|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 8 x^{2} {\mathrm e}^{2 x} \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.369 |
|
|
\[
{}y^{\prime \prime }+y = {\mathrm e}^{-x}+\cos \left (x \right )+x^{3}+{\mathrm e}^{x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
7.945 |
|
|
\[
{}y^{\prime \prime \prime \prime }+y^{\prime \prime }+y = {\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.951 |
|
|
\[
{}y^{\left (6\right )}-2 y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+3 y^{\prime \prime }-2 y^{\prime }+y = \sin \left (\frac {x}{2}\right )^{2}+{\mathrm e}^{x}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
1.694 |
|
|
\[
{}y^{\prime \prime \prime \prime }+y^{\prime \prime }+16 y = 16 x^{2}+256
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.188 |
|
|
\[
{}y^{\prime \prime }+y = 3 \cos \left (x \right )^{2}+2 \sin \left (x \right )^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.928 |
|
|
\[
{}y^{\prime \prime \prime \prime }+10 y^{\prime \prime }+9 y = 96 \sin \left (2 x \right ) \cos \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
1.076 |
|
|
\[
{}y^{\left (5\right )}-13 y^{\prime \prime \prime }+26 y^{\prime \prime }+82 y^{\prime }+104 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.089 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+10 y+37 \sin \left (3 x \right ) = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
13.924 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = 24 x \cos \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.978 |
|
|
\[
{}{y^{\prime }}^{2}-7 y^{\prime }+12 = 0
\] |
[_quadrature] |
✓ |
1.387 |
|
|
\[
{}{y^{\prime }}^{2}-5 y^{\prime }+6 = 0
\] |
[_quadrature] |
✓ |
1.420 |
|
|
\[
{}{y^{\prime }}^{2}-9 y^{\prime }+18 = 0
\] |
[_quadrature] |
✓ |
1.396 |
|
|
\[
{}{y^{\prime }}^{2}+2 y^{\prime } x -3 x^{2} = 0
\] |
[_quadrature] |
✓ |
0.895 |
|
|
\[
{}{y^{\prime }}^{2}+2 y^{\prime } y \cot \left (x \right ) = y^{2}
\] |
[_separable] |
✓ |
1.050 |
|
|
\[
{}{y^{\prime }}^{2}-2 y^{\prime } \cosh \left (x \right )+1 = 0
\] |
[_quadrature] |
✓ |
0.345 |
|
|
\[
{}y^{\prime } \left (y^{\prime }-y\right ) = \left (x +y\right ) x
\] |
[_quadrature] |
✓ |
1.605 |
|
|
\[
{}y {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }-x = 0
\] |
[_quadrature] |
✓ |
4.066 |
|
|
\[
{}x +y {y^{\prime }}^{2} = y^{\prime } \left (1+x y\right )
\] |
[_quadrature] |
✓ |
2.072 |
|
|
\[
{}x {y^{\prime }}^{2}+\left (y-x \right ) y^{\prime }-y = 0
\] |
[_quadrature] |
✓ |
2.737 |
|
|
\[
{}{y^{\prime }}^{3}-a \,x^{4} = 0
\] |
[_quadrature] |
✓ |
0.323 |
|
|
\[
{}{y^{\prime }}^{2}+y^{\prime } x +y y^{\prime }+x y = 0
\] |
[_quadrature] |
✓ |
1.734 |
|
|
\[
{}{y^{\prime }}^{3}-y^{\prime } \left (x^{2}+x y+y^{2}\right )+x y \left (x +y\right ) = 0
\] |
[_quadrature] |
✓ |
2.717 |
|
|
\[
{}\left (y^{\prime }+y+x \right ) \left (y+x +y^{\prime } x \right ) \left (y^{\prime }+2 x \right ) = 0
\] |
[_quadrature] |
✓ |
3.776 |
|
|
\[
