|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}-y+y^{\prime } x = x^{3}+3 x^{2}-2 x
\] |
[_linear] |
✓ |
0.150 |
|
|
\[
{}y^{\prime }+y \tan \left (x \right ) = \sin \left (x \right )
\] |
[_linear] |
✓ |
0.201 |
|
|
\[
{}-y+y^{\prime } x = x^{3} \cos \left (x \right )
\] |
[_linear] |
✓ |
0.325 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+3 y x = 5 x
\] |
[_separable] |
✓ |
0.530 |
|
|
\[
{}y^{\prime }+y \cot \left (x \right ) = 5 \,{\mathrm e}^{\cos \left (x \right )}
\] |
[_linear] |
✓ |
0.340 |
|
|
\[
{}\left (3 x +3 y-4\right ) y^{\prime } = -x -y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.180 |
|
|
\[
{}x -x y^{2} = \left (x +x^{2} y\right ) y^{\prime }
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.636 |
|
|
\[
{}x -y-1+\left (4 y+x -1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.700 |
|
|
\[
{}3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.178 |
|
|
\[
{}y \left (y x +1\right )+x \left (1+y x +x^{2} y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.506 |
|
|
\[
{}y^{\prime }+y = x y^{3}
\] |
[_Bernoulli] |
✓ |
0.372 |
|
|
\[
{}y^{\prime }+y = y^{4} {\mathrm e}^{x}
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
0.287 |
|
|
\[
{}2 y^{\prime }+y = y^{3} \left (x -1\right )
\] |
[_Bernoulli] |
✓ |
0.368 |
|
|
\[
{}y^{\prime }-2 y \tan \left (x \right ) = y^{2} \tan \left (x \right )^{2}
\] |
[_Bernoulli] |
✓ |
0.292 |
|
|
\[
{}y^{\prime }+y \tan \left (x \right ) = y^{3} \sec \left (x \right )^{4}
\] |
[_Bernoulli] |
✓ |
0.393 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime } = y x +1
\] |
[_linear] |
✓ |
1.057 |
|
|
\[
{}x y y^{\prime }-\left (x +1\right ) \sqrt {-1+y} = 0
\] |
[_separable] |
✓ |
1.647 |
|
|
\[
{}x^{2}-2 y x +5 y^{2} = \left (x^{2}+2 y x +y^{2}\right ) y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
6.063 |
|
|
\[
{}y^{\prime }-y \cot \left (x \right ) = y^{2} \sec \left (x \right )^{2}
\] |
[_Bernoulli] |
✓ |
2.816 |
|
|
\[
{}y+\left (x^{2}-4 x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.449 |
|
|
\[
{}y^{\prime }-y \tan \left (x \right ) = \cos \left (x \right )-2 x \sin \left (x \right )
\] |
[_linear] |
✓ |
2.310 |
|
|
\[
{}y^{\prime } = \frac {2 y x +y^{2}}{x^{2}+2 y x}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
73.071 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = x \left (1+y\right )
\] |
[_separable] |
✓ |
1.073 |
|
|
\[
{}y^{\prime } x +2 y = 3 x -1
\] |
[_linear] |
✓ |
1.638 |
|
|
\[
{}x^{2} y^{\prime } = y^{2}-x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
9.603 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{3 x -2 y}
\] |
[_separable] |
✓ |
2.831 |
|
|
\[
{}y^{\prime }+\frac {y}{x} = \sin \left (2 x \right )
\] |
[_linear] |
✓ |
1.562 |
|
|
\[
{}y^{2}+x^{2} y^{\prime } = x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
36.701 |
|
|
\[
{}2 x y y^{\prime } = x^{2}-y^{2}
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
3.892 |
|
|
\[
{}y^{\prime } = \frac {x -2 y+1}{2 x -4 y}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.513 |
|
|
\[
{}\left (-x^{3}+1\right ) y^{\prime }+x^{2} y = x^{2} \left (-x^{3}+1\right )
\] |
[_linear] |
✓ |
2.521 |
|
|
\[
{}y^{\prime }+\frac {y}{x} = \sin \left (x \right )
\] |
[_linear] |
✓ |
1.374 |
|
|
\[
{}y^{\prime }+x +x y^{2} = 0
\] |
[_separable] |
✓ |
2.271 |
|
|
\[
{}y^{\prime }+\left (\frac {1}{x}-\frac {2 x}{-x^{2}+1}\right ) y = \frac {1}{-x^{2}+1}
\] |
[_linear] |
✓ |
1.123 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+y x = \left (x^{2}+1\right )^{{3}/{2}}
\] |
[_linear] |
✓ |
1.618 |
|
|
\[
{}x \left (1+y^{2}\right )-y \left (x^{2}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
3.125 |
|
|
\[
{}\frac {r \tan \left (\theta \right ) r^{\prime }}{a^{2}-r^{2}} = 1
\] |
[_separable] |
✓ |
2.832 |
|
|
\[
{}y^{\prime }+y \cot \left (x \right ) = \cos \left (x \right )
\] |
[_linear] |
✓ |
1.837 |
|
|
\[
{}y^{\prime }+\frac {y}{x} = x y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
1.690 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 8
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.867 |
|
|
\[
{}y^{\prime \prime }-4 y = 10 \,{\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.935 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.946 |
|
|
\[
{}y^{\prime \prime }+25 y = 5 x^{2}+x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.459 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 4 \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.151 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = 2 \,{\mathrm e}^{-2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.720 |
|
|
\[
{}3 y^{\prime \prime }-2 y^{\prime }-y = 2 x -3
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.946 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+8 y = 8 \,{\mathrm e}^{4 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.969 |
|
|
\[
{}2 y^{\prime \prime }-7 y^{\prime }-4 y = {\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.987 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 54 x +18
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.977 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = 100 \sin \left (4 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.430 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 4 \sinh \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.933 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = 2 \cosh \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.456 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }+10 y = 20-{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
