|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }+6 y^{\prime }+10 y = 50 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
7.698 |
|
|
\[
{}x^{\prime \prime }+2 x^{\prime }+2 x = 85 \sin \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
10.930 |
|
|
\[
{}y^{\prime \prime } = 3 \sin \left (x \right )-4 y
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.634 |
|
|
\[
{}\frac {x^{\prime \prime }}{2} = -48 x
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.722 |
|
|
\[
{}x^{\prime \prime }+5 x^{\prime }+6 x = \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.027 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 4 x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.324 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.289 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.661 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+25 y = 2 \sin \left (\frac {t}{2}\right )-\cos \left (\frac {t}{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
57.434 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+25 y = 64 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
12.200 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+25 y = 50 t^{3}-36 t^{2}-63 t +18
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
14.641 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = 2 x \,{\mathrm e}^{-x}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.144 |
|
|
\[
{}y^{\prime \prime } = 9 x^{2}+2 x -1
\] |
[[_2nd_order, _quadrature]] |
✓ |
2.002 |
|
|
\[
{}y^{\prime \prime }-5 y = 2 \,{\mathrm e}^{5 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.508 |
|
|
\[
{}y^{\prime }-5 y = \left (x -1\right ) \sin \left (x \right )+\left (x +1\right ) \cos \left (x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
2.062 |
|
|
\[
{}y^{\prime }-5 y = 3 \,{\mathrm e}^{x}-2 x +1
\] |
[[_linear, ‘class A‘]] |
✓ |
1.476 |
|
|
\[
{}y^{\prime }-5 y = x^{2} {\mathrm e}^{x}-x \,{\mathrm e}^{5 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.673 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = x^{2}-1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.397 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 4 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.377 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 4 \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.654 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 3 \,{\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.368 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.409 |
|
|
\[
{}y^{\prime }-y = {\mathrm e}^{x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.153 |
|
|
\[
{}y^{\prime }-y = x \,{\mathrm e}^{2 x}+1
\] |
[[_linear, ‘class A‘]] |
✓ |
1.358 |
|
|
\[
{}y^{\prime }-y = \sin \left (x \right )+\cos \left (2 x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
2.092 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = 1+{\mathrm e}^{x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.141 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime } = \sec \left (x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.533 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = \frac {{\mathrm e}^{x}}{1+{\mathrm e}^{-x}}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.265 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.447 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.245 |
|
|
\[
{}x^{\prime \prime }+4 x = \sin \left (2 t \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.723 |
|
|
\[
{}t^{2} N^{\prime \prime }-2 t N^{\prime }+2 N = t \ln \left (t \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.025 |
|
|
\[
{}y^{\prime }+\frac {4 y}{x} = x^{4}
\] |
[_linear] |
✓ |
1.608 |
|
|
\[
{}y^{\prime \prime \prime \prime } = 5 x
\] |
[[_high_order, _quadrature]] |
✓ |
0.114 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{x^{5}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.421 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.926 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.259 |
|
|
\[
{}y^{\prime \prime }-60 y^{\prime }-900 y = 5 \,{\mathrm e}^{10 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.685 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime } = -3
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.133 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}} = \ln \left (x \right )
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.205 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x = x^{3} {\mathrm e}^{x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.001 |
|
|
\[
{}y^{\prime }-\frac {y}{x} = x^{2}
\] |
[_linear] |
✓ |
1.580 |
|
|
\[
{}y^{\prime }+2 y = 0
\] |
[_quadrature] |
✓ |
0.367 |
|
|
\[
{}y^{\prime }+2 y = 2
\] |
[_quadrature] |
✓ |
0.335 |
|
|
\[
{}y^{\prime }+2 y = {\mathrm e}^{x}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.394 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.204 |
|
|
\[
{}y^{\prime \prime }-y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.298 |
