|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x y^{2} \left ({y^{\prime }}^{2}+2\right ) = 2 y^{\prime } y^{3}+x^{3}
\] |
[_separable] |
✓ |
16.443 |
|
|
\[
{}y = -x y^{\prime }+x^{4} {y^{\prime }}^{2}
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
3.773 |
|
|
\[
{}{y^{\prime }}^{2}-9 y^{\prime }+18 = 0
\] |
[_quadrature] |
✓ |
1.114 |
|
|
\[
{}a y {y^{\prime }}^{2}+\left (2 x -b \right ) y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
1.628 |
|
|
\[
{}\left (-y+x y^{\prime }\right )^{2} = a \left (1+{y^{\prime }}^{2}\right ) \left (y^{2}+x^{2}\right )^{{3}/{2}}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
100.286 |
|
|
\[
{}\left (-y+x y^{\prime }\right )^{2} = {y^{\prime }}^{2}-\frac {2 y y^{\prime }}{x}+1
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
23.296 |
|
|
\[
{}3 y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+4 y^{2}-x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
6.244 |
|
|
\[
{}\left (y^{2}+x^{2}\right ) \left (1+y^{\prime }\right )^{2}-2 \left (x +y\right ) \left (1+y^{\prime }\right ) \left (x +y y^{\prime }\right )+\left (x +y y^{\prime }\right )^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
10.158 |
|
|
\[
{}\left (y y^{\prime }+n x \right )^{2} = \left (y^{2}+n \,x^{2}\right ) \left (1+{y^{\prime }}^{2}\right )
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
5.658 |
|
|
\[
{}y^{2} \left (1-{y^{\prime }}^{2}\right ) = b
\] |
[_quadrature] |
✓ |
72.718 |
|
|
\[
{}\left (-y+x y^{\prime }\right ) \left (x +y y^{\prime }\right ) = h^{2} y^{\prime }
\] |
[_rational] |
✓ |
123.604 |
|
|
\[
{}{y^{\prime }}^{2}+2 y^{\prime } y \cot \left (x \right ) = y^{2}
\] |
[_separable] |
✓ |
1.825 |
|
|
\[
{}\left ({y^{\prime }}^{2}-\frac {1}{a^{2}-x^{2}}\right ) \left (y^{\prime }-\sqrt {\frac {y}{x}}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
251.550 |
|
|
\[
{}x +\frac {y^{\prime }}{\sqrt {1+{y^{\prime }}^{2}}} = a
\] |
[_quadrature] |
✓ |
0.886 |
|
|
\[
{}x y {y^{\prime }}^{2}+y^{\prime } \left (3 x^{2}-2 y^{2}\right )-6 x y = 0
\] |
[_separable] |
✓ |
8.223 |
|
|
\[
{}{y^{\prime }}^{3}-4 x y y^{\prime }+8 y^{2} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
507.285 |
|
|
\[
{}{y^{\prime }}^{3}-\left (y^{2}+x y+x^{2}\right ) {y^{\prime }}^{2}+\left (x^{3} y+y^{2} x^{2}+x y^{3}\right ) y^{\prime }-x^{3} y^{3} = 0
\] |
[_quadrature] |
✓ |
2.549 |
|
|
\[
{}{y^{\prime }}^{3}+m {y^{\prime }}^{2} = a \left (y+m x \right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
30.802 |
|
|
\[
{}{\mathrm e}^{3 x} \left (y^{\prime }-1\right )+{y^{\prime }}^{3} {\mathrm e}^{2 y} = 0
\] |
unknown |
✓ |
31.026 |
|
|
\[
{}\left (1-y^{2}+\frac {y^{4}}{x^{2}}\right ) {y^{\prime }}^{2}-\frac {2 y y^{\prime }}{x}+\frac {y^{2}}{x^{2}} = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
16.648 |
|
|
\[
{}y-\frac {1}{\sqrt {1+{y^{\prime }}^{2}}} = b
\] |
[_quadrature] |
✓ |
32.873 |
|
|
\[
{}y = x y^{\prime }+\frac {m}{y^{\prime }}
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
0.542 |
|
|
\[
{}y = 2 x y^{\prime }+y^{2} {y^{\prime }}^{3}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
106.908 |
|
|
\[
{}y = x y^{\prime }+a \sqrt {1+{y^{\prime }}^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
9.283 |
|
|
\[
{}{y^{\prime }}^{2}+x y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.387 |
|
|
\[
{}y^{\prime } \sqrt {x} = \sqrt {y}
\] |
[_separable] |
✓ |
34.188 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-3 x y y^{\prime }+2 y^{2}+x^{3} = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
76.680 |
|
|
\[
{}\left (1+y^{\prime }\right )^{3} = \frac {7 \left (x +y\right ) \left (1-y^{\prime }\right )^{3}}{4 a}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
34.905 |
|
|
\[
{}y^{2} \left (1+{y^{\prime }}^{2}\right ) = r^{2}
\] |
[_quadrature] |
✓ |
424.807 |
|
|
\[
{}x {y^{\prime }}^{2}-\left (x -a \right )^{2} = 0
\] |
[_quadrature] |
✓ |
0.460 |
|
|
\[
{}{y^{\prime }}^{2}+2 x y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.560 |
|
|
\[
{}a {y^{\prime }}^{3} = 27 y
\] |
[_quadrature] |
✓ |
3.963 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }+a x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
3.621 |
|
|
\[
