|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x^{2}+y^{2}+1-2 x y y^{\prime } = 0
\] |
[_rational, _Bernoulli] |
✓ |
2.421 |
|
|
\[
{}x +y y^{\prime } = m \left (-y+x y^{\prime }\right )
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.316 |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = y^{n} \sin \left (2 x \right )
\] |
[_Bernoulli] |
✓ |
6.213 |
|
|
\[
{}\left (x +1\right ) y^{\prime }+1 = 2 \,{\mathrm e}^{y}
\] |
[_separable] |
✓ |
2.180 |
|
|
\[
{}y^{\prime } = x^{3} y^{3}-x y
\] |
[_Bernoulli] |
✓ |
1.515 |
|
|
\[
{}y+\left (a \,x^{2} y^{n}-2 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.687 |
|
|
\[
{}\left (1+6 y^{2}-3 x^{2} y\right ) y^{\prime } = 3 x y^{2}-x^{2}
\] |
[_exact, _rational] |
✓ |
1.648 |
|
|
\[
{}y \left (x^{2}+y^{2}+a^{2}\right ) y^{\prime }+x \left (x^{2}+y^{2}-a^{2}\right ) = 0
\] |
[_exact, _rational] |
✓ |
2.132 |
|
|
\[
{}\left (x^{2} y^{3}+x y\right ) y^{\prime } = 1
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.711 |
|
|
\[
{}y y^{\prime } = a x
\] |
[_separable] |
✓ |
2.990 |
|
|
\[
{}\sqrt {a^{2}+x^{2}}\, y^{\prime }+y = \sqrt {a^{2}+x^{2}}-x
\] |
[_linear] |
✓ |
1.636 |
|
|
\[
{}\left (x +y\right ) y^{\prime }+x -y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
39.365 |
|
|
\[
{}y y^{\prime }+b y^{2} = a \cos \left (x \right )
\] |
[_Bernoulli] |
✓ |
3.026 |
|
|
\[
{}2 x y+\left (y^{2}-x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
5.831 |
|
|
\[
{}y-x y^{\prime } = b \left (1+x^{2} y^{\prime }\right )
\] |
[_separable] |
✓ |
1.045 |
|
|
\[
{}3 y+2 x +4-\left (4 x +6 y+5\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.166 |
|
|
\[
{}\left (x^{3} y^{3}+y^{2} x^{2}+x y+1\right ) y+\left (x^{3} y^{3}-y^{2} x^{2}-x y+1\right ) x y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.207 |
|
|
\[
{}2 y^{2} x^{2}+y-\left (x^{3} y-3 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.617 |
|
|
\[
{}y^{2}+x^{2} y^{\prime } = x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
39.044 |
|
|
\[
{}y^{\prime }+\frac {n y}{x} = a \,x^{-n}
\] |
[_linear] |
✓ |
1.041 |
|
|
\[
{}\left (x -y\right )^{2} y^{\prime } = a^{2}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
3.002 |
|
|
\[
{}{y^{\prime }}^{3}+2 x {y^{\prime }}^{2}-y^{2} {y^{\prime }}^{2}-2 x y^{2} y^{\prime } = 0
\] |
[_quadrature] |
✓ |
2.444 |
|
|
\[
{}{y^{\prime }}^{2}-a \,x^{3} = 0
\] |
[_quadrature] |
✓ |
0.341 |
|
|
\[
{}{y^{\prime }}^{3} \left (x +2 y\right )+3 {y^{\prime }}^{2} \left (x +y\right )+\left (y+2 x \right ) y^{\prime } = 0
\] |
[_quadrature] |
✓ |
2.014 |
|
|
\[
{}{y^{\prime }}^{3} = a \,x^{4}
\] |
[_quadrature] |
✓ |
0.424 |
|
|
\[
{}4 y^{2} {y^{\prime }}^{2}+2 y^{\prime } x y \left (3 x +1\right )+3 x^{3} = 0
\] |
[_separable] |
✓ |
0.877 |
|
|
\[
{}{y^{\prime }}^{2}-7 y^{\prime }+12 = 0
\] |
[_quadrature] |
✓ |
0.338 |
|
|
\[
{}x -y y^{\prime } = a {y^{\prime }}^{2}
\] |
[_dAlembert] |
✓ |
73.482 |
|
|
\[
{}y = -a y^{\prime }+\frac {c +a \arcsin \left (y^{\prime }\right )}{\sqrt {1-{y^{\prime }}^{2}}}
\] |
[_quadrature] |
✓ |
86.848 |
|
|
\[
{}4 y = x^{2}+{y^{\prime }}^{2}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
1.556 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }+a x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.351 |
|
|
\[
{}y = 2 y^{\prime }+3 {y^{\prime }}^{2}
\] |
[_quadrature] |
✓ |
0.437 |
|
|
\[
{}x \left (1+{y^{\prime }}^{2}\right ) = 1
\] |
[_quadrature] |
✓ |
0.366 |
|
|
\[
{}x^{2} = a^{2} \left (1+{y^{\prime }}^{2}\right )
\] |
[_quadrature] |
✓ |
0.430 |
|
|
\[
{}y^{2} = a^{2} \left (1+{y^{\prime }}^{2}\right )
\] |
[_quadrature] |
✓ |
0.847 |
|
|
\[
{}y^{2}+x y y^{\prime }-x^{2} {y^{\prime }}^{2} = 0
\] |
[_separable] |
✓ |
0.731 |
|
|
\[
{}y = y {y^{\prime }}^{2}+2 x y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.753 |
|
|
\[
