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# |
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]] |
✓ |
1.410 |
|
|
\[
{}\left (x^{3}+2 x^{2}\right ) y^{\prime \prime }-x y^{\prime }+\left (1-x \right ) y = x^{2} \left (x +1\right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.491 |
|
|
\[
{}y^{\prime } = 2
\] |
[_quadrature] |
✓ |
0.465 |
|
|
\[
{}y^{\prime } = 2 \,{\mathrm e}^{3 x}
\] |
[_quadrature] |
✓ |
0.316 |
|
|
\[
{}y^{\prime } = \frac {2}{\sqrt {-x^{2}+1}}
\] |
[_quadrature] |
✓ |
0.349 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x^{2}}
\] |
[_quadrature] |
✓ |
0.329 |
|
|
\[
{}y^{\prime } = x \,{\mathrm e}^{x^{2}}
\] |
[_quadrature] |
✓ |
0.305 |
|
|
\[
{}y^{\prime } = \arcsin \left (x \right )
\] |
[_quadrature] |
✓ |
0.290 |
|
|
\[
{}y^{\prime } = x y
\] |
[_separable] |
✓ |
1.146 |
|
|
\[
{}y^{\prime } = x^{2} y^{2}
\] |
[_separable] |
✓ |
1.602 |
|
|
\[
{}y^{\prime } = -x \,{\mathrm e}^{y}
\] |
[_separable] |
✓ |
1.802 |
|
|
\[
{}y^{\prime } \sin \left (y\right ) = x^{2}
\] |
[_separable] |
✓ |
1.341 |
|
|
\[
{}x y^{\prime } = \sqrt {1-y^{2}}
\] |
[_separable] |
✓ |
2.099 |
|
|
\[
{}{y^{\prime }}^{2}-y^{2} = 0
\] |
[_quadrature] |
✓ |
1.763 |
|
|
\[
{}{y^{\prime }}^{2}-3 y^{\prime }+2 = 0
\] |
[_quadrature] |
✓ |
0.816 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = 1
\] |
[_quadrature] |
✓ |
0.384 |
|
|
\[
{}y^{\prime } \sin \left (x \right ) = 1
\] |
[_quadrature] |
✓ |
0.433 |
|
|
\[
{}y^{\prime } = t^{2}+3
\] |
[_quadrature] |
✓ |
0.270 |
|
|
\[
{}y^{\prime } = t \,{\mathrm e}^{2 t}
\] |
[_quadrature] |
✓ |
0.322 |
|
|
\[
{}y^{\prime } = \sin \left (3 t \right )
\] |
[_quadrature] |
✓ |
0.355 |
|
|
\[
{}y^{\prime } = \sin \left (t \right )^{2}
\] |
[_quadrature] |
✓ |
0.363 |
|
|
\[
{}y^{\prime } = \frac {t}{t^{2}+4}
\] |
[_quadrature] |
✓ |
0.323 |
|
|
\[
{}y^{\prime } = \ln \left (t \right )
\] |
[_quadrature] |
✓ |
0.303 |
|
|
\[
{}y^{\prime } = \frac {t}{\sqrt {t}+1}
\] |
[_quadrature] |
✓ |
0.350 |
|
|
\[
{}y^{\prime } = 2 y-4
\] |
[_quadrature] |
✓ |
1.266 |
|
|
\[
{}y^{\prime } = -y^{3}
\] |
[_quadrature] |
✓ |
1.766 |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{t}}{y}
\] |
[_separable] |
✓ |
1.816 |
|
|
\[
{}y^{\prime } = t \,{\mathrm e}^{2 t}
\] |
[_quadrature] |
✓ |
0.522 |
|
|
\[
{}y^{\prime } = \sin \left (t \right )^{2}
\] |
[_quadrature] |
✓ |
0.681 |
|
|
\[
{}y^{\prime } = 8 \,{\mathrm e}^{4 t}+t
\] |
[_quadrature] |
✓ |
0.559 |
|
|
\[
{}y^{\prime } = \frac {y}{t}
\] |
[_separable] |
✓ |
1.228 |
|
|
\[
{}y^{\prime } = -\frac {t}{y}
\] |
[_separable] |
✓ |
2.782 |
|
|
\[
{}y^{\prime } = y^{2}-y
\] |
[_quadrature] |
✓ |
1.385 |
|
|
\[
{}y^{\prime } = -1+y
\] |
[_quadrature] |
✓ |
0.915 |
|
|
\[
{}y^{\prime } = 1-y
\] |
[_quadrature] |
✓ |
0.911 |
|
|
\[
{}y^{\prime } = y^{3}-y^{2}
\] |
[_quadrature] |
✓ |
3.474 |
|
|
\[
{}y^{\prime } = 1-y^{2}
\] |
[_quadrature] |
✓ |
0.930 |
|
|
\[
{}y^{\prime } = \left (t^{2}+1\right ) y
\] |
[_separable] |
✓ |
1.231 |
|
|
\[
{}y^{\prime } = -y
\] |
[_quadrature] |
✓ |
0.988 |
|
|
\[
{}y^{\prime } = 2 y+{\mathrm e}^{-3 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.066 |
|
|
\[
{}y^{\prime } = 2 y+{\mathrm e}^{2 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.951 |
