|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }+6 y^{\prime }+10 y = 50 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
8.691 |
|
|
\[
{}x^{\prime \prime }+2 x^{\prime }+2 x = 85 \sin \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
10.569 |
|
|
\[
{}y^{\prime \prime } = 3 \sin \left (x \right )-4 y
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.623 |
|
|
\[
{}\frac {x^{\prime \prime }}{2} = -48 x
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.786 |
|
|
\[
{}x^{\prime \prime }+5 x^{\prime }+6 x = \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.084 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 4 x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.345 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.282 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.747 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+25 y = 2 \sin \left (\frac {t}{2}\right )-\cos \left (\frac {t}{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
60.015 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+25 y = 64 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
12.749 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+25 y = 50 t^{3}-36 t^{2}-63 t +18
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
17.214 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = 2 x \,{\mathrm e}^{-x}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.148 |
|
|
\[
{}y^{\prime \prime } = 9 x^{2}+2 x -1
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.996 |
|
|
\[
{}y^{\prime \prime }-5 y = 2 \,{\mathrm e}^{5 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.562 |
|
|
\[
{}y^{\prime }-5 y = \left (x -1\right ) \sin \left (x \right )+\left (x +1\right ) \cos \left (x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
2.073 |
|
|
\[
{}y^{\prime }-5 y = 3 \,{\mathrm e}^{x}-2 x +1
\] |
[[_linear, ‘class A‘]] |
✓ |
1.500 |
|
|
\[
{}y^{\prime }-5 y = x^{2} {\mathrm e}^{x}-x \,{\mathrm e}^{5 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.723 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = x^{2}-1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.414 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 4 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.378 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 4 \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.627 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 3 \,{\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.396 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.421 |
|
|
\[
{}y^{\prime }-y = {\mathrm e}^{x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.170 |
|
|
\[
{}y^{\prime }-y = x \,{\mathrm e}^{2 x}+1
\] |
[[_linear, ‘class A‘]] |
✓ |
1.377 |
|
|
\[
{}y^{\prime }-y = \sin \left (x \right )+\cos \left (2 x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
2.157 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = 1+{\mathrm e}^{x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.144 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime } = \sec \left (x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.542 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = \frac {{\mathrm e}^{x}}{1+{\mathrm e}^{-x}}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.247 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.422 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.301 |
|
|
\[
{}x^{\prime \prime }+4 x = \sin \left (2 t \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.801 |
|
|
\[
{}t^{2} N^{\prime \prime }-2 t N^{\prime }+2 N = t \ln \left (t \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.125 |
|
|
\[
{}y^{\prime }+\frac {4 y}{x} = x^{4}
\] |
[_linear] |
✓ |
1.660 |
|
|
\[
{}y^{\prime \prime \prime \prime } = 5 x
\] |
[[_high_order, _quadrature]] |
✓ |
0.120 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{x^{5}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.443 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.023 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.283 |
|
|
\[
{}y^{\prime \prime }-60 y^{\prime }-900 y = 5 \,{\mathrm e}^{10 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.733 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime } = -3
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.164 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}} = \ln \left (x \right )
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.248 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x = x^{3} {\mathrm e}^{x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.982 |
|
|
\[
{}y^{\prime }-\frac {y}{x} = x^{2}
\] |
[_linear] |
✓ |
1.608 |
|
|
\[
{}y^{\prime }+2 y = 0
\] |
[_quadrature] |
✓ |
0.375 |
|
|
\[
{}y^{\prime }+2 y = 2
\] |
[_quadrature] |
✓ |
0.355 |
|
|
\[
{}y^{\prime }+2 y = {\mathrm e}^{x}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.396 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.216 |
|
|
\[
{}y^{\prime \prime }-y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.303 |
|
|
\[
