|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = \frac {2 y}{t}+\frac {y^{2}}{t^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.809 |
|
|
\[
{}t y^{\prime } = y+\sqrt {t^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
4.404 |
|
|
\[
{}2 t y y^{\prime } = 3 y^{2}-t^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
75.423 |
|
|
\[
{}\left (t -\sqrt {t y}\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
8.566 |
|
|
\[
{}y^{\prime } = \frac {y+t}{t -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.595 |
|
|
\[
{}{\mathrm e}^{\frac {t}{y}} \left (y-t \right ) y^{\prime }+y \left (1+{\mathrm e}^{\frac {t}{y}}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.830 |
|
|
\[
{}y^{\prime } = \frac {t +y+1}{t -y+3}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.565 |
|
|
\[
{}1+t -2 y+\left (4 t -3 y-6\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.791 |
|
|
\[
{}t +2 y+3+\left (2 t +4 y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.228 |
|
|
\[
{}2 t \sin \left (y\right )+{\mathrm e}^{t} y^{3}+\left (t^{2} \cos \left (y\right )+3 \,{\mathrm e}^{t} y^{2}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
3.323 |
|
|
\[
{}1+{\mathrm e}^{t y} \left (1+t y\right )+\left (1+{\mathrm e}^{t y} t^{2}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
1.828 |
|
|
\[
{}\sec \left (t \right ) \tan \left (t \right )+\sec \left (t \right )^{2} y+\left (\tan \left (t \right )+2 y\right ) y^{\prime } = 0
\] |
[_exact, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
11.470 |
|
|
\[
{}\frac {y^{2}}{2}-2 \,{\mathrm e}^{t} y+\left (-{\mathrm e}^{t}+y\right ) y^{\prime } = 0
\] |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.072 |
|
|
\[
{}2 t y^{3}+3 t^{2} y^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
2.960 |
|
|
\[
{}2 t \cos \left (y\right )+3 t^{2} y+\left (2 t^{2}+2 y\right ) y^{\prime } = 0
\] |
[‘x=_G(y,y’)‘] |
✗ |
39.473 |
|
|
\[
{}3 t^{2}+4 t y+\left (2 t^{2}+2 y\right ) y^{\prime } = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.728 |
|
|
\[
{}2 t -2 \,{\mathrm e}^{t y} \sin \left (2 t \right )+{\mathrm e}^{t y} \cos \left (2 t \right ) y+\left (-3+{\mathrm e}^{t y} t \cos \left (2 t \right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
37.690 |
|
|
\[
{}3 t y+y^{2}+\left (t^{2}+t y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
5.974 |
|
|
\[
{}y^{\prime } = 2 t \left (1+y\right )
\] |
[_separable] |
✓ |
1.719 |
|
|
\[
{}y^{\prime } = t^{2}+y^{2}
\] |
[[_Riccati, _special]] |
✗ |
1.473 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{t}+y^{2}
\] |
[_Riccati] |
✓ |
2.088 |
|
|
\[
{}y^{\prime } = y^{2}+\cos \left (t \right )^{2}
\] |
[_Riccati] |
✓ |
4.534 |
|
|
\[
{}y^{\prime } = 1+y+y^{2} \cos \left (t \right )
\] |
[_Riccati] |
✗ |
13.406 |
|
|
\[
{}y^{\prime } = t +y^{2}
\] |
[[_Riccati, _special]] |
✓ |
15.464 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-t^{2}}+y^{2}
\] |
[_Riccati] |
✗ |
1.538 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-t^{2}}+y^{2}
\] |
[_Riccati] |
✗ |
1.507 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-t^{2}}+y^{2}
\] |
[_Riccati] |
✗ |
1.524 |
|
|
\[
{}y^{\prime } = y+{\mathrm e}^{-y}+{\mathrm e}^{-t}
\] |
[‘y=_G(x,y’)‘] |
✗ |
1.396 |
|
|
\[
{}y^{\prime } = y^{3}+{\mathrm e}^{-5 t}
\] |
[_Abel] |
✗ |
0.997 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{\left (y-t \right )^{2}}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.736 |
|
|
\[
{}y^{\prime } = \left (4 y+{\mathrm e}^{-t^{2}}\right ) {\mathrm e}^{2 y}
\] |
[‘y=_G(x,y’)‘] |
✗ |
1.562 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-t}+\ln \left (1+y^{2}\right )
\] |
[‘y=_G(x,y’)‘] |
✗ |
1.754 |
|
|
\[
{}y^{\prime } = \frac {\left (1+\cos \left (4 t \right )\right ) y}{4}-\frac {\left (1-\cos \left (4 t \right )\right ) y^{2}}{800}
\] |
[_Bernoulli] |
✓ |
5.602 |
|
|
\[
{}y^{\prime } = t^{2}+y^{2}
\] |
[[_Riccati, _special]] |
✓ |
1.889 |
|
|
\[
{}y^{\prime } = t \left (1+y\right )
\] |
[_separable] |
✓ |
1.546 |
|
|
\[
{}y^{\prime } = t y^{a}
\] |
[_separable] |
✓ |
6.191 |
|
|
\[
{}y^{\prime } = t \sqrt {1-y^{2}}
\] |
[_separable] |
✓ |
4.201 |
|
|
\[
{}y^{\prime } = y+{\mathrm e}^{-y}+2 t
\] |
[‘y=_G(x,y’)‘] |
✗ |
1.296 |
|
|
\[
{}y^{\prime } = 1-t +y^{2}
\] |
[_Riccati] |
✓ |
1.620 |
|
|
\[
{}y^{\prime } = \frac {t^{2}+y^{2}}{1+t +y^{2}}
\] |
[_rational] |
✗ |
1.038 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{t} y^{2}-2 y
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
1.488 |
|
|
\[
{}y^{\prime } = t y^{3}-y
\] |
[_Bernoulli] |
✓ |
4.036 |
|
|
\[
{}2 t^{2} y^{\prime \prime }+3 t y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.870 |
|
|
\[
{}y^{\prime \prime }+t y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.177 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.254 |
|
|
\[
{}6 y^{\prime \prime }-7 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.093 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.329 |
|
|
\[
{}3 y^{\prime \prime }+6 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.393 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.682 |
|
|
\[