|
|
\[
{}y^{\prime } = t -y
\] |
[[_linear, ‘class A‘]] |
✓ |
0.943 |
|
|
\[
{}t y^{\prime }+2 y = \sin \left (t \right )
\] |
[_linear] |
✓ |
1.231 |
|
|
\[
{}y^{\prime } = y \tan \left (t \right )+\sec \left (t \right )
\] |
[_linear] |
✓ |
1.375 |
|
|
\[
{}y^{\prime } = \frac {2 t y}{t^{2}+1}+t +1
\] |
[_linear] |
✓ |
1.708 |
|
|
\[
{}y^{\prime } = y \tan \left (t \right )+\sec \left (t \right )^{3}
\] |
[_linear] |
✓ |
1.486 |
|
|
\[
{}y^{\prime } = y
\] |
[_quadrature] |
✓ |
1.343 |
|
|
\[
{}y^{\prime } = 2 y
\] |
[_quadrature] |
✓ |
1.378 |
|
|
\[
{}t y^{\prime } = y+t^{3}
\] |
[_linear] |
✓ |
1.580 |
|
|
\[
{}y^{\prime } = -y \tan \left (t \right )+\sec \left (t \right )
\] |
[_linear] |
✓ |
1.651 |
|
|
\[
{}y^{\prime } = \frac {2 y}{t +1}
\] |
[_separable] |
✓ |
1.975 |
|
|
\[
{}t y^{\prime } = -y+t^{3}
\] |
[_linear] |
✓ |
1.665 |
|
|
\[
{}y^{\prime }+4 \tan \left (2 t \right ) y = \tan \left (2 t \right )
\] |
[_separable] |
✓ |
2.270 |
|
|
\[
{}t \ln \left (t \right ) y^{\prime } = t \ln \left (t \right )-y
\] |
[_linear] |
✓ |
1.362 |
|
|
\[
{}y^{\prime } = \frac {2 y}{-t^{2}+1}+3
\] |
[_linear] |
✓ |
1.538 |
|
|
\[
{}y^{\prime } = -\cot \left (t \right ) y+6 \cos \left (t \right )^{2}
\] |
[_linear] |
✓ |
2.219 |
|
|
\[
{}y^{\prime }-x y^{3} = 0
\] |
[_separable] |
✓ |
2.119 |
|
|
\[
{}\frac {y^{\prime }}{\tan \left (x \right )}-\frac {y}{x^{2}+1} = 0
\] |
[_separable] |
✓ |
2.868 |
|
|
\[
{}x^{2} y^{\prime }+x y^{2} = 4 y^{2}
\] |
[_separable] |
✓ |
1.463 |
|
|
\[
{}y \left (2 x^{2} y^{2}+1\right ) y^{\prime }+x \left (y^{4}+1\right ) = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
2.332 |
|
|
\[
{}2 x y^{\prime }+3 x +y = 0
\] |
[_linear] |
✓ |
4.342 |
|
|
\[
{}\left (\cos \left (x \right )^{2}+y \sin \left (2 x \right )\right ) y^{\prime }+y^{2} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
3.433 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }+4 x y = \left (-x^{2}+1\right )^{{3}/{2}}
\] |
[_linear] |
✓ |
3.710 |
|
|
\[
{}y^{\prime }-y \cot \left (x \right )+\frac {1}{\sin \left (x \right )} = 0
\] |
[_linear] |
✓ |
2.649 |
|
|
\[
{}\left (x +y^{3}\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
5.255 |
|
|
\[
{}y^{\prime } = -\frac {2 x^{2}+y^{2}+x}{x y}
\] |
[_rational, _Bernoulli] |
✓ |
1.277 |
|
|
\[
{}\left (y-x \right ) y^{\prime }+2 x +3 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.605 |
|
|
\[
{}y^{\prime } = \frac {1}{x +2 y+1}
\] |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
1.408 |
|
|
\[
{}y^{\prime } = -\frac {x +y}{3 x +3 y-4}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.260 |
|
|
\[
{}y^{\prime } = \tan \left (x \right ) \cos \left (y\right ) \left (\cos \left (y\right )+\sin \left (y\right )\right )
\] |
[_separable] |
✓ |
3.763 |
|
|
\[
{}x \left (1-2 x^{2} y\right ) y^{\prime }+y = 3 x^{2} y^{2}
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.464 |
|
|
\[
{}y^{\prime }+\frac {x y}{a^{2}+x^{2}} = x
\] |
[_linear] |
✓ |
3.123 |
|
|
\[
{}y^{\prime } = \frac {4 y^{2}}{x^{2}}-y^{2}
\] |
[_separable] |
✓ |
1.418 |
|
|
\[
{}y^{\prime }-\frac {y}{x} = 1
\] |
[_linear] |
✓ |
1.525 |
|
|
\[
{}y^{\prime }-y \tan \left (x \right ) = 1
\] |
[_linear] |
✓ |
1.424 |
