|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x y {y^{\prime }}^{2}-\left (x^{2}-y^{2}\right ) y^{\prime }-y x = 0
\] |
[_separable] |
✓ |
15.579 |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (a +x^{2}-y^{2}\right ) y^{\prime }-y x = 0
\] |
[_rational] |
✓ |
103.249 |
|
|
\[
{}x y {y^{\prime }}^{2}-\left (a -b \,x^{2}+y^{2}\right ) y^{\prime }-b x y = 0
\] |
[_rational] |
✓ |
162.640 |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (3 x^{2}-2 y^{2}\right ) y^{\prime }-6 y x = 0
\] |
[_separable] |
✓ |
12.507 |
|
|
\[
{}x \left (x -2 y\right ) {y^{\prime }}^{2}-2 x y y^{\prime }-2 y x +y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
9.530 |
|
|
\[
{}x \left (x -2 y\right ) {y^{\prime }}^{2}+6 x y y^{\prime }-2 y x +y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
87.795 |
|
|
\[
{}y^{2} {y^{\prime }}^{2} = a^{2}
\] |
[_quadrature] |
✓ |
0.664 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}-a^{2}+y^{2} = 0
\] |
[_quadrature] |
✓ |
3.137 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}-3 y^{\prime } x +y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
10.935 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}-6 x^{3} y^{\prime }+4 x^{2} y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
7.380 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}-4 a y y^{\prime }+4 a^{2}-4 a x +y^{2} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
159.171 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}-\left (x +1\right ) y y^{\prime }+x = 0
\] |
[_quadrature] |
✓ |
14.786 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}+2 x y y^{\prime }+x^{2} = 0
\] |
[_separable] |
✓ |
4.347 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}+2 x y y^{\prime }+a -y^{2} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
16.852 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }-x^{2}+2 y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
9.616 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+a -x^{2}+2 y^{2} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
6.967 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}+2 a x y y^{\prime }+\left (a -1\right ) b +a \,x^{2}+\left (1-a \right ) y^{2} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
9.449 |
|
|
\[
{}\left (1-y^{2}\right ) {y^{\prime }}^{2} = 1
\] |
[_quadrature] |
✓ |
0.681 |
|
|
\[
{}\left (a^{2}-y^{2}\right ) {y^{\prime }}^{2} = y^{2}
\] |
[_quadrature] |
✓ |
3.383 |
|
|
\[
{}\left (a^{2}-2 a x y+y^{2}\right ) {y^{\prime }}^{2}+2 a y y^{\prime }+y^{2} = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
273.329 |
|
|
\[
{}\left (\left (1-a \right ) x^{2}+y^{2}\right ) {y^{\prime }}^{2}+2 a x y y^{\prime }+x^{2}+\left (1-a \right ) y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
84.996 |
|
|
\[
{}\left (\left (-4 a^{2}+1\right ) x^{2}+y^{2}\right ) {y^{\prime }}^{2}-8 a^{2} x y y^{\prime }+x^{2}+\left (-4 a^{2}+1\right ) y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
94.587 |
|
|
\[
{}\left (\left (-a^{2}+1\right ) x^{2}+y^{2}\right ) {y^{\prime }}^{2}+2 a^{2} x y y^{\prime }+x^{2}+\left (-a^{2}+1\right ) y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
60.322 |
|
|
\[
{}\left (x +y\right )^{2} {y^{\prime }}^{2} = y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
