\sqrt {t^{2}+y^{2}}}+\frac {y y^{\prime }}{\sqrt {t^{2}+y^{2}}} = 0
\] |
[_separable] |
✓ |
3.392 |
|
|
\[
{}y \cos \left (t y\right )+t \cos \left (t y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.759 |
|
|
\[
{}\sec \left (t \right )^{2} y+2 t +\tan \left (t \right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
12.898 |
|
|
\[
{}3 t y^{2}+y^{3} y^{\prime } = 0
\] |
[_separable] |
✓ |
3.527 |
|
|
\[
{}t -\sin \left (t \right ) y+\left (y^{6}+\cos \left (t \right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
3.106 |
|
|
\[
{}\sin \left (2 t \right ) y+\left (\sqrt {y}+\cos \left (2 t \right )\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
6.167 |
|
|
\[
{}\ln \left (t y\right )+\frac {t y^{\prime }}{y} = 0
\] |
[[_homogeneous, ‘class G‘], _exact] |
✓ |
2.172 |
|
|
\[
{}{\mathrm e}^{t y}+\frac {t \,{\mathrm e}^{t y} y^{\prime }}{y} = 0
\] |
[_separable] |
✓ |
1.709 |
|
|
\[
{}3 t^{2}-y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.302 |
|
|
\[
{}-1+3 y^{2} y^{\prime } = 0
\] |
[_quadrature] |
✓ |
1.078 |
|
|
\[
{}y^{2}+2 t y y^{\prime } = 0
\] |
[_separable] |
✓ |
1.841 |
|
|
\[
{}\frac {3 t^{2}}{y}-\frac {t^{3} y^{\prime }}{y^{2}} = 0
\] |
[_separable] |
✓ |
1.814 |
|
|
\[
{}2 t +y^{3}+\left (3 t y^{2}+4\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
1.344 |
|
|
\[
{}-\frac {1}{y}+\left (\frac {t}{y^{2}}+3 y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
1.591 |
|
|
\[
{}2 t y+\left (t^{2}+y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
3.175 |
|
|
\[
{}2 t y^{3}+\left (1+3 t^{2} y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
1.812 |
|
|
\[
{}\sin \left (y\right )^{2}+t \sin \left (2 y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
6.091 |
|
|
\[
{}3 t^{2}+3 y^{2}+6 t y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
3.624 |
|
|
\[
{}{\mathrm e}^{t} \sin \left (y\right )+\left (1+{\mathrm e}^{t} \cos \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
2.205 |
|
|
\[
{}3 t^{2} y+3 y^{2}-1+\left (t^{3}+6 t y\right ) y^{\prime } = 0
\] |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.731 |
|
|
\[
{}-2 t y^{2} \sin \left (t^{2}\right )+2 y \cos \left (t^{2}\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
3.290 |
|
|
\[
{}2 t -y^{2} \sin \left (t y\right )+\left (\cos \left (t y\right )-t y \sin \left (t y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
41.275 |
|
|
\[
{}1-y^{2} \cos \left (t y\right )+\left (t y \cos \left (t y\right )+\sin \left (t y\right )\right ) y^{\prime } = 0
\] |
[‘y=_G(x,y’)‘] |
✗ |
62.290 |
|
|
\[
{}2 t \sin \left (y\right )-2 t y \sin \left (t^{2}\right )+\left (t^{2} \cos \left (y\right )+\cos \left (t^{2}\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
38.152 |
|
|
\[
{}\left (t +3\right ) \cos \left (t +y\right )+\sin \left (t +y\right )+\left (t +3\right ) \cos \left (t +y\right ) y^{\prime } = 0
\] |
[[_1st_order, _with_linear_symmetries], _exact] |
✓ |
22.855 |
|
|
\[
{}\frac {2 t^{2} y \cos \left (t^{2}\right )-y \sin \left (t^{2}\right )}{t^{2}}+\frac {\left (2 t y+\sin \left (t^{2}\right )\right ) y^{\prime }}{t} = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
9.367 |
|
|
\[
{}-\frac {y^{2} {\mathrm e}^{\frac {y}{t}}}{t^{2}}+1+{\mathrm e}^{\frac {y}{t}} \left (1+\frac {y}{t}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
4.526 |
|
|
\[
{}2 t \sin \left (\frac {y}{t}\right )-y \cos \left (\frac {y}{t}\right )+t \cos \left (\frac {y}{t}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
4.593 |
|
|
\[
{}2 t y^{2}+2 t^{2} y y^{\prime } = 0
\] |
[_separable] |
✓ |
1.990 |
|
|
\[
{}1+\frac {y}{t^{2}}-\frac {y^{\prime }}{t} = 0
\] |
[_linear] |
✓ |
1.374 |
|
|
\[
{}2 t y+3 t^{2}+\left (t^{2}-1\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
1.462 |
|
|
\[
{}1+5 t -y-\left (t +2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.323 |
|
|
\[
{}{\mathrm e}^{y}-2 t y+\left (t \,{\mathrm e}^{y}-t^{2}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
2.118 |
|
|
\[
{}2 t y \,{\mathrm e}^{t^{2}}+2 t \,{\mathrm e}^{-y}+\left ({\mathrm e}^{t^{2}}-t^{2} {\mathrm e}^{-y}+1\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
37.780 |
|
|
\[
{}y^{2}-2 \sin \left (2 t \right )+\left (1+2 t y\right ) y^{\prime } = 0
\] |
[_exact, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
36.629 |
|
|
\[
{}\cos \left (t \right )^{2}-\sin \left (t \right )^{2}+y+\left (\sec \left (y\right ) \tan \left (y\right )+t \right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
41.635 |
|
|
\[
{}\frac {1}{t^{2}+1}-y^{2}-2 t y y^{\prime } = 0
\] |
[_exact, _rational, _Bernoulli] |
✓ |
2.163 |
|
|
\[
{}\frac {2 t}{t^{2}+1}+y+\left ({\mathrm e}^{y}+t \right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
3.067 |
|
|
\[
{}-2 x -y \cos \left (x y\right )+\left (2 y-x \cos \left (x y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
11.780 |
|
|
\[
{}-4 x^{3}+6 y \sin \left (6 x y\right )+\left (4 y^{3}+6 x \sin \left (6 x y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
50.225 |
|
|
\[
{}t^{2} y+t^{3} y^{\prime } = 0
\] |
[_separable] |
✓ |
1.436 |
|
|
\[
{}y \left (2 \,{\mathrm e}^{t}+4 t \right )+3 \left ({\mathrm e}^{t}+t^{2}\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.862 |
|
|
\[
{}y+\left (2 t -y \,{\mathrm e}^{y}\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.370 |
|
|
\[
{}2 t y+y^{2}-t^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.186 |
|
|
\[
{}y+2 t^{2}+\left (t^{2} y-t \right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.503 |
|
|
\[
{}5 t y+4 y^{2}+1+\left (t^{2}+2 t y\right ) y^{\prime } = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.635 |
|
|
\[
{}5 t y^{2}+y+\left (2 t^{3}-t \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
3.425 |
|