|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+\left (x +1\right ) y = x \left (x^{2}+x +1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.939 |
|
|
\[
{}\left (x^{3}+2 x^{2}\right ) y^{\prime \prime }-x y^{\prime }+\left (1-x \right ) y = x^{2} \left (x +1\right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.009 |
|
|
\[
{}y^{\prime } = 2
\] |
[_quadrature] |
✓ |
0.815 |
|
|
\[
{}y^{\prime } = 2 \,{\mathrm e}^{3 x}
\] |
[_quadrature] |
✓ |
0.470 |
|
|
\[
{}y^{\prime } = \frac {2}{\sqrt {-x^{2}+1}}
\] |
[_quadrature] |
✓ |
0.483 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x^{2}}
\] |
[_quadrature] |
✓ |
0.563 |
|
|
\[
{}y^{\prime } = x \,{\mathrm e}^{x^{2}}
\] |
[_quadrature] |
✓ |
0.559 |
|
|
\[
{}y^{\prime } = \arcsin \left (x \right )
\] |
[_quadrature] |
✓ |
0.416 |
|
|
\[
{}y^{\prime } = x y
\] |
[_separable] |
✓ |
1.642 |
|
|
\[
{}y^{\prime } = y^{2} x^{2}
\] |
[_separable] |
✓ |
2.196 |
|
|
\[
{}y^{\prime } = -x \,{\mathrm e}^{y}
\] |
[_separable] |
✓ |
2.165 |
|
|
\[
{}y^{\prime } \sin \left (y\right ) = x^{2}
\] |
[_separable] |
✓ |
1.578 |
|
|
\[
{}x y^{\prime } = \sqrt {1-y^{2}}
\] |
[_separable] |
✓ |
6.532 |
|
|
\[
{}{y^{\prime }}^{2}-y^{2} = 0
\] |
[_quadrature] |
✓ |
0.765 |
|
|
\[
{}{y^{\prime }}^{2}-3 y^{\prime }+2 = 0
\] |
[_quadrature] |
✓ |
0.332 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = 1
\] |
[_quadrature] |
✓ |
0.602 |
|
|
\[
{}y^{\prime } \sin \left (x \right ) = 1
\] |
[_quadrature] |
✓ |
0.679 |
|
|
\[
{}y^{\prime } = t^{2}+3
\] |
[_quadrature] |
✓ |
0.460 |
|
|
\[
{}y^{\prime } = t \,{\mathrm e}^{2 t}
\] |
[_quadrature] |
✓ |
0.497 |
|
|
\[
{}y^{\prime } = \sin \left (3 t \right )
\] |
[_quadrature] |
✓ |
0.524 |
|
|
\[
{}y^{\prime } = \sin \left (t \right )^{2}
\] |
[_quadrature] |
✓ |
0.600 |
|
|
\[
{}y^{\prime } = \frac {t}{t^{2}+4}
\] |
[_quadrature] |
✓ |
0.472 |
|
|
\[
{}y^{\prime } = \ln \left (t \right )
\] |
[_quadrature] |
✓ |
0.394 |
|
|
\[
{}y^{\prime } = \frac {t}{\sqrt {t}+1}
\] |
[_quadrature] |
✓ |
0.308 |
|
|
\[
{}y^{\prime } = 2 y-4
\] |
[_quadrature] |
✓ |
2.016 |
|
|
\[
{}y^{\prime } = -y^{3}
\] |
[_quadrature] |
✓ |
3.470 |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{t}}{y}
\] |
[_separable] |
✓ |
2.303 |
|
|
\[
{}y^{\prime } = t \,{\mathrm e}^{2 t}
\] |
[_quadrature] |
✓ |
0.774 |
|
|
\[
{}y^{\prime } = \sin \left (t \right )^{2}
\] |
[_quadrature] |
✓ |
0.900 |
|
|
\[
{}y^{\prime } = 8 \,{\mathrm e}^{4 t}+t
\] |
[_quadrature] |
✓ |
0.712 |
|
|
\[
{}y^{\prime } = \frac {y}{t}
\] |
[_separable] |
✓ |
1.615 |
|
|
\[
{}y^{\prime } = -\frac {t}{y}
\] |
[_separable] |
✓ |
4.046 |
|
|
\[
{}y^{\prime } = y^{2}-y
\] |
[_quadrature] |
✓ |
1.882 |
|
|
\[
{}y^{\prime } = -1+y
\] |
[_quadrature] |
✓ |
1.323 |
|
|
\[
{}y^{\prime } = 1-y
\] |
[_quadrature] |
✓ |
1.386 |
|
|
\[
{}y^{\prime } = y^{3}-y^{2}
\] |
[_quadrature] |
✓ |
18.510 |
|
|
\[
{}y^{\prime } = 1-y^{2}
\] |
[_quadrature] |
✓ |
2.541 |
|
|
\[
{}y^{\prime } = \left (t^{2}+1\right ) y
\] |
[_separable] |
✓ |
1.726 |
|
|
\[
{}y^{\prime } = -y
\] |
[_quadrature] |
✓ |
1.566 |
|
|
\[
{}y^{\prime } = 2 y+{\mathrm e}^{-3 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.356 |
|
|
\[
{}y^{\prime } = 2 y+{\mathrm e}^{2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.273 |