30.125 |
|
|
\[
{}\left (x +y\right )^{2} {y^{\prime }}^{2}-\left (x^{2}-y x -2 y^{2}\right ) y^{\prime }-\left (x -y\right ) y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
41.638 |
|
|
\[
{}\left (a^{2}-\left (x -y\right )^{2}\right ) {y^{\prime }}^{2}+2 a^{2} y^{\prime }+a^{2}-\left (x -y\right )^{2} = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
38.846 |
|
|
\[
{}2 y^{2} {y^{\prime }}^{2}+2 x y y^{\prime }-1+x^{2}+y^{2} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
156.059 |
|
|
\[
{}3 y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }-x^{2}+4 y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
8.685 |
|
|
\[
{}4 y^{2} {y^{\prime }}^{2}+2 \left (1+3 x \right ) x y y^{\prime }+3 x^{3} = 0
\] |
[_separable] |
✓ |
17.125 |
|
|
\[
{}\left (x^{2}-4 y^{2}\right ) {y^{\prime }}^{2}+6 x y y^{\prime }-4 x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
75.474 |
|
|
\[
{}9 y^{2} {y^{\prime }}^{2}-3 y^{\prime } x +y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
13.417 |
|
|
\[
{}\left (2-3 y\right )^{2} {y^{\prime }}^{2} = 4-4 y
\] |
[_quadrature] |
✓ |
0.402 |
|
|
\[
{}\left (-a^{2}+1\right ) y^{2} {y^{\prime }}^{2}-3 a^{2} x y y^{\prime }-a^{2} x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
196.574 |
|
|
\[
{}\left (a -b \right ) y^{2} {y^{\prime }}^{2}-2 b x y y^{\prime }-a b -b \,x^{2}+a y^{2} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
11.801 |
|
|
\[
{}a^{2} \left (b^{2}-\left (c x -a y\right )^{2}\right ) {y^{\prime }}^{2}+2 a \,b^{2} c y^{\prime }+c^{2} \left (b^{2}-\left (c x -a y\right )^{2}\right ) = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
54.921 |
|
|
\[
{}x y^{2} {y^{\prime }}^{2}-y^{3} y^{\prime }+a^{2} x = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
32.237 |
|
|
\[
{}x y^{2} {y^{\prime }}^{2}+\left (a -x^{3}-y^{3}\right ) y^{\prime }+x^{2} y = 0
\] |
[_rational] |
✓ |
13.706 |
|
|
\[
{}2 x y^{2} {y^{\prime }}^{2}-y^{3} y^{\prime }-a = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
42.483 |
|
|
\[
{}4 x^{2} y^{2} {y^{\prime }}^{2} = \left (x^{2}+y^{2}\right )^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
57.948 |
|
|
\[
{}4 y^{3} {y^{\prime }}^{2}-4 y^{\prime } x +y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
8.585 |
|
|
\[
{}3 x y^{4} {y^{\prime }}^{2}-y^{5} y^{\prime }+1 = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
120.744 |
|
|
\[
{}9 x y^{4} {y^{\prime }}^{2}-3 y^{5} y^{\prime }-a = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
21.760 |
|
|
\[
{}9 \left (-x^{2}+1\right ) y^{4} {y^{\prime }}^{2}+6 x y^{5} y^{\prime }+4 x^{2} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
8.878 |
|
|
\[
{}{y^{\prime }}^{3} = b x +a
\] |
[_quadrature] |
✓ |
0.362 |
|
|
\[
{}{y^{\prime }}^{3} = a \,x^{n}
\] |
[_quadrature] |
✓ |
0.629 |
|
|
\[
{}{y^{\prime }}^{3}+x -y = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
22.842 |
|
|
\[
{}{y^{\prime }}^{3} = \left (a +b y+c y^{2}\right ) f \left (x \right )
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
5.618 |
|
|
\[
{}{y^{\prime }}^{3} = \left (y-a \right )^{2} \left (y-b \right )^{2}
\] |
[_quadrature] |
✓ |
1.258 |
|
|
\[
{}{y^{\prime }}^{3}+f \left (x \right ) \left (y-a \right )^{2} \left (y-b \right )^{2} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.799 |
