|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }+9 y = \cos \left (2 x \right )+\sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.615 |
|
|
\[
{}y^{\prime \prime }+a^{2} y = \cos \left (a x \right )+\cos \left (b x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.671 |
|
|
\[
{}y^{\prime \prime }+4 y = {\mathrm e}^{x}+\sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.637 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }-12 y = \cos \left (4 x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.211 |
|
|
\[
{}y^{\prime \prime }-4 y = 2 \sin \left (\frac {x}{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.529 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (3 x \right )-\cos \left (\frac {x}{2}\right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.395 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.088 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y = x
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.092 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }-6 y^{\prime } = x^{2}+1
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.101 |
|
|
\[
{}y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime } = {\mathrm e}^{2 x}+x^{2}+x
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.123 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.102 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = {\mathrm e}^{2 x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
28.595 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+4 y = {\mathrm e}^{x} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
66.583 |
|
|
\[
{}y^{\prime \prime }-y = \cosh \left (x \right ) \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.938 |
|
|
\[
{}y^{\prime \prime \prime }-7 y^{\prime }-6 y = {\mathrm e}^{2 x} \left (x +1\right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.119 |
|
|
\[
{}y^{\prime \prime \prime \prime }+y^{\prime \prime }+y = a \,x^{2}+b \,{\mathrm e}^{-x} \sin \left (2 x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
1.047 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }-12 y = \left (-1+x \right ) {\mathrm e}^{2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.251 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = x \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.546 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = x^{2} \cos \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.923 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = x \sin \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.620 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = x \,{\mathrm e}^{x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.495 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 8 x^{2} {\mathrm e}^{2 x} \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
36.977 |
|
|
\[
{}y^{\prime \prime }+y = {\mathrm e}^{-x}+\cos \left (x \right )+x^{3}+{\mathrm e}^{x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
8.203 |
|
|
\[
{}y^{\prime \prime \prime \prime }+y^{\prime \prime }+y = {\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
1.063 |
|
|
\[
{}y^{\left (6\right )}-2 y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+3 y^{\prime \prime }-2 y^{\prime }+y = \sin \left (\frac {x}{2}\right )^{2}+{\mathrm e}^{x}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
1.507 |
|
|
\[
{}y^{\prime \prime \prime \prime }+y^{\prime \prime }+16 y = 16 x^{2}+256
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.244 |
|
|
\[
{}y^{\prime \prime }+y = 3 \cos \left (x \right )^{2}+2 \sin \left (x \right )^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.111 |
|
|
\[
{}y^{\prime \prime \prime \prime }+10 y^{\prime \prime }+9 y = 96 \sin \left (2 x \right ) \cos \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.905 |
|
|
\[
{}y^{\left (5\right )}-13 y^{\prime \prime \prime }+26 y^{\prime \prime }+82 y^{\prime }+104 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.073 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+10 y+37 \sin \left (3 x \right ) = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
