|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}t y^{\prime }-{y^{\prime }}^{3} = y
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.500 |
|
|
\[
{}t y^{\prime }-y-2 \left (t y^{\prime }-y\right )^{2} = y^{\prime }+1
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
0.709 |
|
|
\[
{}t y^{\prime }-y-1 = {y^{\prime }}^{2}-y^{\prime }
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.492 |
|
|
\[
{}1+y-t y^{\prime } = \ln \left (y^{\prime }\right )
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
1.807 |
|
|
\[
{}1-2 t y^{\prime }+2 y = \frac {1}{{y^{\prime }}^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
1.006 |
|
|
\[
{}y = -t y^{\prime }+\frac {{y^{\prime }}^{5}}{5}
\] |
[_dAlembert] |
✓ |
0.805 |
|
|
\[
{}y = t {y^{\prime }}^{2}+3 {y^{\prime }}^{2}-2 {y^{\prime }}^{3}
\] |
[_dAlembert] |
✓ |
11.263 |
|
|
\[
{}y = t \left (y^{\prime }+1\right )+2 y^{\prime }+1
\] |
[_linear] |
✓ |
1.204 |
|
|
\[
{}y = t \left (2-y^{\prime }\right )+2 {y^{\prime }}^{2}+1
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.507 |
|
|
\[
{}t^{{1}/{3}} y^{{2}/{3}}+t +\left (t^{{2}/{3}} y^{{1}/{3}}+y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
37.217 |
|
|
\[
{}y^{\prime } = \frac {y^{2}-t^{2}}{t y}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
8.399 |
|
|
\[
{}y \sin \left (\frac {t}{y}\right )-\left (t +t \sin \left (\frac {t}{y}\right )\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
17.926 |
|
|
\[
{}y^{\prime } = \frac {2 t^{5}}{5 y^{2}}
\] |
[_separable] |
✓ |
2.195 |
|
|
\[
{}\cos \left (4 x \right )-8 \sin \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.859 |
|
|
\[
{}y^{\prime }-\frac {y}{t} = \frac {y^{2}}{t}
\] |
[_separable] |
✓ |
1.970 |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{8 y}}{t}
\] |
[_separable] |
✓ |
1.328 |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{5 t}}{y^{4}}
\] |
[_separable] |
✓ |
1.248 |
|
|
\[
{}-\frac {1}{x^{5}}+\frac {1}{x^{3}} = \left (2 y^{4}-6 y^{9}\right ) y^{\prime }
\] |
[_separable] |
✓ |
1.743 |
|
|
\[
{}y^{\prime } = \frac {y \,{\mathrm e}^{-2 t}}{\ln \left (y\right )}
\] |
[_separable] |
✓ |
1.376 |
|
|
\[
{}y^{\prime } = \frac {\left (4-7 x \right ) \left (2 y-3\right )}{\left (x -1\right ) \left (2 x -5\right )}
\] |
[_separable] |
✓ |
1.740 |
|
|
\[
{}y^{\prime }+3 y = -10 \sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.247 |
|
|
\[
{}3 t +\left (t -4 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
4.957 |
|
|
\[
{}y-t +\left (y+t \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.656 |
|
|
\[
{}y-x +y^{\prime } = 0
\] |
[[_linear, ‘class A‘]] |
✓ |
0.948 |
|
|
\[
{}y^{2}+\left (t y+t^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
6.059 |
|
|
\[
{}r^{\prime } = \frac {r^{2}+t^{2}}{r t}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
4.483 |
|
|
\[
{}x^{\prime } = \frac {5 t x}{x^{2}+t^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
51.573 |
|
|
\[
{}t^{2}-y+\left (-t +y\right ) y^{\prime } = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.126 |
|
|
\[
{}t^{2} y+\sin \left (t \right )+\left (\frac {t^{3}}{3}-\cos \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
4.446 |
|
|
\[
{}\tan \left (y\right )-t +\left (t \sec \left (y\right )^{2}+1\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
3.897 |
|
|
\[
{}t \ln \left (y\right )+\left (\frac {t^{2}}{2 y}+1\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.441 |
|
|
\[
{}y^{\prime }+y = 5
\] |
[_quadrature] |
✓ |
0.916 |
|
|
\[
{}y^{\prime }+t y = t
\] |
[_separable] |
✓ |
1.347 |
|
|
\[
{}x^{\prime }+\frac {x}{y} = y^{2}
\] |
[_linear] |
✓ |
1.195 |
|
|
\[
{}t r^{\prime }+r = t \cos \left (t \right )
\] |
[_linear] |
✓ |
1.193 |
|
|
\[
{}y^{\prime }-y = t y^{3}
\] |
[_Bernoulli] |
✓ |
2.319 |
|
|
\[
{}y^{\prime }+y = \frac {{\mathrm e}^{t}}{y^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
2.044 |
|
|
\[
{}y = t y^{\prime }+3 {y^{\prime }}^{4}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
2.542 |
|
|
\[
{}y-t y^{\prime } = 2 y^{2} \ln \left (t \right )
\] |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
2.494 |
|
|
\[
{}y-t y^{\prime } = -2 {y^{\prime }}^{3}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.432 |
|
|
\[
{}y-t y^{\prime } = -4 {y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.350 |
|
|
\[
{}2 x -y-2+\left (2 y-x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.334 |
|
|
\[
{}\cos \left (t -y\right )+\left (1-\cos \left (t -y\right )\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
125.768 |
|
|
\[
{}{\mathrm e}^{t y} y-2 t +t \,{\mathrm e}^{t y} y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.878 |
|
|
\[
{}\sin \left (y\right )-y \cos \left (t \right )+\left (t \cos \left (y\right )-\sin \left (t \right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
9.025 |
|
|
\[
{}y^{2}+\left (2 t y-2 \cos \left (y\right ) \sin \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
2.125 |
|
|