{}x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+a^{3} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
24.017 |
|
|
\[
{}y^{2}-2 x y y^{\prime }+{y^{\prime }}^{2} \left (x^{2}-1\right ) = m^{2}
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
0.803 |
|
|
\[
{}y = x y^{\prime }+\sqrt {b^{2}+a^{2} y^{\prime }}
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
3.877 |
|
|
\[
{}y = x y^{\prime }-{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.500 |
|
|
\[
{}4 {y^{\prime }}^{2} = 9 x
\] |
[_quadrature] |
✓ |
0.419 |
|
|
\[
{}4 x \left (x -1\right ) \left (-2+x \right ) {y^{\prime }}^{2}-\left (3 x^{2}-6 x +2\right )^{2} = 0
\] |
[_quadrature] |
✓ |
0.435 |
|
|
\[
{}\left (8 {y^{\prime }}^{3}-27\right ) x = 12 {y^{\prime }}^{2} y
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
1.046 |
|
|
\[
{}{y^{\prime }}^{2} \left (-a^{2}+x^{2}\right )-2 x y y^{\prime }+y^{2}-b^{2} = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
6.636 |
|
|
\[
{}\left (-y+x y^{\prime }\right ) \left (x -y y^{\prime }\right ) = 2 y^{\prime }
\] |
[_rational] |
✓ |
92.792 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-54 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.780 |
|
|
\[
{}y^{\prime \prime }-m^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
13.832 |
|
|
\[
{}2 y^{\prime \prime }+5 y^{\prime }-12 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.638 |
|
|
\[
{}9 y^{\prime \prime }+18 y^{\prime }-16 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.621 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.134 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-9 y^{\prime \prime }-11 y^{\prime }-4 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.115 |
|
|
\[
{}y^{\prime \prime }+8 y^{\prime }+25 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.322 |
|
|
\[
{}y^{\prime \prime \prime \prime }-m^{2} y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.098 |
|
|
\[
{}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+8 y^{\prime \prime }-8 y^{\prime }+4 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.069 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{4 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.630 |
|
|
\[
{}y^{\prime \prime }-y = 2+5 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.651 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 2 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.631 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }-8 y^{\prime }+12 y = X \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.375 |
|
|
\[
{}y^{\prime \prime \prime }+y = 3+{\mathrm e}^{-x}+5 \,{\mathrm e}^{2 x}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.145 |
|
|
\[
{}y^{\prime \prime \prime }-y = \left (1+{\mathrm e}^{x}\right )^{2}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.269 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 3 \,{\mathrm e}^{\frac {5 x}{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.760 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime } = x^{2}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.117 |
|
|
\[
{}y^{\prime \prime \prime }+8 y = x^{4}+2 x +1
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.135 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y = \cos \left (2 x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.102 |
|
|
\[
{}y^{\prime \prime }+a^{2} y = \cos \left (a x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.764 |
|
|
\[
{}y^{\prime \prime }-4 y = 2 \sin \left (\frac {x}{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.138 |
|
|
\[
{}y^{\prime \prime \prime }+y = \sin \left (3 x \right )-\cos \left (\frac {x}{2}\right )^{2}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.355 |
|
|
\[
{}y^{\prime \prime \prime \prime }+y = x \,{\mathrm e}^{2 x}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.222 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{2 x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.231 |
|
|
\[
{}y^{\prime \prime }+2 y = x^{2} {\mathrm e}^{3 x}+{\mathrm e}^{x} \cos \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
11.739 |
|
|
\[
{}y^{\prime \prime }+4 y = x \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.492 |