{}y^{\prime \prime }-y = {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.272 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-3 y = \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.428 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.322 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.465 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 3 \,{\mathrm e}^{-2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.357 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }-3 y = \operatorname {Heaviside}\left (x -4\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.125 |
|
|
\[
{}y^{\prime \prime \prime }-y = 5
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.485 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.359 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = x^{2} {\mathrm e}^{x}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.322 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+4 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.243 |
|
|
\[
{}q^{\prime \prime }+9 q^{\prime }+14 q = \frac {\sin \left (t \right )}{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.335 |
|
|
\[
{}\left (x +1\right ) y^{\prime \prime }+\frac {y^{\prime }}{x}+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.786 |
|
|
\[
{}x^{3} y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✗ |
0.118 |
|
|
\[
{}y^{\prime \prime }+x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.470 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x -2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.575 |
|
|
\[
{}y^{\prime \prime }+x^{2} y^{\prime }+2 x y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.590 |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.592 |
|
|
\[
{}y^{\prime \prime }+2 x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.463 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.542 |
|
|
\[
{}y^{\prime \prime }-x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.471 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x +x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.580 |
|
|
\[
{}y^{\prime } x = 2 y
\] |
[_separable] |
✓ |
2.219 |
|
|
\[
{}y y^{\prime }+x = 0
\] |
[_separable] |
✓ |
3.500 |
|
|
\[
{}y = y^{\prime } x +{y^{\prime }}^{4}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
2.165 |
|
|
\[
{}2 x^{3} y^{\prime } = y \left (y^{2}+3 x^{2}\right )
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
77.977 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.207 |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.285 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.281 |
|
|
\[
{}y^{\prime \prime }-y = -x +4
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.309 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.084 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = 2 \,{\mathrm e}^{x} \left (1-x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.372 |
|
|
\[
{}4 y+y^{\prime } x = 0
\] |
[_separable] |
✓ |
2.213 |
|
|
\[
{}1+2 y+\left (-x^{2}+4\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.732 |
|
|
\[
{}y^{2}-x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
2.825 |
|
|
\[
{}1+y-\left (x +1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.856 |
|
|
\[
{}x y^{2}+y+\left (x^{2} y-x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.791 |
|
|
\[
{}x \sin \left (\frac {y}{x}\right )-y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.247 |
|
|
\[
{}y^{2} \left (x^{2}+2\right )+\left (x^{3}+y^{3}\right ) \left (y-y^{\prime } x \right ) = 0
\] |
[[_homogeneous, ‘class D‘], _rational] |
✓ |
1.805 |
|
|
\[
{}y \sqrt {x^{2}+y^{2}}-x \left (x +\sqrt {x^{2}+y^{2}}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
5.117 |
|
|
\[
{}x +y+1+\left (2 x +2 y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.819 |
|
|
\[
{}1+2 y-\left (-x +4\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.950 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+x y = 0
\] |
[_separable] |
✓ |
1.741 |
|
|
\[
{}x +2 y+\left (2 x +3 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.185 |
|
|
\[
{}2 y^{\prime } x -2 y = \sqrt {x^{2}+4 y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
6.590 |
|
|
\[
{}\left (3-3 x +7 y\right ) y^{\prime }+7-7 x +3 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.319 |
|
|
\[
{}x y y^{\prime } = \left (1+y\right ) \left (1-x \right )
\] |
[_separable] |
✓ |
1.332 |
|
|
\[
{}y^{2}-x^{2}+x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
4.926 |
|
|
\[
{}y \left (1+2 x y\right )+x \left (1-x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.833 |
|
|
\[
{}1+\left (-x^{2}+1\right ) \cot \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.343 |
|
|
\[
{}x^{3}+y^{3}+3 x y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
10.069 |
|
|
\[
{}3 x +2 y+1-\left (3 x +2 y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.916 |
|
|
\[
{}y^{\prime } x +2 y = 0
\] |
[_separable] |
✓ |
2.745 |
|
|
\[
{}x^{2}+y^{2}+x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
6.537 |
|