18.756 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = 24 x \cos \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.790 |
|
|
\[
{}{y^{\prime }}^{2}-7 y^{\prime }+12 = 0
\] |
[_quadrature] |
✓ |
0.332 |
|
|
\[
{}{y^{\prime }}^{2}-5 y^{\prime }+6 = 0
\] |
[_quadrature] |
✓ |
0.331 |
|
|
\[
{}{y^{\prime }}^{2}-9 y^{\prime }+18 = 0
\] |
[_quadrature] |
✓ |
0.327 |
|
|
\[
{}{y^{\prime }}^{2}+2 x y^{\prime }-3 x^{2} = 0
\] |
[_quadrature] |
✓ |
0.391 |
|
|
\[
{}{y^{\prime }}^{2}+2 y^{\prime } y \cot \left (x \right ) = y^{2}
\] |
[_separable] |
✓ |
1.155 |
|
|
\[
{}{y^{\prime }}^{2}-2 y^{\prime } \cosh \left (x \right )+1 = 0
\] |
[_quadrature] |
✓ |
0.383 |
|
|
\[
{}y^{\prime } \left (y^{\prime }-y\right ) = \left (x +y\right ) x
\] |
[_quadrature] |
✓ |
0.519 |
|
|
\[
{}y {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }-x = 0
\] |
[_quadrature] |
✓ |
0.473 |
|
|
\[
{}x +y {y^{\prime }}^{2} = y^{\prime } \left (1+x y\right )
\] |
[_quadrature] |
✓ |
0.434 |
|
|
\[
{}x {y^{\prime }}^{2}+\left (y-x \right ) y^{\prime }-y = 0
\] |
[_quadrature] |
✓ |
0.450 |
|
|
\[
{}{y^{\prime }}^{3}-a \,x^{4} = 0
\] |
[_quadrature] |
✓ |
0.414 |
|
|
\[
{}{y^{\prime }}^{2}+x y^{\prime }+y y^{\prime }+x y = 0
\] |
[_quadrature] |
✓ |
0.511 |
|
|
\[
{}{y^{\prime }}^{3}-y^{\prime } \left (y^{2}+x y+x^{2}\right )+x y \left (x +y\right ) = 0
\] |
[_quadrature] |
✓ |
0.952 |
|
|
\[
{}\left (y^{\prime }+y+x \right ) \left (y+x +x y^{\prime }\right ) \left (y^{\prime }+2 x \right ) = 0
\] |
[_quadrature] |
✓ |
1.021 |
|
|
\[
{}x^{2} {y^{\prime }}^{3}+y \left (1+x^{2} y\right ) {y^{\prime }}^{2}+y^{2} y^{\prime } = 0
\] |
[_quadrature] |
✓ |
24.958 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+x y y^{\prime }-6 y^{2} = 0
\] |
[_separable] |
✓ |
1.089 |
|
|
\[
{}{y^{\prime }}^{3}+2 x {y^{\prime }}^{2}-y^{2} {y^{\prime }}^{2}-2 x y^{2} y^{\prime } = 0
\] |
[_quadrature] |
✓ |
2.307 |
|
|
\[
{}{y^{\prime }}^{2} \left (2-3 y\right )^{2} = 4-4 y
\] |
[_quadrature] |
✓ |
0.405 |
|
|
\[
{}y = 3 x +a \ln \left (y^{\prime }\right )
\] |
[_separable] |
✓ |
5.630 |
|
|
\[
{}{y^{\prime }}^{2}-y y^{\prime }+x = 0
\] |
[_dAlembert] |
✓ |
1.448 |
|
|
\[
{}y = x +a \arctan \left (y^{\prime }\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
9.494 |
|
|
\[
{}3 {y^{\prime }}^{5}-y y^{\prime }+1 = 0
\] |
[_quadrature] |
✓ |
0.987 |
|
|
\[
{}y = x {y^{\prime }}^{2}+y^{\prime }
\] |
[_rational, _dAlembert] |
✓ |
0.995 |
|
|
\[
{}x {y^{\prime }}^{2}+a x = 2 y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.310 |
|
|
\[
{}{y^{\prime }}^{3}+y^{\prime } = {\mathrm e}^{y}
\] |
[_quadrature] |
✓ |
0.647 |
|
|
\[
{}y = \sin \left (y^{\prime }\right )-y^{\prime } \cos \left (y^{\prime }\right )
\] |
[_quadrature] |
✓ |
10.900 |
|
|
\[
{}y = \sin \left (x \right ) y^{\prime }+\cos \left (x \right )
\] |
[_linear] |
✓ |
2.075 |
|
|
\[
{}y = y^{\prime } \tan \left (y^{\prime }\right )+\ln \left (\cos \left (y^{\prime }\right )\right )
\] |
[_dAlembert] |
✓ |
2.230 |
|
|
\[
{}x = y y^{\prime }-{y^{\prime }}^{2}
\] |
[_dAlembert] |
✓ |
1.451 |
|
|
\[
{}\left (2 x -b \right ) y^{\prime } = y-a y {y^{\prime }}^{2}
\] |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
0.866 |
|
|
\[
{}x = y+a \ln \left (y^{\prime }\right )
\] |
[_separable] |
✓ |
4.085 |
|
|
\[
{}y {y^{\prime }}^{2}+2 x y^{\prime } = y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.688 |
|
|
\[
{}x \left (1+{y^{\prime }}^{2}\right ) = 1
\] |
[_quadrature] |
✓ |
0.354 |
|
|
\[
{}x^{2} = a^{2} \left (1+{y^{\prime }}^{2}\right )
\] |
[_quadrature] |
✓ |
0.417 |
|
|
\[
{}y = x y^{\prime }+\frac {a}{y^{\prime }}
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
0.469 |
|
|
\[
{}y = x y^{\prime }+y^{\prime }-{y^{\prime }}^{3}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.431 |
|
|
\[
{}y = x y^{\prime }+a y^{\prime } \left (1-y^{\prime }\right )
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.488 |
|
|
\[
{}y = x y^{\prime }+\sqrt {1+{y^{\prime }}^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