|
|
\[
{}y^{\prime } = -y+t
\] |
[[_linear, ‘class A‘]] |
✓ |
1.236 |
|
|
\[
{}t y^{\prime }+2 y = \sin \left (t \right )
\] |
[_linear] |
✓ |
1.497 |
|
|
\[
{}y^{\prime } = y \tan \left (t \right )+\sec \left (t \right )
\] |
[_linear] |
✓ |
1.720 |
|
|
\[
{}y^{\prime } = \frac {2 t y}{t^{2}+1}+t +1
\] |
[_linear] |
✓ |
2.027 |
|
|
\[
{}y^{\prime } = y \tan \left (t \right )+\sec \left (t \right )^{3}
\] |
[_linear] |
✓ |
1.908 |
|
|
\[
{}y^{\prime } = y
\] |
[_quadrature] |
✓ |
2.852 |
|
|
\[
{}y^{\prime } = 2 y
\] |
[_quadrature] |
✓ |
2.171 |
|
|
\[
{}t y^{\prime } = y+t^{3}
\] |
[_linear] |
✓ |
1.990 |
|
|
\[
{}y^{\prime } = -y \tan \left (t \right )+\sec \left (t \right )
\] |
[_linear] |
✓ |
1.958 |
|
|
\[
{}y^{\prime } = \frac {2 y}{t +1}
\] |
[_separable] |
✓ |
2.370 |
|
|
\[
{}t y^{\prime } = -y+t^{3}
\] |
[_linear] |
✓ |
1.951 |
|
|
\[
{}y^{\prime }+4 \tan \left (2 t \right ) y = \tan \left (2 t \right )
\] |
[_separable] |
✓ |
2.775 |
|
|
\[
{}t \ln \left (t \right ) y^{\prime } = t \ln \left (t \right )-y
\] |
[_linear] |
✓ |
1.353 |
|
|
\[
{}y^{\prime } = \frac {2 y}{-t^{2}+1}+3
\] |
[_linear] |
✓ |
1.728 |
|
|
\[
{}y^{\prime } = -\cot \left (t \right ) y+6 \cos \left (t \right )^{2}
\] |
[_linear] |
✓ |
2.492 |
|
|
\[
{}y^{\prime }-x y^{3} = 0
\] |
[_separable] |
✓ |
3.495 |
|
|
\[
{}\frac {y^{\prime }}{\tan \left (x \right )}-\frac {y}{x^{2}+1} = 0
\] |
[_separable] |
✓ |
2.302 |
|
|
\[
{}x^{2} y^{\prime }+x y^{2} = 4 y^{2}
\] |
[_separable] |
✓ |
1.839 |
|
|
\[
{}y \left (2 y^{2} x^{2}+1\right ) y^{\prime }+x \left (y^{4}+1\right ) = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
2.329 |
|
|
\[
{}2 x y^{\prime }+3 x +y = 0
\] |
[_linear] |
✓ |
5.242 |
|
|
\[
{}\left (\cos \left (x \right )^{2}+y \sin \left (2 x \right )\right ) y^{\prime }+y^{2} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
4.246 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }+4 x y = \left (-x^{2}+1\right )^{{3}/{2}}
\] |
[_linear] |
✓ |
5.040 |
|
|
\[
{}y^{\prime }-y \cot \left (x \right )+\frac {1}{\sin \left (x \right )} = 0
\] |
[_linear] |
✓ |
3.237 |
|
|
\[
{}\left (x +y^{3}\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.595 |
|
|
\[
{}y^{\prime } = -\frac {2 x^{2}+y^{2}+x}{x y}
\] |
[_rational, _Bernoulli] |
✓ |
1.643 |
|
|
\[
{}\left (y-x \right ) y^{\prime }+2 x +3 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
40.443 |
|
|
\[
{}y^{\prime } = \frac {1}{x +2 y+1}
\] |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
1.911 |
|
|
\[
{}y^{\prime } = -\frac {x +y}{3 x +3 y-4}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.848 |
|
|
\[
{}y^{\prime } = \tan \left (x \right ) \cos \left (y\right ) \left (\cos \left (y\right )+\sin \left (y\right )\right )
\] |
[_separable] |
✓ |
4.120 |
|
|
\[
{}x \left (1-2 x^{2} y\right ) y^{\prime }+y = 3 y^{2} x^{2}
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.713 |
|
|
\[
{}y^{\prime }+\frac {x y}{a^{2}+x^{2}} = x
\] |
[_linear] |
✓ |
3.540 |
|
|
\[
{}y^{\prime } = \frac {4 y^{2}}{x^{2}}-y^{2}
\] |
[_separable] |
✓ |
1.810 |
|
|
\[
{}y^{\prime }-\frac {y}{x} = 1
\] |
[_linear] |
✓ |
1.981 |
|
|
\[
{}y^{\prime }-y \tan \left (x \right ) = 1
\] |
[_linear] |
