Number of problems in this table is 115
Column notations: A is ODE degree. B is Program Number of solutions generated. C is CAS Number of solutions generated.
|
# |
ODE |
A |
B |
C |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}y = x y^{\prime }+{y^{\prime }}^{2} \] |
2 |
2 |
2 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.156 |
|
|
\[ {}y = x y^{\prime }+\frac {1}{y^{\prime }} \] |
2 |
3 |
3 |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
✓ |
0.181 |
|
|
\[ {}y = x y^{\prime }-\sqrt {y^{\prime }} \] |
2 |
2 |
2 |
[[_homogeneous, ‘class G‘], _Clairaut] |
✓ |
✓ |
0.559 |
|
|
\[ {}y = x y^{\prime }+\ln \left (y^{\prime }\right ) \] |
0 |
2 |
2 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.453 |
|
|
\[ {}y = x y^{\prime }+\frac {3}{{y^{\prime }}^{2}} \] |
3 |
4 |
4 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.516 |
|
|
\[ {}y = x y^{\prime }-{y^{\prime }}^{\frac {2}{3}} \] |
3 |
2 |
3 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
1.579 |
|
|
\[ {}y = x y^{\prime }+{\mathrm e}^{y^{\prime }} \] |
0 |
2 |
2 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.355 |
|
|
\[ {}\left (y-x y^{\prime }\right )^{2} = 1+{y^{\prime }}^{2} \] |
2 |
4 |
4 |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
0.42 |
|
|
\[ {}{y^{\prime }}^{2} x -y y^{\prime }-2 = 0 \] |
2 |
3 |
3 |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
✓ |
0.205 |
|
|
\[ {}\left (y-x y^{\prime }\right )^{2} = 1+{y^{\prime }}^{2} \] |
2 |
4 |
4 |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
0.375 |
|
|
\[ {}x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+1 = 0 \] |
3 |
4 |
4 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
1.201 |
|
|
\[ {}y = x y^{\prime }+{y^{\prime }}^{3} \] |
3 |
3 |
3 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.59 |
|
|
\[ {}2 {y^{\prime }}^{2} \left (y-x y^{\prime }\right ) = 1 \] |
3 |
4 |
4 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.995 |
|
|
\[ {}{y^{\prime }}^{2}+x y^{\prime }-y = 0 \] |
2 |
2 |
2 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.206 |
|
|
\[ {}{y^{\prime }}^{2}-x y^{\prime }+y = 0 \] |
2 |
2 |
2 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.213 |
|
|
\[ {}{y^{\prime }}^{2}+\left (1-x \right ) y^{\prime }+y = 0 \] |
2 |
2 |
2 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.199 |
|
|
\[ {}{y^{\prime }}^{2}-\left (1+x \right ) y^{\prime }+y = 0 \] |
2 |
2 |
2 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.222 |
|
|
\[ {}{y^{\prime }}^{2}-\left (2-x \right ) y^{\prime }+1-y = 0 \] |
2 |
2 |
2 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.239 |
|
|
\[ {}{y^{\prime }}^{2}+\left (x +a \right ) y^{\prime }-y = 0 \] |
2 |
2 |
2 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.212 |
|
|
\[ {}{y^{\prime }}^{2}-2 x y^{\prime }+2 y = 0 \] |
2 |
2 |
2 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.225 |
|
|
\[ {}{y^{\prime }}^{2}-4 \left (1+x \right ) y^{\prime }+4 y = 0 \] |
2 |
2 |
2 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.201 |
|
|
\[ {}{y^{\prime }}^{2}-a x y^{\prime }+a y = 0 \] |
2 |
2 |
2 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.234 |
|
|
\[ {}{y^{\prime }}^{2}+\left (b x +a \right ) y^{\prime }+c = b y \] |
2 |
2 |
2 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.229 |
|
|
\[ {}2 {y^{\prime }}^{2}-\left (1-x \right ) y^{\prime }-y = 0 \] |
2 |
2 |
2 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.204 |
|
|
\[ {}{y^{\prime }}^{2} x -y y^{\prime }+a = 0 \] |
2 |
3 |
3 |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
✓ |
0.263 |
|
|