{}x^{2} {y^{\prime }}^{3}+y \left (1+x^{2} y\right ) {y^{\prime }}^{2}+y^{2} y^{\prime } = 0
\] |
[_quadrature] |
✓ |
12.233 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+x y y^{\prime }-6 y^{2} = 0
\] |
[_separable] |
✓ |
4.217 |
|
|
\[
{}{y^{\prime }}^{3}+2 x {y^{\prime }}^{2}-y^{2} {y^{\prime }}^{2}-2 x y^{2} y^{\prime } = 0
\] |
[_quadrature] |
✓ |
2.266 |
|
|
\[
{}{y^{\prime }}^{2} \left (2-3 y\right )^{2} = 4-4 y
\] |
[_quadrature] |
✓ |
0.453 |
|
|
\[
{}y = 3 x +a \ln \left (y^{\prime }\right )
\] |
[_separable] |
✓ |
7.671 |
|
|
\[
{}{y^{\prime }}^{2}-y y^{\prime }+x = 0
\] |
[_dAlembert] |
✓ |
1.289 |
|
|
\[
{}y = x +a \arctan \left (y^{\prime }\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
21.378 |
|
|
\[
{}3 {y^{\prime }}^{5}-y y^{\prime }+1 = 0
\] |
[_quadrature] |
✓ |
0.483 |
|
|
\[
{}y = x {y^{\prime }}^{2}+y^{\prime }
\] |
[_rational, _dAlembert] |
✓ |
0.875 |
|
|
\[
{}x {y^{\prime }}^{2}+a x = 2 y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.432 |
|
|
\[
{}{y^{\prime }}^{3}+y^{\prime } = {\mathrm e}^{y}
\] |
[_quadrature] |
✓ |
0.965 |
|
|
\[
{}y = \sin \left (y^{\prime }\right )-y^{\prime } \cos \left (y^{\prime }\right )
\] |
[_quadrature] |
✓ |
2.019 |
|
|
\[
{}y = \sin \left (x \right ) y^{\prime }+\cos \left (x \right )
\] |
[_linear] |
✓ |
1.952 |
|
|
\[
{}y = y^{\prime } \tan \left (y^{\prime }\right )+\ln \left (\cos \left (y^{\prime }\right )\right )
\] |
[_dAlembert] |
✓ |
1.872 |
|
|
\[
{}x = y y^{\prime }-{y^{\prime }}^{2}
\] |
[_dAlembert] |
✓ |
1.297 |
|
|
\[
{}\left (2 x -b \right ) y^{\prime } = y-a y {y^{\prime }}^{2}
\] |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
0.891 |
|
|
\[
{}x = y+a \ln \left (y^{\prime }\right )
\] |
[_separable] |
✓ |
5.346 |
|
|
\[
{}y {y^{\prime }}^{2}+2 y^{\prime } x = y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.887 |
|
|
\[
{}x \left ({y^{\prime }}^{2}+1\right ) = 1
\] |
[_quadrature] |
✓ |
0.273 |
|
|
\[
{}x^{2} = a^{2} \left ({y^{\prime }}^{2}+1\right )
\] |
[_quadrature] |
✓ |
0.332 |
|
|
\[
{}y = y^{\prime } x +\frac {a}{y^{\prime }}
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
0.440 |
|
|
\[
{}y = y^{\prime } x +y^{\prime }-{y^{\prime }}^{3}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.492 |
|
|
\[
{}y = y^{\prime } x +a y^{\prime } \left (1-y^{\prime }\right )
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.477 |
|
|
\[
{}y = y^{\prime } x +\sqrt {{y^{\prime }}^{2}+1}
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
1.375 |
|
|
\[
{}y = y^{\prime } x +\sqrt {b^{2}-a^{2} {y^{\prime }}^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
3.039 |
|
|
\[
{}\left (y-y^{\prime } x \right ) \left (y^{\prime }-1\right ) = y^{\prime }
\] |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
0.531 |
|
|
\[
{}x {y^{\prime }}^{2}-y y^{\prime }+a = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
0.364 |
|
|
\[
{}y = y^{\prime } \left (x -b \right )+\frac {a}{y^{\prime }}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.514 |
|
|
\[