|
|
\[
{}{y^{\prime }}^{3}+f \left (x \right ) \left (y-a \right )^{2} \left (y-b \right )^{2} \left (y-c \right )^{2} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
6.715 |
|
|
\[
{}{y^{\prime }}^{3}+y^{\prime }+a -b x = 0
\] |
[_quadrature] |
✓ |
2.984 |
|
|
\[
{}{y^{\prime }}^{3}+y^{\prime }-y = 0
\] |
[_quadrature] |
✓ |
4.243 |
|
|
\[
{}{y^{\prime }}^{3}+y^{\prime } = {\mathrm e}^{y}
\] |
[_quadrature] |
✓ |
1.102 |
|
|
\[
{}{y^{\prime }}^{3}-7 y^{\prime }+6 = 0
\] |
[_quadrature] |
✓ |
1.073 |
|
|
\[
{}{y^{\prime }}^{3}-y^{\prime } x +a y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.736 |
|
|
\[
{}{y^{\prime }}^{3}+2 y^{\prime } x -y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.556 |
|
|
\[
{}{y^{\prime }}^{3}-2 y^{\prime } x -y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.482 |
|
|
\[
{}{y^{\prime }}^{3}-a x y^{\prime }+x^{3} = 0
\] |
[_quadrature] |
✓ |
0.850 |
|
|
\[
{}{y^{\prime }}^{3}+a x y^{\prime }-a y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.553 |
|
|
\[
{}{y^{\prime }}^{3}-\left (b x +a \right ) y^{\prime }+b y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.692 |
|
|
\[
{}{y^{\prime }}^{3}-2 y y^{\prime }+y^{2} = 0
\] |
[_quadrature] |
✓ |
4.278 |
|
|
\[
{}{y^{\prime }}^{3}-a x y y^{\prime }+2 a y^{2} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
17.645 |
|
|
\[
{}{y^{\prime }}^{3}-x y^{4} y^{\prime }-y^{5} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
25.027 |
|
|
\[
{}{y^{\prime }}^{3}+{\mathrm e}^{3 x -2 y} \left (y^{\prime }-1\right ) = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
5.036 |
|
|
\[
{}{y^{\prime }}^{3}+{\mathrm e}^{-2 y} \left ({\mathrm e}^{2 x}+{\mathrm e}^{3 x}\right ) y^{\prime }-{\mathrm e}^{3 x -2 y} = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
237.924 |
|
|
\[
{}{y^{\prime }}^{3}+{y^{\prime }}^{2}-y = 0
\] |
[_quadrature] |
✓ |
121.846 |
|
|
\[
{}{y^{\prime }}^{3}-{y^{\prime }}^{2}+y^{2} = 0
\] |
[_quadrature] |
✓ |
41.054 |
|
|
\[
{}{y^{\prime }}^{3}-{y^{\prime }}^{2}+y^{\prime } x -y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.711 |
|
|
\[
{}{y^{\prime }}^{3}-a {y^{\prime }}^{2}+b y+a b x = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
4.928 |
|
|
\[
{}{y^{\prime }}^{3}+\operatorname {a0} {y^{\prime }}^{2}+\operatorname {a1} y^{\prime }+\operatorname {a2} +\operatorname {a3} y = 0
\] |
[_quadrature] |
✓ |
158.174 |
|
|
\[
{}{y^{\prime }}^{3}+\left (1-3 x \right ) {y^{\prime }}^{2}-x \left (1-3 x \right ) y^{\prime }-1-x^{3} = 0
\] |
[_quadrature] |
✓ |
1.053 |
|
|
\[
{}{y^{\prime }}^{3}-y {y^{\prime }}^{2}+y^{2} = 0
\] |
[_quadrature] |
✓ |
9.380 |
|
|
\[
{}{y^{\prime }}^{3}+\left (\cos \left (x \right ) \cot \left (x \right )-y\right ) {y^{\prime }}^{2}-\left (1+y \cos \left (x \right ) \cot \left (x \right )\right ) y^{\prime }+y = 0
\] |
[_quadrature] |
✓ |
1.576 |
|
|
\[
{}{y^{\prime }}^{3}+\left (2 x -y^{2}\right ) {y^{\prime }}^{2}-2 x y^{2} y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.912 |
|
|
\[
{}{y^{\prime }}^{3}-\left (2 x +y^{2}\right ) {y^{\prime }}^{2}+\left (x^{2}-y^{2}+2 x y^{2}\right ) y^{\prime }-\left (x^{2}-y^{2}\right ) y^{2} = 0
\] |
[_quadrature] |
✓ |
6.183 |
|
|
\[
