|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}2 x^{3} y+y^{3}-\left (x^{4}+2 x y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
62.418 |
|
|
\[
{}1+y \cos \left (x \right )-\sin \left (x \right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
0.657 |
|
|
\[
{}\left (\sin \left (y\right )^{2}+x \cot \left (y\right )\right ) y^{\prime } = 0
\] |
[_quadrature] |
✓ |
6.133 |
|
|
\[
{}1-\left (y-2 y x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
9.194 |
|
|
\[
{}1-\left (1+2 x \tan \left (y\right )\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
3.251 |
|
|
\[
{}\left (y^{3}+\frac {x}{y}\right ) y^{\prime } = 1
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
12.523 |
|
|
\[
{}1+\left (x -y^{2}\right ) y^{\prime } = 0
\] |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
1.658 |
|
|
\[
{}y^{2}+\left (y x +y^{2}-1\right ) y^{\prime } = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
1.806 |
|
|
\[
{}y = \left ({\mathrm e}^{y}+2 y x -2 x \right ) y^{\prime }
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
9.938 |
|
|
\[
{}\left (2 x +3\right ) y^{\prime } = y+\sqrt {2 x +3}
\] |
[_linear] |
✓ |
0.184 |
|
|
\[
{}y+\left (y^{2} {\mathrm e}^{y}-x \right ) y^{\prime } = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
3.096 |
|
|
\[
{}y^{\prime } = 1+3 y \tan \left (x \right )
\] |
[_linear] |
✓ |
0.394 |
|
|
\[
{}\left (\cos \left (x \right )+1\right ) y^{\prime } = \sin \left (x \right ) \left (\sin \left (x \right )+\sin \left (x \right ) \cos \left (x \right )-y\right )
\] |
[_linear] |
✓ |
0.615 |
|
|
\[
{}y^{\prime } = \left (\sin \left (x \right )^{2}-y\right ) \cos \left (x \right )
\] |
[_linear] |
✓ |
0.297 |
|
|
\[
{}\left (x +1\right ) y^{\prime }-y = x \left (x +1\right )^{2}
\] |
[_linear] |
✓ |
0.152 |
|
|
\[
{}1+y+\left (x -y \left (1+y\right )^{2}\right ) y^{\prime } = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
16.014 |
|
|
\[
{}y^{\prime }+y^{2} = x^{2}+1
\] |
[_Riccati] |
✓ |
0.882 |
|
|
\[
{}3 y^{\prime } x -3 x y^{4} \ln \left (x \right )-y = 0
\] |
[_Bernoulli] |
✓ |
9.295 |
|
|
\[
{}y^{\prime } = \frac {4 x^{3} y^{2}}{x^{4} y+2}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
26.937 |
|
|
\[
{}y \left (6 y^{2}-x -1\right )+2 y^{\prime } x = 0
\] |
[_rational, _Bernoulli] |
✓ |
0.955 |
|
|
\[
{}\left (x +1\right ) \left (y^{\prime }+y^{2}\right )-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
0.283 |
|
|
\[
{}x y y^{\prime }+y^{2}-\sin \left (x \right ) = 0
\] |
[_Bernoulli] |
✓ |
8.087 |
|
|
\[
{}2 x^{3}-y^{4}+x y^{3} y^{\prime } = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
2.424 |
|
|
\[
{}y^{\prime }-y \tan \left (x \right )+y^{2} \cos \left (x \right ) = 0
\] |
[_Bernoulli] |
✓ |
0.580 |
|
|
\[
{}6 y^{2}-x \left (2 x^{3}+y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
22.620 |
|
|
\[
{}x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+1 = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
1.198 |
|
|
\[
{}y = y^{\prime } x +{y^{\prime }}^{3}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.818 |
|
|
\[
{}x \left ({y^{\prime }}^{2}-1\right ) = 2 y^{\prime }
\] |
[_quadrature] |
✓ |
0.293 |
|
|
\[
{}x y^{\prime } \left (y^{\prime }+2\right ) = y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
3.855 |
|
|
\[
{}x = y^{\prime } \sqrt {1+{y^{\prime }}^{2}}
\] |
[_quadrature] |
✓ |
1.593 |
|
|
\[
{}2 {y^{\prime }}^{2} \left (y-y^{\prime } x \right ) = 1
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.692 |
|
|
\[
{}y = 2 y^{\prime } x +y^{2} {y^{\prime }}^{3}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
237.747 |
|
|
\[
{}{y^{\prime }}^{3}+y^{2} = x y y^{\prime }
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
32.384 |
|
|
\[
{}2 y^{\prime } x -y = y^{\prime } \ln \left (y y^{\prime }\right )