✓ |
1.725 |
|
|
\[
{}y^{\prime }-\frac {y^{2}}{x^{2}} = {\frac {1}{4}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
2.938 |
|
|
\[
{}y^{\prime }-\frac {y^{2}}{x^{2}} = {\frac {1}{4}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
2.284 |
|
|
\[
{}y^{\prime } \sin \left (x \right )+2 y \cos \left (x \right ) = 1
\] |
[_linear] |
✓ |
2.409 |
|
|
\[
{}\left (5 x +y-7\right ) y^{\prime } = 3 x +3 y+3
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.372 |
|
|
\[
{}x y^{\prime }+y-\frac {y^{2}}{x^{{3}/{2}}} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
5.755 |
|
|
\[
{}\left (2 \sin \left (y\right )-x \right ) y^{\prime } = \tan \left (y\right )
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
7.762 |
|
|
\[
{}\left (2 \sin \left (y\right )-x \right ) y^{\prime } = \tan \left (y\right )
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
54.032 |
|
|
\[
{}y^{\prime \prime }+{y^{\prime }}^{2}+y^{\prime } = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.341 |
|
|
\[
{}x^{\prime \prime }+\omega _{0}^{2} x = a \cos \left (\omega t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.499 |
|
|
\[
{}f^{\prime \prime }+2 f^{\prime }+5 f = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.909 |
|
|
\[
{}f^{\prime \prime }+2 f^{\prime }+5 f = {\mathrm e}^{-t} \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.641 |
|
|
\[
{}f^{\prime \prime }+6 f^{\prime }+9 f = {\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.293 |
|
|
\[
{}f^{\prime \prime }+8 f^{\prime }+12 f = 12 \,{\mathrm e}^{-4 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.271 |
|
|
\[
{}f^{\prime \prime }+8 f^{\prime }+12 f = 12 \,{\mathrm e}^{-4 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.622 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 4 \,{\mathrm e}^{-x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.198 |
|
|
\[
{}y^{\prime \prime \prime }-12 y^{\prime }+16 y = 32 x -8
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.098 |
|
|
\[
{}-\frac {{y^{\prime }}^{2}}{y^{2}}+\frac {y^{\prime \prime }}{y}+\frac {2 a \coth \left (2 a x \right ) y^{\prime }}{y} = 2 a^{2}
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✗ |
1.514 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.586 |
|
|
\[
{}\left (x +1\right )^{2} y^{\prime \prime }+3 \left (x +1\right ) y^{\prime }+y = x^{2}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.677 |
|
|
\[
{}\left (-2+x \right ) y^{\prime \prime }+3 y^{\prime }+\frac {4 y}{x^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.842 |
|
|
\[
{}y^{\prime \prime }-y = x^{n}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.616 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 2 x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.206 |
|
|
\[
{}2 y y^{\prime \prime \prime }+2 \left (y+3 y^{\prime }\right ) y^{\prime \prime }+2 {y^{\prime }}^{2} = \sin \left (x \right )
\] |
[[_3rd_order, _exact, _nonlinear]] |
✗ |
0.051 |
|
|
\[
{}x y^{\prime \prime \prime }+2 y^{\prime \prime } = A x
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.129 |
|
|
\[
{}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+6\right ) y = {\mathrm e}^{-x^{2}} \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.825 |
|