|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime }-\frac {y}{t} = \frac {y^{2}}{t}
\] |
[_separable] |
✓ |
1.520 |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{8 y}}{t}
\] |
[_separable] |
✓ |
1.175 |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{5 t}}{y^{4}}
\] |
[_separable] |
✓ |
1.063 |
|
|
\[
{}-\frac {1}{x^{5}}+\frac {1}{x^{3}} = \left (2 y^{4}-6 y^{9}\right ) y^{\prime }
\] |
[_separable] |
✓ |
1.663 |
|
|
\[
{}y^{\prime } = \frac {y \,{\mathrm e}^{-2 t}}{\ln \left (y\right )}
\] |
[_separable] |
✓ |
1.366 |
|
|
\[
{}y^{\prime } = \frac {\left (4-7 x \right ) \left (2 y-3\right )}{\left (x -1\right ) \left (2 x -5\right )}
\] |
[_separable] |
✓ |
1.490 |
|
|
\[
{}y^{\prime }+3 y = -10 \sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.177 |
|
|
\[
{}3 t +\left (t -4 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
36.817 |
|
|
\[
{}y-t +\left (y+t \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.503 |
|
|
\[
{}y-x +y^{\prime } = 0
\] |
[[_linear, ‘class A‘]] |
✓ |
0.863 |
|
|
\[
{}y^{2}+\left (t y+t^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
4.333 |
|
|
\[
{}r^{\prime } = \frac {r^{2}+t^{2}}{r t}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
4.211 |
|
|
\[
{}x^{\prime } = \frac {5 t x}{t^{2}+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
33.388 |
|
|
\[
{}t^{2}-y+\left (y-t \right ) y^{\prime } = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.059 |
|
|
\[
{}t^{2} y+\sin \left (t \right )+\left (\frac {t^{3}}{3}-\cos \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
6.407 |
|
|
\[
{}\tan \left (y\right )-t +\left (t \sec \left (y\right )^{2}+1\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
4.111 |
|
|
\[
{}t \ln \left (y\right )+\left (\frac {t^{2}}{2 y}+1\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.434 |
|
|
\[
{}y^{\prime }+y = 5
\] |
[_quadrature] |
✓ |
0.361 |
|
|
\[
{}y^{\prime }+t y = t
\] |
[_separable] |
✓ |
1.220 |
|
|
\[
{}x^{\prime }+\frac {x}{y} = y^{2}
\] |
[_linear] |
✓ |
1.119 |
|
|
\[
{}t r^{\prime }+r = t \cos \left (t \right )
\] |
[_linear] |
✓ |
1.144 |
|
|
\[
{}y^{\prime }-y = t y^{3}
\] |
[_Bernoulli] |
✓ |
1.879 |
|
|
\[
{}y^{\prime }+y = \frac {{\mathrm e}^{t}}{y^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
1.924 |
|
|
\[
{}y = t y^{\prime }+3 {y^{\prime }}^{4}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
2.192 |
|
|
\[
{}y-t y^{\prime } = 2 y^{2} \ln \left (t \right )
\] |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
2.202 |
|
|
\[
{}y-t y^{\prime } = -2 {y^{\prime }}^{3}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.396 |
|
|
\[
{}y-t y^{\prime } = -4 {y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.318 |
|
|
\[
{}2 x -y-2+\left (2 y-x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.398 |
|
|
\[
{}\cos \left (t -y\right )+\left (1-\cos \left (t -y\right )\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
126.254 |
|
|
\[
{}{\mathrm e}^{t y} y-2 t +t \,{\mathrm e}^{t y} y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.436 |
|
|
\[
{}\sin \left (y\right )-y \cos \left (t \right )+\left (t \cos \left (y\right )-\sin \left (t \right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
15.102 |
|
|
\[
{}y^{2}+\left (2 t y-2 \cos \left (y\right ) \sin \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.909 |
|
|
\[
{}\frac {y}{t}+\ln \left (y\right )+\left (\frac {t}{y}+\ln \left (t \right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
1.937 |
|
|
\[
{}y^{\prime } = y^{2}-x
\] |
[[_Riccati, _special]] |
✓ |
1.056 |
|
|
\[
{}y^{\prime } = \sqrt {x -y}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.503 |
|
|
\[
{}y^{\prime } = t y^{3}
\] |
[_separable] |
✓ |
2.487 |
|
|
\[
{}y^{\prime } = \frac {t}{y^{3}}
\] |
[_separable] |
✓ |
5.424 |
|
|
\[
{}y^{\prime } = -\frac {y}{t -2}
\] |
[_separable] |
✓ |
1.960 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.795 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.740 |
|
|
\[
{}2 t^{2} y^{\prime \prime }-3 t y^{\prime }-3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.880 |
|
|
\[
{}y^{\prime \prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.671 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.005 |
|
|
\[
{}y^{\prime \prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.484 |
|
|
\[
{}3 t^{2} y^{\prime \prime }-5 t y^{\prime }-3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.718 |
|
|
\[
{}t^{2} y^{\prime \prime }+7 t y^{\prime }-7 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.685 |
|
|
\[
{}y^{\prime \prime }+y = 2 \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.582 |
|
|
\[
{}y^{\prime \prime }+10 y^{\prime }+24 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.730 |