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
30.025 |
|
|
\[
{}y = y^{\prime } x -x^{2} {y^{\prime }}^{3}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
43.421 |
|
|
\[
{}y \left (y-2 y^{\prime } x \right )^{3} = {y^{\prime }}^{2}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
254.895 |
|
|
\[
{}y^{\prime } x +y = 4 \sqrt {y^{\prime }}
\] |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
39.665 |
|
|
\[
{}2 y^{\prime } x -y = \ln \left (y^{\prime }\right )
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
43.004 |
|
|
\[
{}x y^{2} \left (y^{\prime } x +y\right ) = 1
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
18.455 |
|
|
\[
{}5 y+{y^{\prime }}^{2} = x \left (x +y^{\prime }\right )
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
13.370 |
|
|
\[
{}y^{\prime } = \frac {y+2}{x +1}
\] |
[_separable] |
✓ |
3.841 |
|
|
\[
{}y^{\prime } x = y-x \,{\mathrm e}^{\frac {y}{x}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
77.473 |
|
|
\[
{}1+y^{2} \sin \left (2 x \right )-2 y \cos \left (x \right )^{2} y^{\prime } = 0
\] |
[_exact, _Bernoulli] |
✓ |
27.375 |
|
|
\[
{}2 \sqrt {y x}-y-y^{\prime } x = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
56.287 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{\frac {x y^{\prime }}{y}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
28.619 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }-2 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.059 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime }+9 y^{\prime }+9 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.056 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.052 |
|
|
\[
{}y^{\prime \prime \prime }+8 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.056 |
|
|
\[
{}y^{\prime \prime \prime }-8 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.053 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.061 |
|
|
\[
{}y^{\prime \prime \prime \prime }+18 y^{\prime \prime }+81 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.067 |
|
|
\[
{}y^{\prime \prime \prime \prime }-4 y^{\prime \prime }+16 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.225 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }+y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.065 |
|
|
\[
{}y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+5 y^{\prime \prime }+5 y^{\prime }-6 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.059 |
|
|
\[
{}y^{\left (5\right )}-6 y^{\prime \prime \prime \prime }+9 y^{\prime \prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.062 |
|
|
\[
{}y^{\left (6\right )}-64 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.086 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+10 y = 3 x \,{\mathrm e}^{-3 x}-2 \,{\mathrm e}^{3 x} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
23.354 |
|
|
\[
{}y^{\prime \prime }-8 y^{\prime }+17 y = {\mathrm e}^{4 x} \left (x^{2}-3 x \sin \left (x \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
27.119 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = \left (x +{\mathrm e}^{x}\right ) \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
45.506 |
|
|
\[
{}y^{\prime \prime }+4 y = \sinh \left (x \right ) \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
36.431 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = \cosh \left (x \right ) \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
24.540 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime } = \sin \left (x \right )+x \cos \left (x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
1.242 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime }+4 y^{\prime }-8 y = {\mathrm e}^{2 x} \sin \left (2 x \right )+2 x^{2}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