|
|
\[
{}y^{\prime \prime }-y = {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.257 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-3 y = \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.414 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.304 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.446 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 3 \,{\mathrm e}^{-2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.337 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }-3 y = \operatorname {Heaviside}\left (x -4\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.073 |
|
|
\[
{}y^{\prime \prime \prime }-y = 5
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.409 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.353 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = x^{2} {\mathrm e}^{x}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.294 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+4 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.226 |
|
|
\[
{}q^{\prime \prime }+9 q^{\prime }+14 q = \frac {\sin \left (t \right )}{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.388 |
|
|
\[
{}\left (x +1\right ) y^{\prime \prime }+\frac {y^{\prime }}{x}+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.766 |
|
|
\[
{}x^{3} y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✗ |
0.112 |
|
|
\[
{}y^{\prime \prime }+x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.488 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x -2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.513 |
|
|
\[
{}y^{\prime \prime }+x^{2} y^{\prime }+2 x y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.553 |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.582 |
|
|
\[
{}y^{\prime \prime }+2 x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.461 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.569 |
|
|
\[
{}y^{\prime \prime }-x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.450 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x +x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.506 |
|
|
\[
{}y^{\prime } x = 2 y
\] |
[_separable] |
✓ |
2.183 |
|
|
\[
{}y^{\prime } y+x = 0
\] |
[_separable] |
✓ |
3.541 |
|
|
\[
{}y = y^{\prime } x +{y^{\prime }}^{4}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
2.947 |
|
|
\[
{}2 x^{3} y^{\prime } = y \left (y^{2}+3 x^{2}\right )
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
81.162 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.188 |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.263 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.205 |
|
|
\[
{}y^{\prime \prime }-y = 4-x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.295 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.076 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = 2 \,{\mathrm e}^{x} \left (1-x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.381 |
|
|
\[
{}4 y+y^{\prime } x = 0
\] |
[_separable] |
✓ |
2.255 |
|
|
\[
{}1+2 y+\left (-x^{2}+4\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.710 |
|
|
\[
{}y^{2}-x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
2.601 |
|
|
\[
{}1+y-\left (x +1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.858 |
|
|
\[
{}x y^{2}+y+\left (x^{2} y-x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.779 |
|
|
\[
{}x \sin \left (\frac {y}{x}\right )-y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.110 |
|
|
\[
{}y^{2} \left (x^{2}+2\right )+\left (x^{3}+y^{3}\right ) \left (y-y^{\prime } x \right ) = 0
\] |
[[_homogeneous, ‘class D‘], _rational] |
✓ |
1.762 |
|
|
\[
{}y \sqrt {x^{2}+y^{2}}-x \left (x +\sqrt {x^{2}+y^{2}}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
4.257 |
|
|
\[
{}x +y+1+\left (2 x +2 y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.741 |
|
|
\[
{}1+2 y-\left (4-x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.911 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+x y = 0
\] |
[_separable] |
✓ |
1.756 |
|
|
\[
{}x +2 y+\left (2 x +3 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.110 |
|
|
\[
{}2 y^{\prime } x -2 y = \sqrt {x^{2}+4 y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
6.286 |
|
|
\[
{}3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.070 |
|
|
\[
{}x y y^{\prime } = \left (1+y\right ) \left (1-x \right )
\] |
[_separable] |
✓ |
1.264 |
|
|
\[
{}y^{2}-x^{2}+x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
4.763 |
|
|
\[
{}y \left (1+2 x y\right )+x \left (1-x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.807 |
|
|
\[
{}1+\left (-x^{2}+1\right ) \cot \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.210 |
|
|
\[
{}x^{3}+y^{3}+3 x y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
10.100 |
|
|
\[
{}3 x +2 y+1-\left (3 x +2 y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.033 |
|
|
\[
{}y^{\prime } x +2 y = 0
\] |
[_separable] |
✓ |
2.802 |
|
|
\[
{}x^{2}+y^{2}+x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
6.417 |
|