{}y = \left (1+y^{\prime }\right ) x +{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.576 |
|
|
\[
{}x^{2} \left (y-x y^{\prime }\right ) = y {y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
2.954 |
|
|
\[
{}y = x y^{\prime }+\arcsin \left (y^{\prime }\right )
\] |
[_Clairaut] |
✓ |
1.767 |
|
|
\[
{}{\mathrm e}^{4 x} \left (y^{\prime }-1\right )+{\mathrm e}^{2 y} {y^{\prime }}^{2} = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.254 |
|
|
\[
{}x y \left (y-x y^{\prime }\right ) = x +y y^{\prime }
\] |
[_separable] |
✓ |
4.258 |
|
|
\[
{}y^{\prime }+2 x y = x^{2}+y^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
1.750 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+2 y^{2}-x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.573 |
|
|
\[
{}y = y^{\prime } \left (x -b \right )+\frac {a}{y^{\prime }}
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
0.567 |
|
|
\[
{}x y^{2} \left ({y^{\prime }}^{2}+2\right ) = 2 y^{\prime } y^{3}+x^{3}
\] |
[_separable] |
✓ |
1.679 |
|
|
\[
{}y = -x y^{\prime }+x^{4} {y^{\prime }}^{2}
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.815 |
|
|
\[
{}{y^{\prime }}^{2}-9 y^{\prime }+18 = 0
\] |
[_quadrature] |
✓ |
0.336 |
|
|
\[
{}a y {y^{\prime }}^{2}+\left (2 x -b \right ) y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
0.863 |
|
|
\[
{}\left (-y+x y^{\prime }\right )^{2} = a \left (1+{y^{\prime }}^{2}\right ) \left (x^{2}+y^{2}\right )^{{3}/{2}}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
57.105 |
|
|
\[
{}\left (-y+x y^{\prime }\right )^{2} = {y^{\prime }}^{2}-\frac {2 y y^{\prime }}{x}+1
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
13.107 |
|
|
\[
{}3 y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+4 y^{2}-x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.479 |
|
|
\[
{}\left (x^{2}+y^{2}\right ) \left (1+y^{\prime }\right )^{2}-2 \left (x +y\right ) \left (1+y^{\prime }\right ) \left (x +y y^{\prime }\right )+\left (x +y y^{\prime }\right )^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
148.690 |
|
|
\[
{}\left (y y^{\prime }+n x \right )^{2} = \left (y^{2}+n \,x^{2}\right ) \left (1+{y^{\prime }}^{2}\right )
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
3.688 |
|
|
\[
{}y^{2} \left (1-{y^{\prime }}^{2}\right ) = b
\] |
[_quadrature] |
✓ |
0.444 |
|
|
\[
{}\left (-y+x y^{\prime }\right ) \left (x +y y^{\prime }\right ) = h^{2} y^{\prime }
\] |
[_rational] |
✓ |
125.257 |
|
|
\[
{}{y^{\prime }}^{2}+2 y^{\prime } y \cot \left (x \right ) = y^{2}
\] |
[_separable] |
✓ |
1.158 |
|
|
\[
{}\left ({y^{\prime }}^{2}-\frac {1}{a^{2}-x^{2}}\right ) \left (y^{\prime }-\sqrt {\frac {y}{x}}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
2.180 |
|
|
\[
{}x +\frac {y^{\prime }}{\sqrt {1+{y^{\prime }}^{2}}} = a
\] |
[_quadrature] |
✓ |
0.605 |
|
|
\[
{}x y {y^{\prime }}^{2}+y^{\prime } \left (3 x^{2}-2 y^{2}\right )-6 x y = 0
\] |
[_separable] |
✓ |
1.412 |
|
|
\[
{}{y^{\prime }}^{3}-4 x y y^{\prime }+8 y^{2} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
10.272 |
|
|
\[
{}{y^{\prime }}^{3}-\left (y^{2}+x y+x^{2}\right ) {y^{\prime }}^{2}+\left (x^{3} y+y^{2} x^{2}+x y^{3}\right ) y^{\prime }-x^{3} y^{3} = 0
\] |
[_quadrature] |
✓ |
1.126 |
|
|
\[
{}{y^{\prime }}^{3}+m {y^{\prime }}^{2} = a \left (y+m x \right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
0.860 |
|
|
\[
{}{\mathrm e}^{3 x} \left (y^{\prime }-1\right )+{y^{\prime }}^{3} {\mathrm e}^{2 y} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], _dAlembert] |
✓ |
1.711 |
|
|
\[
{}\left (1-y^{2}+\frac {y^{4}}{x^{2}}\right ) {y^{\prime }}^{2}-\frac {2 y y^{\prime }}{x}+\frac {y^{2}}{x^{2}} = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
24.480 |
|
|
\[
{}y-\frac {1}{\sqrt {1+{y^{\prime }}^{2}}} = b
\] |
[_quadrature] |
✓ |
1.680 |
|
|
\[