1.849 |
|
|
\[
{}y = x y^{\prime }+\sqrt {b^{2}-a^{2} {y^{\prime }}^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
3.287 |
|
|
\[
{}\left (y-x y^{\prime }\right ) \left (y^{\prime }-1\right ) = y^{\prime }
\] |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
0.600 |
|
|
\[
{}x {y^{\prime }}^{2}-y y^{\prime }+a = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
0.441 |
|
|
\[
{}y = y^{\prime } \left (x -b \right )+\frac {a}{y^{\prime }}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.543 |
|
|
\[
{}y = x y^{\prime }+{y^{\prime }}^{3}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.409 |
|
|
\[
{}4 y {y^{\prime }}^{2}+2 x y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.497 |
|
|
\[
{}y {y^{\prime }}^{2}+2 x y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.682 |
|
|
\[
{}x +\frac {y^{\prime }}{\sqrt {1+{y^{\prime }}^{2}}} = a
\] |
[_quadrature] |
✓ |
0.527 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+2 y^{2} = x^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.539 |
|
|
\[
{}y = x y^{\prime }+x \sqrt {1+{y^{\prime }}^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
8.857 |
|
|
\[
{}x +y^{\prime } y \left (2 {y^{\prime }}^{2}+3\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
6.994 |
|
|
\[
{}y = \frac {2 a {y^{\prime }}^{2}}{\left (1+{y^{\prime }}^{2}\right )^{2}}
\] |
[_quadrature] |
✓ |
1.056 |
|
|
\[
{}\left (-y+x y^{\prime }\right )^{2} = a \left (1+{y^{\prime }}^{2}\right ) \left (x^{2}+y^{2}\right )^{{3}/{2}}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
55.843 |
|
|
\[
{}4 x {y^{\prime }}^{2}+4 y y^{\prime } = y^{4}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
2.389 |
|
|
\[
{}2 {y^{\prime }}^{3}-\left (2 x +4 \sin \left (x \right )-\cos \left (x \right )\right ) {y^{\prime }}^{2}-\left (x \cos \left (x \right )-4 x \sin \left (x \right )+\sin \left (2 x \right )\right ) y^{\prime }+x \sin \left (2 x \right ) = 0
\] |
[_quadrature] |
✓ |
1.029 |
|
|
\[
{}\left (-y+x y^{\prime }\right )^{2} = {y^{\prime }}^{2}-\frac {2 y y^{\prime }}{x}+1
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
12.612 |
|
|
\[
{}y-x y^{\prime } = x +y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
37.942 |
|
|
\[
{}a^{2} y {y^{\prime }}^{2}-4 x y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.779 |
|
|
\[
{}x^{2} \left (y-x y^{\prime }\right ) = y {y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
2.825 |
|
|
\[
{}\left ({y^{\prime }}^{2}-\frac {1}{a^{2}-x^{2}}\right ) \left (y^{\prime }-\sqrt {\frac {y}{x}}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
2.093 |
|
|
\[
{}{y^{\prime }}^{2} \left (-a^{2}+x^{2}\right )-2 x y y^{\prime }+y^{2}+a^{4} = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
1.250 |
|
|
\[
{}x +y y^{\prime } = a {y^{\prime }}^{2}
\] |
[_dAlembert] |
✓ |
46.297 |
|
|
\[
{}x y {y^{\prime }}^{2}+y^{\prime } \left (3 x^{2}-2 y^{2}\right )-6 x y = 0
\] |
[_separable] |
✓ |
1.405 |
|
|
\[
{}2 y = x y^{\prime }+\frac {a}{y^{\prime }}
\] |
[[_homogeneous, ‘class G‘], _rational, _dAlembert] |
✓ |
0.660 |
|
|
\[
{}y = a y^{\prime }+\sqrt {1+{y^{\prime }}^{2}}
\] |
[_quadrature] |
✓ |
2.000 |
|
|
\[
{}\left (a {y^{\prime }}^{2}-b \right ) x y+\left (b \,x^{2}-a y^{2}+c \right ) y^{\prime } = 0
\] |
[_rational] |
✓ |
166.756 |
|
|
\[
{}y = a y^{\prime }+b {y^{\prime }}^{2}
\] |
[_quadrature] |
✓ |
0.515 |
|
|
\[
{}{y^{\prime }}^{3}-\left (y+2 x -{\mathrm e}^{x -y}\right ) {y^{\prime }}^{2}+\left (2 x y-2 x \,{\mathrm e}^{x -y}-y \,{\mathrm e}^{x -y}\right ) y^{\prime }+2 x y \,{\mathrm e}^{x -y} = 0
\] |
[_quadrature] |
✓ |
1.616 |
|
|
\[
{}\left (1+6 y^{2}-3 x^{2} y\right ) y^{\prime } = 3 x y^{2}-x^{2}
\] |
[_exact, _rational] |
✓ |
1.585 |
|
|
\[
{}\left (x^{2}+1\right ) {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2} = 1
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
0.658 |
|
|
\[
{}\left (x^{3} y^{3}+y^{2} x^{2}+x y+1\right ) y+\left (x^{3} y^{3}-y^{2} x^{2}-x y+1\right ) x y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.162 |
|