2.025 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime \prime }+3 y^{\prime } = x^{2}+x \,{\mathrm e}^{2 x}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.181 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime } = 7 x -3 \cos \left (x \right )
\] |
[[_high_order, _missing_y]] |
✓ |
0.280 |
|
|
\[
{}y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y = \sin \left (x \right ) \cos \left (2 x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
8.851 |
|
|
\[
{}y^{\prime } = a f \left (x \right )
\] |
[_quadrature] |
✓ |
0.351 |
|
|
\[
{}y^{\prime } = x +\sin \left (x \right )+y
\] |
[[_linear, ‘class A‘]] |
✓ |
2.838 |
|
|
\[
{}y^{\prime } = x^{2}+3 \cosh \left (x \right )+2 y
\] |
[[_linear, ‘class A‘]] |
✓ |
2.756 |
|
|
\[
{}y^{\prime } = a +b x +c y
\] |
[[_linear, ‘class A‘]] |
✓ |
9.326 |
|
|
\[
{}y^{\prime } = a \cos \left (b x +c \right )+k y
\] |
[[_linear, ‘class A‘]] |
✓ |
3.047 |
|
|
\[
{}y^{\prime } = a \sin \left (b x +c \right )+k y
\] |
[[_linear, ‘class A‘]] |
✓ |
2.787 |
|
|
\[
{}y^{\prime } = a +b \,{\mathrm e}^{k x}+c y
\] |
[[_linear, ‘class A‘]] |
✓ |
11.191 |
|
|
\[
{}y^{\prime } = x \left (x^{2}-y\right )
\] |
[_linear] |
✓ |
2.458 |
|
|
\[
{}y^{\prime } = x \left ({\mathrm e}^{-x^{2}}+a y\right )
\] |
[_linear] |
✓ |
2.313 |
|
|
\[
{}y^{\prime } = x^{2} \left (a \,x^{3}+b y\right )
\] |
[_linear] |
✓ |
11.932 |
|
|
\[
{}y^{\prime } = a \,x^{n} y
\] |
[_separable] |
✓ |
4.139 |
|
|
\[
{}y^{\prime } = \sin \left (x \right ) \cos \left (x \right )+y \cos \left (x \right )
\] |
[_linear] |
✓ |
10.430 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{\sin \left (x \right )}+y \cos \left (x \right )
\] |
[_linear] |
✓ |
2.980 |
|
|
\[
{}y^{\prime } = y \cot \left (x \right )
\] |
[_separable] |
✓ |
4.122 |
|
|
\[
{}y^{\prime } = 1-y \cot \left (x \right )
\] |
[_linear] |
✓ |
9.036 |
|
|
\[
{}y^{\prime } = x \csc \left (x \right )-y \cot \left (x \right )
\] |
[_linear] |
✓ |
3.570 |
|
|
\[
{}y^{\prime } = \left (2 \csc \left (2 x \right )+\cot \left (x \right )\right ) y
\] |
[_separable] |
✓ |
15.875 |
|
|
\[
{}y^{\prime } = \sec \left (x \right )-y \cot \left (x \right )
\] |
[_linear] |
✓ |
3.812 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x} \sin \left (x \right )+y \cot \left (x \right )
\] |
[_linear] |
✓ |
3.577 |
|
|
\[
{}y^{\prime }+\csc \left (x \right )+2 y \cot \left (x \right ) = 0
\] |
[_linear] |
✓ |
10.121 |
|
|
\[
{}y^{\prime } = 4 \csc \left (x \right ) x \sec \left (x \right )^{2}-2 y \cot \left (2 x \right )
\] |
[_linear] |
✓ |
57.180 |
|
|
\[
{}y^{\prime } = 2 \cot \left (x \right )^{2} \cos \left (2 x \right )-2 y \csc \left (2 x \right )
\] |
[_linear] |
✓ |
8.155 |
|
|
\[
{}y^{\prime } = 4 \csc \left (x \right ) x \left (\sin \left (x \right )^{3}+y\right )
\] |
[_linear] |
✓ |
43.731 |
|
|
\[
{}y^{\prime } = 4 \csc \left (x \right ) x \left (1-\tan \left (x \right )^{2}+y\right )
\] |
[_linear] |
✓ |
32.772 |
|
|
\[
{}y^{\prime } = y \sec \left (x \right )
\] |
[_separable] |
✓ |
5.763 |
|
|
\[
{}y^{\prime }+\tan \left (x \right ) = \left (1-y\right ) \sec \left (x \right )
\] |
[_linear] |
✓ |
11.711 |
|
|
\[
{}y^{\prime } = y \tan \left (x \right )
\] |
[_separable] |
✓ |
4.636 |
|
|
\[
{}y^{\prime } = \cos \left (x \right )+y \tan \left (x \right )
\] |
[_linear] |
✓ |
3.074 |
|
|
\[
{}y^{\prime } = \cos \left (x \right )-y \tan \left (x \right )
\] |
[_linear] |
✓ |
10.361 |
|
|
\[
{}y^{\prime } = \sec \left (x \right )-y \tan \left (x \right )
\] |
[_linear] |
✓ |
3.517 |
|
|
\[
{}y^{\prime } = \sin \left (2 x \right )+y \tan \left (x \right )
\] |
[_linear] |
✓ |
3.394 |
|
|
\[
{}y^{\prime } = \sin \left (2 x \right )-y \tan \left (x \right )
\] |
[_linear] |
✓ |
10.790 |
|
|
\[
{}y^{\prime } = \sin \left (x \right )+2 y \tan \left (x \right )
\] |
[_linear] |
✓ |
3.072 |
|