{}y = y^{\prime } x +{y^{\prime }}^{3}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.451 |
|
|
\[
{}4 y {y^{\prime }}^{2}+2 y^{\prime } x -y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.721 |
|
|
\[
{}y {y^{\prime }}^{2}+2 y^{\prime } x -y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.054 |
|
|
\[
{}x +\frac {y^{\prime }}{\sqrt {{y^{\prime }}^{2}+1}} = a
\] |
[_quadrature] |
✓ |
0.515 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+2 y^{2} = x^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.963 |
|
|
\[
{}y = y^{\prime } x +x \sqrt {{y^{\prime }}^{2}+1}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
35.171 |
|
|
\[
{}x +y^{\prime } y \left (2 {y^{\prime }}^{2}+3\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.986 |
|
|
\[
{}y = \frac {2 a {y^{\prime }}^{2}}{\left ({y^{\prime }}^{2}+1\right )^{2}}
\] |
[_quadrature] |
✓ |
2.860 |
|
|
\[
{}\left (-y+y^{\prime } x \right )^{2} = a \left ({y^{\prime }}^{2}+1\right ) \left (x^{2}+y^{2}\right )^{{3}/{2}}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
45.410 |
|
|
\[
{}4 x {y^{\prime }}^{2}+4 y y^{\prime } = y^{4}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
13.656 |
|
|
\[
{}2 {y^{\prime }}^{3}-\left (2 x +4 \sin \left (x \right )-\cos \left (x \right )\right ) {y^{\prime }}^{2}-\left (x \cos \left (x \right )-4 x \sin \left (x \right )+\sin \left (2 x \right )\right ) y^{\prime }+x \sin \left (2 x \right ) = 0
\] |
[_quadrature] |
✓ |
0.823 |
|
|
\[
{}\left (-y+y^{\prime } x \right )^{2} = {y^{\prime }}^{2}-\frac {2 y y^{\prime }}{x}+1
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
10.983 |
|
|
\[
{}y-y^{\prime } x = x +y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.665 |
|
|
\[
{}a^{2} y {y^{\prime }}^{2}-4 y^{\prime } x +y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.568 |
|
|
\[
{}x^{2} \left (y-y^{\prime } x \right ) = y {y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
3.032 |
|
|
\[
{}\left ({y^{\prime }}^{2}-\frac {1}{a^{2}-x^{2}}\right ) \left (y^{\prime }-\sqrt {\frac {y}{x}}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
13.385 |
|
|
\[
{}{y^{\prime }}^{2} \left (-a^{2}+x^{2}\right )-2 x y y^{\prime }+y^{2}+a^{4} = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
1.634 |
|
|
\[
{}x +y y^{\prime } = a {y^{\prime }}^{2}
\] |
[_dAlembert] |
✓ |
50.253 |
|
|
\[
{}x y {y^{\prime }}^{2}+y^{\prime } \left (3 x^{2}-2 y^{2}\right )-6 x y = 0
\] |
[_separable] |
✓ |
5.503 |
|
|
\[
{}2 y = y^{\prime } x +\frac {a}{y^{\prime }}
\] |
[[_homogeneous, ‘class G‘], _rational, _dAlembert] |
✓ |
0.572 |
|
|
\[
{}y = a y^{\prime }+\sqrt {{y^{\prime }}^{2}+1}
\] |
[_quadrature] |
✓ |
1.633 |
|
|
\[
{}\left (a {y^{\prime }}^{2}-b \right ) x y+\left (b \,x^{2}-a y^{2}+c \right ) y^{\prime } = 0
\] |
[_rational] |
✓ |
171.082 |
|
|
\[
{}y = a y^{\prime }+b {y^{\prime }}^{2}
\] |
[_quadrature] |
✓ |
0.587 |
|
|
\[
{}{y^{\prime }}^{3}-\left (y+2 x -{\mathrm e}^{x -y}\right ) {y^{\prime }}^{2}+\left (2 x y-2 x \,{\mathrm e}^{x -y}-y \,{\mathrm e}^{x -y}\right ) y^{\prime }+2 x y \,{\mathrm e}^{x -y} = 0