{}2 y^{\prime \prime }+y^{\prime }-10 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.750 |
|
|
\[
{}5 y^{\prime \prime }+5 y^{\prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.852 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.803 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.154 |
|
|
\[
{}t^{2} y^{\prime \prime }+\alpha t y^{\prime }+\beta y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.888 |
|
|
\[
{}t^{2} y^{\prime \prime }+5 t y^{\prime }-2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.886 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.355 |
|
|
\[
{}2 y^{\prime \prime }+3 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.280 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.221 |
|
|
\[
{}4 y^{\prime \prime }-y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.342 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.414 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.056 |
|
|
\[
{}2 y^{\prime \prime }-y^{\prime }+3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
4.292 |
|
|
\[
{}3 y^{\prime \prime }-2 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
5.444 |
|
|
\[
{}y^{\prime \prime }+w^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.788 |
|
|
\[
{}t^{2} y^{\prime \prime }+t y^{\prime }+y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.281 |
|
|
\[
{}t^{2} y^{\prime \prime }+2 t y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.888 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.200 |
|
|
\[
{}4 y^{\prime \prime }-12 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.208 |
|
|
\[
{}9 y^{\prime \prime }+6 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.592 |
|
|
\[
{}4 y^{\prime \prime }-4 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.533 |
|
|
\[
{}6 y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.764 |
|
|
\[
{}9 y^{\prime \prime }-12 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.661 |
|
|
\[
{}y^{\prime \prime }-\frac {2 \left (1+t \right ) y^{\prime }}{t^{2}+2 t -1}+\frac {2 y}{t^{2}+2 t -1} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.349 |
|
|
\[
{}y^{\prime \prime }-4 t y^{\prime }+\left (4 t^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.338 |
|
|
\[
{}\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y = 0
\] |
[_Gegenbauer] |
✓ |
0.353 |
|
|
\[
{}\left (t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.341 |
|
|
\[
{}\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+6 y = 0
\] |
[_Gegenbauer] |
✓ |
0.358 |
|
|
\[
{}\left (2 t +1\right ) y^{\prime \prime }-4 \left (1+t \right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.350 |
|
|
\[
{}t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.378 |
|
|
\[
{}t y^{\prime \prime }-\left (1+3 t \right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.358 |
|
|
\[
{}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.298 |
|
|
\[
{}t^{2} y^{\prime \prime }-t y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.187 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.928 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = t \,{\mathrm e}^{2 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.420 |
|
|
\[
{}2 y^{\prime \prime }-3 y^{\prime }+y = \left (t^{2}+1\right ) {\mathrm e}^{t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.420 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = t \,{\mathrm e}^{3 t}+1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.350 |
|
|
\[
{}3 y^{\prime \prime }+4 y^{\prime }+y = \sin \left (t \right ) {\mathrm e}^{-t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.123 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = t^{{5}/{2}} {\mathrm e}^{-2 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.511 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = \sqrt {1+t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.234 |
|
|
\[
{}y^{\prime \prime }-y = f \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.767 |
|
|
\[
{}t^{2} y^{\prime \prime }-2 y = t^{2}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.083 |
|
|
\[
{}y^{\prime \prime }+p \left (t \right ) y^{\prime }+q \left (t \right ) y = 1+t
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.595 |
|
|
\[
{}y^{\prime \prime }-\frac {2 t y^{\prime }}{t^{2}+1}+\frac {2 y}{t^{2}+1} = t^{2}+1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.730 |
|
|
\[
{}y^{\prime \prime }+3 y = t^{3}-1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.453 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = t \,{\mathrm e}^{\alpha t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.497 |
|
|
\[
{}y^{\prime \prime }-y = t^{2} {\mathrm e}^{t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.506 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = t^{2}+t +1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
29.140 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.386 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+4 y = t^{2} {\mathrm e}^{7 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.363 |
|
|
\[
{}y^{\prime \prime }+4 y = t \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.202 |
|