|
|
\[
{}y^{\prime \prime }-y = x^{2} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.193 |
|
|
\[
{}y^{\prime \prime \prime \prime }+4 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.163 |
|
|
\[
{}y^{\left (5\right )}-13 y^{\prime \prime \prime }+26 y^{\prime \prime }+82 y^{\prime }+104 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.139 |
|
|
\[
{}y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime } = {\mathrm e}^{2 x}+x^{2}+x
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.152 |
|
|
\[
{}y^{\prime \prime }+4 y = \sin \left (3 x \right )+{\mathrm e}^{x}+x^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.207 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = x +{\mathrm e}^{m x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.829 |
|
|
\[
{}y^{\prime \prime }-a^{2} y = {\mathrm e}^{a x}+{\mathrm e}^{n x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.194 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }-6 y^{\prime }+8 y = x
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.092 |
|
|
\[
{}y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }+y^{\prime \prime } = x^{2} \left (b x +a \right )
\] |
[[_high_order, _missing_y]] |
✓ |
0.126 |
|
|
\[
{}y^{\prime \prime \prime }-13 y^{\prime }+12 y = x
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.086 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 n^{2} y^{\prime \prime }+n^{4} y = \cos \left (m x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.148 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = x^{2} \cos \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.964 |
|
|
\[
{}y^{\prime \prime }+a^{2} y = \sec \left (a x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.142 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = x^{2} {\mathrm e}^{3 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.316 |
|
|
\[
{}y^{\prime \prime }+n^{2} y = x^{4} {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
17.934 |
|
|
\[
{}y^{\prime \prime \prime \prime }-a^{4} y = x^{4}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.122 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime } = x
\] |
[[_high_order, _missing_y]] |
✓ |
0.243 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = {\mathrm e}^{x} \cos \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.105 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
96.143 |
|
|
\[
{}y^{\prime \prime \prime }-7 y^{\prime }-6 y = {\mathrm e}^{2 x} \left (x +1\right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.111 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+4 y = {\mathrm e}^{x} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
391.687 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y = {\mathrm e}^{-x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.797 |
|
|
\[
{}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }+4 y = {\mathrm e}^{x} x^{2}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.218 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = x \,{\mathrm e}^{x}+{\mathrm e}^{x}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.207 |
|
|
\[
{}y^{\prime \prime }-y = x \sin \left (x \right )+\left (x^{2}+1\right ) {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
190.173 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+3 y = {\mathrm e}^{x} \cos \left (2 x \right )+\cos \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
160.967 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y = {\mathrm e}^{x}+\cos \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.349 |
|
|
\[
{}y^{\prime \prime }-9 y^{\prime }+20 y = 20 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
153.252 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y = {\mathrm e}^{3 x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.151 |
|
|
\[
{}y^{\prime \prime \prime }+y = {\mathrm e}^{2 x} \sin \left (x \right )+{\mathrm e}^{\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
4.046 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+y = 2 \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.095 |
|
|
\[
{}x^{2} y^{\prime \prime }+y = 3 x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.079 |
|