\[
{}\frac {y}{t}+\ln \left (y\right )+\left (\frac {t}{y}+\ln \left (t \right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
2.066 |
|
|
\[
{}y^{\prime } = y^{2}-x
\] |
[[_Riccati, _special]] |
✓ |
17.343 |
|
|
\[
{}y^{\prime } = \sqrt {x -y}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.357 |
|
|
\[
{}y^{\prime } = t y^{3}
\] |
[_separable] |
✓ |
3.331 |
|
|
\[
{}y^{\prime } = \frac {t}{y^{3}}
\] |
[_separable] |
✓ |
5.007 |
|
|
\[
{}y^{\prime } = -\frac {y}{t -2}
\] |
[_separable] |
✓ |
2.023 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.997 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.844 |
|
|
\[
{}2 t^{2} y^{\prime \prime }-3 t y^{\prime }-3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.097 |
|
|
\[
{}y^{\prime \prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.990 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.490 |
|
|
\[
{}y^{\prime \prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.813 |
|
|
\[
{}3 t^{2} y^{\prime \prime }-5 t y^{\prime }-3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.937 |
|
|
\[
{}t^{2} y^{\prime \prime }+7 t y^{\prime }-7 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.865 |
|
|
\[
{}y^{\prime \prime }+y = 2 \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.607 |
|
|
\[
{}y^{\prime \prime }+10 y^{\prime }+24 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.836 |
|
|
\[
{}y^{\prime \prime }+16 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.014 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+18 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.785 |
|
|
\[
{}t^{2} y^{\prime \prime }+t y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.300 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.417 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+8 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.438 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.474 |
|
|
\[
{}y^{\prime \prime }+10 y^{\prime }+25 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.417 |
|
|
\[
{}y^{\prime \prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.588 |
|
|
\[
{}y^{\prime \prime }+49 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.464 |
|
|
\[
{}t^{2} y^{\prime \prime }+4 t y^{\prime }-4 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.332 |
|
|
\[
{}t^{2} y^{\prime \prime }+6 t y^{\prime }+6 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.327 |
|
|
\[
{}t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.378 |
|
|
\[
{}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.317 |
|
|
\[
{}a y^{\prime \prime }+b y^{\prime }+c y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.239 |
|
|
\[
{}t^{2} y^{\prime \prime }+a t y^{\prime }+b y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.990 |
|
|
\[
{}4 t^{2} y^{\prime \prime }+4 t y^{\prime }+\left (36 t^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.312 |
|
|
\[
{}t y^{\prime \prime }+2 y^{\prime }+16 t y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.395 |
|
|
\[
{}y^{\prime \prime }+b \left (t \right ) y^{\prime }+c \left (t \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.106 |
|
|
\[
{}y^{\prime \prime }+b \left (t \right ) y^{\prime }+c \left (t \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.142 |
|
|
\[
{}y^{\prime \prime } = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.369 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }-12 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.839 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.266 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.845 |
|
|
\[
{}y^{\prime \prime }+8 y^{\prime }+12 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.850 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.116 |
|
|
\[
{}8 y^{\prime \prime }+6 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.820 |
|
|
\[
{}4 y^{\prime \prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.012 |
|
|
\[
{}y^{\prime \prime }+16 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.021 |
|
|
\[
{}y^{\prime \prime }+8 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.040 |
|
|
\[
{}y^{\prime \prime }+7 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.105 |
|
|
\[
{}4 y^{\prime \prime }+21 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.855 |
|
|
\[
{}7 y^{\prime \prime }+4 y^{\prime }-3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.864 |
|
|
\[
{}4 y^{\prime \prime }+4 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.888 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.882 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.621 |
|
|
\[
{}3 y^{\prime \prime }-y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.964 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-12 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.380 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+12 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.108 |
|