{}{y^{\prime }}^{3}-\left (x^{2}+y x +y^{2}\right ) {y^{\prime }}^{2}+x y \left (x^{2}+y x +y^{2}\right ) y^{\prime }-x^{3} y^{3} = 0
\] |
[_quadrature] |
✓ |
1.948 |
|
|
\[
{}{y^{\prime }}^{3}-\left (x^{2}+x y^{2}+y^{4}\right ) {y^{\prime }}^{2}+x y^{2} \left (x^{2}+x y^{2}+y^{4}\right ) y^{\prime }-x^{3} y^{6} = 0
\] |
[_quadrature] |
✓ |
12.415 |
|
|
\[
{}2 {y^{\prime }}^{3}+y^{\prime } x -2 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.557 |
|
|
\[
{}2 {y^{\prime }}^{3}+{y^{\prime }}^{2}-y = 0
\] |
[_quadrature] |
✓ |
84.172 |
|
|
\[
{}3 {y^{\prime }}^{3}-x^{4} y^{\prime }+2 x^{3} y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
250.355 |
|
|
\[
{}4 {y^{\prime }}^{3}+4 y^{\prime } = x
\] |
[_quadrature] |
✓ |
0.725 |
|
|
\[
{}8 {y^{\prime }}^{3}+12 {y^{\prime }}^{2} = 27 x +27 y
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.170 |
|
|
\[
{}x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+a = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
1.073 |
|
|
\[
{}x {y^{\prime }}^{3}-\left (x +x^{2}+y\right ) {y^{\prime }}^{2}+\left (x^{2}+y+y x \right ) y^{\prime }-y x = 0
\] |
[_quadrature] |
✓ |
2.475 |
|
|
\[
{}x {y^{\prime }}^{3}-2 y {y^{\prime }}^{2}+4 x^{2} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
346.086 |
|
|
\[
{}2 x {y^{\prime }}^{3}-3 y {y^{\prime }}^{2}-x = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.771 |
|
|
\[
{}4 x {y^{\prime }}^{3}-6 y {y^{\prime }}^{2}-x +3 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
5.126 |
|
|
\[
{}8 x {y^{\prime }}^{3}-12 y {y^{\prime }}^{2}+9 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
1.503 |
|
|
\[
{}x^{2} {y^{\prime }}^{3}-2 x y {y^{\prime }}^{2}+y^{2} y^{\prime }+1 = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
8.325 |
|
|
\[
{}\left (a^{2}-x^{2}\right ) {y^{\prime }}^{3}+b x \left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}-y^{\prime }-b x = 0
\] |
[_quadrature] |
✓ |
0.477 |
|
|
\[
{}x {y^{\prime }}^{3}-3 x^{2} y {y^{\prime }}^{2}+x \left (x^{5}+3 y^{2}\right ) y^{\prime }-2 x^{5} y-y^{3} = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
477.077 |
|
|
\[
{}2 x^{3} {y^{\prime }}^{3}+6 x^{2} y {y^{\prime }}^{2}-\left (1-6 y x \right ) y y^{\prime }+2 y^{3} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
32.034 |
|
|
\[
{}x^{4} {y^{\prime }}^{3}-x^{3} y {y^{\prime }}^{2}-x^{2} y^{2} y^{\prime }+x y^{3} = 1
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
203.322 |
|
|
\[
{}x^{6} {y^{\prime }}^{3}-y^{\prime } x -y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
25.704 |
|
|
\[
{}y {y^{\prime }}^{3}-3 y^{\prime } x +3 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
18.681 |
|
|
\[
{}2 y {y^{\prime }}^{3}-3 y^{\prime } x +2 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
3.755 |
|
|
\[
{}\left (x +2 y\right ) {y^{\prime }}^{3}+3 \left (x +y\right ) {y^{\prime }}^{2}+\left (y+2 x \right ) y^{\prime } = 0
\] |
[_quadrature] |
✓ |
28.889 |
|
|
\[
{}y^{2} {y^{\prime }}^{3}-y^{\prime } x +y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
248.036 |
|
|
\[
{}y^{2} {y^{\prime }}^{3}+2 y^{\prime } x -y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
239.076 |
|
|
\[
{}4 y^{2} {y^{\prime }}^{3}-2 y^{\prime } x +y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
236.650 |
|