{}y = x y^{\prime }+\frac {m}{y^{\prime }}
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
0.477 |
|
|
\[
{}y = 2 x y^{\prime }+y^{2} {y^{\prime }}^{3}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
109.109 |
|
|
\[
{}y = x y^{\prime }+a \sqrt {1+{y^{\prime }}^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
1.727 |
|
|
\[
{}{y^{\prime }}^{2}+x y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.419 |
|
|
\[
{}y^{\prime } \sqrt {x} = \sqrt {y}
\] |
[_separable] |
✓ |
12.358 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-3 x y y^{\prime }+2 y^{2}+x^{3} = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
70.800 |
|
|
\[
{}\left (1+y^{\prime }\right )^{3} = \frac {7 \left (x +y\right ) \left (1-y^{\prime }\right )^{3}}{4 a}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
34.799 |
|
|
\[
{}y^{2} \left (1+{y^{\prime }}^{2}\right ) = r^{2}
\] |
[_quadrature] |
✓ |
0.599 |
|
|
\[
{}x {y^{\prime }}^{2}-\left (x -a \right )^{2} = 0
\] |
[_quadrature] |
✓ |
0.389 |
|
|
\[
{}{y^{\prime }}^{2}+2 x y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.457 |
|
|
\[
{}a {y^{\prime }}^{3} = 27 y
\] |
[_quadrature] |
✓ |
0.462 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }+a x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.422 |
|
|
\[
{}x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+a^{3} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
3.281 |
|
|
\[
{}y^{2}-2 x y y^{\prime }+\left (x^{2}-1\right ) {y^{\prime }}^{2} = m^{2}
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
0.690 |
|
|
\[
{}y = x y^{\prime }+\sqrt {b^{2}+a^{2} y^{\prime }}
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
2.588 |
|
|
\[
{}y = x y^{\prime }-{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.407 |
|
|
\[
{}4 {y^{\prime }}^{2} = 9 x
\] |
[_quadrature] |
✓ |
0.333 |
|
|
\[
{}4 x \left (-1+x \right ) \left (-2+x \right ) {y^{\prime }}^{2}-\left (3 x^{2}-6 x +2\right )^{2} = 0
\] |
[_quadrature] |
✓ |
0.369 |
|
|
\[
{}\left (8 {y^{\prime }}^{3}-27\right ) x = 12 y {y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.740 |
|
|
\[
{}{y^{\prime }}^{2} \left (-a^{2}+x^{2}\right )-2 x y y^{\prime }+y^{2}-b^{2} = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.989 |
|
|
\[
{}\left (-y+x y^{\prime }\right ) \left (x -y y^{\prime }\right ) = 2 y^{\prime }
\] |
[_rational] |
✓ |
162.658 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-54 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.869 |
|
|
\[
{}y^{\prime \prime }-m^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.666 |
|
|
\[
{}2 y^{\prime \prime }+5 y^{\prime }-12 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.875 |
|
|
\[
{}9 y^{\prime \prime }+18 y^{\prime }-16 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.874 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.053 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-9 y^{\prime \prime }-11 y^{\prime }-4 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.061 |
|
|
\[
{}y^{\prime \prime }+8 y^{\prime }+25 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.743 |
|
|
\[
{}y^{\prime \prime \prime \prime }-m^{2} y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.080 |
|
|
\[
{}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+8 y^{\prime \prime }-8 y^{\prime }+4 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.075 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{4 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.987 |
|
|
\[
{}y^{\prime \prime }-y = 2+5 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.130 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 2 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.140 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }-8 y^{\prime }+12 y = X \left (x \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.345 |
|