|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = 3 x^{2} \left (y+7\right )
\] |
[_separable] |
✓ |
1.198 |
|
|
\[
{}y^{\prime } = -x y+x y^{3}
\] |
[_separable] |
✓ |
3.538 |
|
|
\[
{}y^{\prime } = \frac {-3 x^{2}-2 y^{2}}{4 x y}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
61.815 |
|
|
\[
{}y^{\prime } = \frac {3 y+x}{y-3 x}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.688 |
|
|
\[
{}y^{\prime } = \frac {2 x y+2 x}{x^{2}+1}
\] |
[_separable] |
✓ |
1.278 |
|
|
\[
{}y^{\prime } = \cot \left (x \right ) \left (\sqrt {y}-y\right )
\] |
[_separable] |
✓ |
8.147 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.512 |
|
|
\[
{}y^{\prime \prime }-9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.596 |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.128 |
|
|
\[
{}y^{\prime \prime }+25 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.053 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.072 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.492 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.928 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.873 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.172 |
|
|
\[
{}y^{\prime \prime }-10 y^{\prime }+25 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.150 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.459 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+13 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.533 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
2.104 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.423 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.091 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.803 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.819 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-15 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.889 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.380 |
|
|
\[
{}2 y^{\prime \prime }+3 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.418 |
|
|
\[
{}2 y^{\prime \prime }-y^{\prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.846 |
|
|
\[
{}4 y^{\prime \prime }+8 y^{\prime }+3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.846 |
|
|
\[
{}4 y^{\prime \prime }+4 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.845 |
|
|
\[
{}9 y^{\prime \prime }-12 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.875 |
|
|
\[
{}6 y^{\prime \prime }-7 y^{\prime }-20 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.858 |
|
|
\[
{}35 y^{\prime \prime }-y^{\prime }-12 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.813 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.261 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x y^{\prime }-12 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.046 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+8 x y^{\prime }-3 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.056 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.755 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.158 |
|
|
\[
{}y^{\prime \prime }+y = 3 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.098 |
|
|
\[
{}y^{\prime \prime }-4 y = 12
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.894 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-3 y = 6
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.554 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = 2 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
8.601 |
|
|
\[
{}y^{\prime \prime }+2 y = 4
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.323 |
|
|
\[
{}y^{\prime \prime }+2 y = 6 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.243 |
|
|
\[
{}y^{\prime \prime }+2 y = 4+6 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.030 |
|
|
\[
{}y^{\prime \prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.094 |
|
|
\[
{}2 y^{\prime \prime }-3 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.362 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-10 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.832 |
|
|
\[
{}2 y^{\prime \prime }-7 y^{\prime }+3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.832 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.849 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.099 |
|
|
\[
{}4 y^{\prime \prime }-12 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.865 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+13 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.811 |
|
|
\[
{}y^{\prime \prime }+8 y^{\prime }+25 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.895 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.471 |
|
|
\[
{}9 y^{\prime \prime }+6 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.824 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+25 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.775 |
|
|
\[
{}y^{\prime \prime }-2 i y^{\prime }+3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.801 |
|
|
\[
{}y^{\prime \prime }-i y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.829 |
|
|
\[
{}y^{\prime \prime } = \left (-2+2 i \sqrt {3}\right ) y
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.649 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+9 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.573 |
|
|
\[
{}x^{2} y^{\prime \prime }+7 x y^{\prime }+25 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.447 |
|
|
\[
{}\frac {x^{\prime \prime }}{2}+3 x^{\prime }+4 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.134 |
|
|
\[
{}3 x^{\prime \prime }+30 x^{\prime }+63 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.417 |
|
|
\[
{}x^{\prime \prime }+8 x^{\prime }+16 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.206 |
|
|
\[
{}2 x^{\prime \prime }+12 x^{\prime }+50 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.059 |
|
|
\[
{}4 x^{\prime \prime }+20 x^{\prime }+169 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.700 |
|
|
\[
{}2 x^{\prime \prime }+16 x^{\prime }+40 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.549 |
|
|
\[
{}x^{\prime \prime }+10 x^{\prime }+125 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.786 |
|
|
\[
{}y^{\prime \prime }+16 y = {\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.473 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 3 x +4
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.081 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-6 y = 2 \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.464 |
|
|
\[
{}4 y^{\prime \prime }+4 y^{\prime }+y = 3 x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.091 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
75.376 |
|
|
\[
{}2 y^{\prime \prime }+4 y^{\prime }+7 y = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
22.687 |
|
|
\[
{}y^{\prime \prime }-4 y = \sinh \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.830 |
|
|
\[
{}y^{\prime \prime }-4 y = \cosh \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.951 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-3 y = 1+x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.320 |
|
|
\[
{}y^{\prime \prime }+9 y = 2 \cos \left (3 x \right )+3 \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.823 |
|
|
\[
{}y^{\prime \prime }+9 y = 2 x^{2} {\mathrm e}^{3 x}+5
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.483 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = {\mathrm e}^{x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.414 |
|
|
\[
{}y^{\prime \prime }+4 y = 3 x \cos \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.874 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = x \left ({\mathrm e}^{-x}-{\mathrm e}^{-2 x}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.308 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+13 y = x \,{\mathrm e}^{3 x} \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
15.096 |
|
|
\[
{}y^{\prime \prime }+4 y = 2 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.187 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.359 |
|
|
\[
{}y^{\prime \prime }+9 y = \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.606 |
|
|
\[
{}y^{\prime \prime }+y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.329 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = x +1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
8.960 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right ) \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
75.948 |
|
|
\[
{}y^{\prime \prime }+9 y = \sin \left (x \right )^{4}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.772 |
|
|
\[
{}y^{\prime \prime }+y = x \cos \left (x \right )^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.200 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 4 \,{\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.034 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-8 y = 3 \,{\mathrm e}^{-2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.110 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 2 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.072 |
|
|
\[
{}y^{\prime \prime }-4 y = \sinh \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.156 |
|
|
\[
{}y^{\prime \prime }+4 y = \cos \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.890 |
|
|
\[
{}y^{\prime \prime }+9 y = \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.541 |
|
|
\[
{}y^{\prime \prime }+9 y = 2 \sec \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.368 |
|
|
\[
{}y^{\prime \prime }+y = \csc \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.168 |
|
|
\[
{}y^{\prime \prime }+4 y = \sin \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.608 |
|