|
|
\[
{}y^{\prime }-\frac {y^{2}}{x^{2}} = {\frac {1}{4}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
2.464 |
|
|
\[
{}y^{\prime }-\frac {y^{2}}{x^{2}} = {\frac {1}{4}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
1.784 |
|
|
\[
{}y^{\prime } \sin \left (x \right )+2 y \cos \left (x \right ) = 1
\] |
[_linear] |
✓ |
2.116 |
|
|
\[
{}\left (5 x +y-7\right ) y^{\prime } = 3 x +3 y+3
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.626 |
|
|
\[
{}x y^{\prime }+y-\frac {y^{2}}{x^{{3}/{2}}} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
4.044 |
|
|
\[
{}\left (2 \sin \left (y\right )-x \right ) y^{\prime } = \tan \left (y\right )
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
5.490 |
|
|
\[
{}\left (2 \sin \left (y\right )-x \right ) y^{\prime } = \tan \left (y\right )
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
23.607 |
|
|
\[
{}y^{\prime \prime }+{y^{\prime }}^{2}+y^{\prime } = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.712 |
|
|
\[
{}x^{\prime \prime }+\omega _{0}^{2} x = a \cos \left (\omega t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.638 |
|
|
\[
{}f^{\prime \prime }+2 f^{\prime }+5 f = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.796 |
|
|
\[
{}f^{\prime \prime }+2 f^{\prime }+5 f = {\mathrm e}^{-t} \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
7.960 |
|
|
\[
{}f^{\prime \prime }+6 f^{\prime }+9 f = {\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.262 |
|
|
\[
{}f^{\prime \prime }+8 f^{\prime }+12 f = 12 \,{\mathrm e}^{-4 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.380 |
|
|
\[
{}f^{\prime \prime }+8 f^{\prime }+12 f = 12 \,{\mathrm e}^{-4 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.359 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 4 \,{\mathrm e}^{-x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.155 |
|
|
\[
{}y^{\prime \prime \prime }-12 y^{\prime }+16 y = 32 x -8
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.130 |
|
|
\[
{}-\frac {{y^{\prime }}^{2}}{y^{2}}+\frac {y^{\prime \prime }}{y}+\frac {2 a \coth \left (2 a x \right ) y^{\prime }}{y} = 2 a^{2}
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✗ |
1.444 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.083 |
|
|
\[
{}\left (x +1\right )^{2} y^{\prime \prime }+3 \left (x +1\right ) y^{\prime }+y = x^{2}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.136 |
|
|
\[
{}\left (-2+x \right ) y^{\prime \prime }+3 y^{\prime }+\frac {4 y}{x^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.201 |
|
|
\[
{}y^{\prime \prime }-y = x^{n}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.693 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 2 x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.183 |
|
|
\[
{}2 y y^{\prime \prime \prime }+2 \left (y+3 y^{\prime }\right ) y^{\prime \prime }+2 {y^{\prime }}^{2} = \sin \left (x \right )
\] |
[[_3rd_order, _exact, _nonlinear]] |
✗ |
0.059 |
|
|
\[
{}x y^{\prime \prime \prime }+2 y^{\prime \prime } = A x
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.339 |
|
|
\[
{}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+6\right ) y = {\mathrm e}^{-x^{2}} \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.454 |
|