\] |
[_quadrature] |
✓ |
3.785 |
|
|
\[
{}\left (1+6 y^{2}-3 x^{2} y\right ) y^{\prime } = 3 x y^{2}-x^{2}
\] |
[_exact, _rational] |
✓ |
1.556 |
|
|
\[
{}\left (x^{2}+1\right ) {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2} = 1
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
0.571 |
|
|
\[
{}\left (x^{3} y^{3}+x^{2} y^{2}+x y+1\right ) y+\left (x^{3} y^{3}-x^{2} y^{2}-x y+1\right ) x y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.087 |
|
|
\[
{}\left (x \cos \left (\frac {y}{x}\right )+y \sin \left (\frac {y}{x}\right )\right ) y = \left (y \sin \left (\frac {y}{x}\right )-x \cos \left (\frac {y}{x}\right )\right ) x y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
7.073 |
|
|
\[
{}\left (-y+y^{\prime } x \right ) \left (x +y y^{\prime }\right ) = h^{2} y^{\prime }
\] |
[_rational] |
✓ |
117.046 |
|
|
\[
{}x^{2} y^{2}-3 x y y^{\prime } = 2 y^{2}+x^{3}
\] |
[_rational, _Bernoulli] |
✓ |
3.310 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }+a x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.451 |
|
|
\[
{}y^{2}-2 x y y^{\prime }+\left (x^{2}-1\right ) {y^{\prime }}^{2} = m
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
0.514 |
|
|
\[
{}y = y^{\prime } x -{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.322 |
|
|
\[
{}4 {y^{\prime }}^{2} = 9 x
\] |
[_quadrature] |
✓ |
0.261 |
|
|
\[
{}4 x \left (x -1\right ) \left (x -2\right ) {y^{\prime }}^{2}-\left (3 x^{2}-6 x +2\right )^{2} = 0
\] |
[_quadrature] |
✓ |
0.280 |
|
|
\[
{}\left (8 {y^{\prime }}^{3}-27\right ) x = \frac {12 {y^{\prime }}^{2}}{x}
\] |
[_quadrature] |
✓ |
0.586 |
|
|
\[
{}3 y = 2 y^{\prime } x -\frac {2 {y^{\prime }}^{2}}{x}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
2.642 |
|
|
\[
{}y^{2}+{y^{\prime }}^{2} = 1
\] |
[_quadrature] |
✓ |
0.548 |
|
|
\[
{}{y^{\prime }}^{2} \left (2-3 y\right )^{2} = 4-4 y
\] |
[_quadrature] |
✓ |
0.455 |
|
|
\[
{}4 x {y^{\prime }}^{2} = \left (3 x -1\right )^{2}
\] |
[_quadrature] |
✓ |
0.273 |
|
|
\[
{}x {y^{\prime }}^{2}-\left (x -a \right )^{2} = 0
\] |
[_quadrature] |
✓ |
0.282 |
|
|
\[
{}y {y^{\prime }}^{2}-2 y^{\prime } x +y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.832 |
|
|
\[
{}3 x {y^{\prime }}^{2}-6 y y^{\prime }+x +2 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.298 |
|
|
\[
{}{y^{\prime }}^{2}+2 x^{3} y^{\prime }-4 x^{2} y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
2.264 |
|
|
\[
{}y^{2} \left (y-y^{\prime } x \right ) = x^{4} {y^{\prime }}^{2}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
3.374 |
|
|
\[
{}{y^{\prime }}^{2} \left (-a^{2}+x^{2}\right )-2 x y y^{\prime }-x^{2} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
26.601 |
|
|
\[
{}{y^{\prime }}^{4} = 4 y \left (y^{\prime } x -2 y\right )^{2}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
0.618 |
|
|
\[
{}\left (1-y^{2}\right ) {y^{\prime }}^{2} = 1
\] |
[_quadrature] |
✓ |
0.579 |
|