22.737 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = 2 \cos \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.096 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+3 y = x +{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.999 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+3 y = x^{2}-1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
13.379 |
|
|
\[
{}y^{\prime \prime }-9 y = {\mathrm e}^{3 x}+\sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.764 |
|
|
\[
{}x^{\prime \prime }+4 x^{\prime }+3 x = {\mathrm e}^{-3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.224 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = 6 \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.312 |
|
|
\[
{}x^{\prime \prime }-3 x^{\prime }+2 x = \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.608 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 3 \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.505 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+10 y = 50 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
7.375 |
|
|
\[
{}x^{\prime \prime }+2 x^{\prime }+2 x = 85 \sin \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
10.745 |
|
|
\[
{}y^{\prime \prime } = 3 \sin \left (x \right )-4 y
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.359 |
|
|
\[
{}\frac {x^{\prime \prime }}{2} = -48 x
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.166 |
|
|
\[
{}x^{\prime \prime }+5 x^{\prime }+6 x = \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.633 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 4 x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.072 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.892 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.393 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+25 y = 2 \sin \left (\frac {t}{2}\right )-\cos \left (\frac {t}{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
46.196 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+25 y = 64 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
18.420 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+25 y = 50 t^{3}-36 t^{2}-63 t +18
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
27.663 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = 2 x \,{\mathrm e}^{-x}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.120 |
|
|
\[
{}y^{\prime \prime } = 9 x^{2}+2 x -1
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.114 |
|
|
\[
{}y^{\prime \prime }-5 y = 2 \,{\mathrm e}^{5 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.047 |
|
|
\[
{}y^{\prime }-5 y = \left (x -1\right ) \sin \left (x \right )+\left (x +1\right ) \cos \left (x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.705 |
|
|
\[
{}y^{\prime }-5 y = 3 \,{\mathrm e}^{x}-2 x +1
\] |
[[_linear, ‘class A‘]] |
✓ |
1.108 |
|
|
\[
{}y^{\prime }-5 y = x^{2} {\mathrm e}^{x}-x \,{\mathrm e}^{5 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.431 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = x^{2}-1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.961 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 4 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.926 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 4 \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.187 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 3 \,{\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.964 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.946 |
|
|
\[
{}y^{\prime }-y = {\mathrm e}^{x}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.799 |
|
|
\[
{}y^{\prime }-y = x \,{\mathrm e}^{2 x}+1
\] |
[[_linear, ‘class A‘]] |
✓ |
1.104 |
|
|
\[
{}y^{\prime }-y = \sin \left (x \right )+\cos \left (2 x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.838 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = 1+{\mathrm e}^{x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.126 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime } = \sec \left (x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.526 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = \frac {{\mathrm e}^{x}}{1+{\mathrm e}^{-x}}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.240 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.970 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.891 |
|
|
\[
{}x^{\prime \prime }+4 x = \sin \left (2 t \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.255 |
|
|
\[
{}t^{2} N^{\prime \prime }-2 t N^{\prime }+2 N = t \ln \left (t \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.066 |
|
|
\[
{}y^{\prime }+\frac {4 y}{x} = x^{4}
\] |
[_linear] |
✓ |
1.234 |
|
|
\[
{}y^{\prime \prime \prime \prime } = 5 x
\] |
[[_high_order, _quadrature]] |
✓ |
0.105 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{x^{5}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.079 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.240 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.918 |
|
|
\[
{}y^{\prime \prime }-60 y^{\prime }-900 y = 5 \,{\mathrm e}^{10 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.317 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime } = -3
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.370 |
|