|
|
\[
{}y^{\prime \prime }+16 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.739 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+18 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.435 |
|
|
\[
{}t^{2} y^{\prime \prime }+t y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.130 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.386 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+8 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.368 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.431 |
|
|
\[
{}y^{\prime \prime }+10 y^{\prime }+25 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.361 |
|
|
\[
{}y^{\prime \prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.526 |
|
|
\[
{}y^{\prime \prime }+49 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.422 |
|
|
\[
{}t^{2} y^{\prime \prime }+4 t y^{\prime }-4 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.290 |
|
|
\[
{}t^{2} y^{\prime \prime }+6 t y^{\prime }+6 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.293 |
|
|
\[
{}t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.355 |
|
|
\[
{}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.292 |
|
|
\[
{}a y^{\prime \prime }+b y^{\prime }+c y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.140 |
|
|
\[
{}t^{2} y^{\prime \prime }+a t y^{\prime }+b y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.510 |
|
|
\[
{}4 t^{2} y^{\prime \prime }+4 t y^{\prime }+\left (36 t^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.291 |
|
|
\[
{}t y^{\prime \prime }+2 y^{\prime }+16 t y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.373 |
|
|
\[
{}y^{\prime \prime }+b \left (t \right ) y^{\prime }+c \left (t \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.367 |
|
|
\[
{}y^{\prime \prime }+b \left (t \right ) y^{\prime }+c \left (t \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.497 |
|
|
\[
{}y^{\prime \prime } = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.090 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }-12 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.723 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.112 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.727 |
|
|
\[
{}y^{\prime \prime }+8 y^{\prime }+12 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.719 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.921 |
|
|
\[
{}8 y^{\prime \prime }+6 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.719 |
|
|
\[
{}4 y^{\prime \prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.648 |
|
|
\[
{}y^{\prime \prime }+16 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.772 |
|
|
\[
{}y^{\prime \prime }+8 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.794 |
|
|
\[
{}y^{\prime \prime }+7 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.839 |
|
|
\[
{}4 y^{\prime \prime }+21 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.772 |
|
|
\[
{}7 y^{\prime \prime }+4 y^{\prime }-3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.750 |
|
|
\[
{}4 y^{\prime \prime }+4 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.744 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.756 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.426 |
|
|
\[
{}3 y^{\prime \prime }-y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.724 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-12 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.000 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+12 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.982 |
|
|
\[
{}2 y^{\prime \prime }-7 y^{\prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.981 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+10 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.968 |
|
|
\[
{}y^{\prime \prime }+36 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.740 |
|
|
\[
{}y^{\prime \prime }+100 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.619 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.000 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.060 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.806 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+20 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.844 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.354 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.061 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.300 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.361 |
|
|
\[
{}6 y^{\prime \prime }+5 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.820 |
|
|
\[
{}9 y^{\prime \prime }+6 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.763 |
|