\[ {}{y^{\prime }}^{2} x +\left (-y+a \right ) y^{\prime }+b = 0 \] |
2 |
3 |
3 |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
0.294 |
|
|
\[ {}{y^{\prime }}^{2} x +\left (x -y\right ) y^{\prime }+1-y = 0 \] |
2 |
3 |
3 |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
✓ |
0.258 |
|
|
\[ {}{y^{\prime }}^{2} x +\left (a +x -y\right ) y^{\prime }-y = 0 \] |
2 |
3 |
3 |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
✓ |
0.279 |
|
|
\[ {}\left (1+x \right ) {y^{\prime }}^{2}-\left (x +y\right ) y^{\prime }+y = 0 \] |
2 |
3 |
3 |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
✓ |
0.295 |
|
|
\[ {}\left (a -x \right ) {y^{\prime }}^{2}+y y^{\prime }-b = 0 \] |
2 |
3 |
3 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.297 |
|
|
\[ {}\left (1+3 x \right ) {y^{\prime }}^{2}-3 \left (y+2\right ) y^{\prime }+9 = 0 \] |
2 |
3 |
3 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.311 |
|
|
\[ {}x^{2} {y^{\prime }}^{2}-\left (1+2 x y\right ) y^{\prime }+1+y^{2} = 0 \] |
2 |
4 |
3 |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
0.423 |
|
|
\[ {}x^{2} {y^{\prime }}^{2}-\left (a +2 x y\right ) y^{\prime }+y^{2} = 0 \] |
2 |
4 |
3 |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
✓ |
0.525 |
|
|
\[ {}\left (a^{2}+x^{2}\right ) {y^{\prime }}^{2}-2 x y y^{\prime }+b +y^{2} = 0 \] |
2 |
6 |
4 |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
2.242 |
|
|
\[ {}{y^{\prime }}^{3}+a x y^{\prime }-a y = 0 \] |
3 |
3 |
3 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.434 |
|
|
\[ {}{y^{\prime }}^{3}-\left (b x +a \right ) y^{\prime }+b y = 0 \] |
3 |
3 |
3 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.503 |
|
|
\[ {}{y^{\prime }}^{3}-{y^{\prime }}^{2}+x y^{\prime }-y = 0 \] |
3 |
3 |
3 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.56 |
|
|
\[ {}x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+a = 0 \] |
3 |
4 |
4 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.745 |
|
|
\[ {}x^{2} {y^{\prime }}^{3}-2 x y {y^{\prime }}^{2}+y^{2} y^{\prime }+1 = 0 \] |
3 |
8 |
5 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
3.786 |
|
|
\[ {}2 \sqrt {a y^{\prime }}+x y^{\prime }-y = 0 \] |
2 |
2 |
1 |
[[_homogeneous, ‘class G‘], _Clairaut] |
✓ |
✓ |
2.11 |
|
|
\[ {}\sqrt {a^{2}+b^{2} {y^{\prime }}^{2}}+x y^{\prime }-y = 0 \] |
2 |
3 |
1 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
4.38 |
|
|
\[ {}a \sqrt {1+{y^{\prime }}^{2}}+x y^{\prime }-y = 0 \] |
2 |
3 |
1 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
2.182 |
|
|
\[ {}a \left (1+{y^{\prime }}^{3}\right )^{\frac {1}{3}}+x y^{\prime }-y = 0 \] |
3 |
7 |
1 |
[_Clairaut] |
✓ |
✓ |
183.375 |
|
|
\[ {}\cos \left (y^{\prime }\right )+x y^{\prime } = y \] |
0 |
2 |
2 |
[_Clairaut] |
✓ |
✓ |
0.425 |
|
|
\[ {}\left (1+{y^{\prime }}^{2}\right ) \sin \left (-y+x y^{\prime }\right )^{2} = 1 \] |
0 |
6 |
6 |
[_Clairaut] |
✓ |
✓ |
3.925 |
|
|
\[ {}\ln \left (y^{\prime }\right )+x y^{\prime }+a = y \] |
0 |
2 |
2 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.879 |
|
|
\[ {}\ln \left (y^{\prime }\right )+a \left (-y+x y^{\prime }\right ) = 0 \] |
0 |
2 |
2 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.828 |
|
|
\[ {}y^{\prime } \ln \left (y^{\prime }\right )-\left (1+x \right ) y^{\prime }+y = 0 \] |
0 |
2 |
2 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.868 |
|
|
\[ {}y^{\prime } \ln \left (y^{\prime }+\sqrt {a +{y^{\prime }}^{2}}\right )-\sqrt {1+{y^{\prime }}^{2}}-x y^{\prime }+y = 0 \] |
0 |
2 |
0 |
[_Clairaut] |
✓ |
✓ |
7.899 |
|
|
\[ {}y = x y^{\prime }+\frac {a y^{\prime }}{\sqrt {1+{y^{\prime }}^{2}}} \] |
4 |
7 |
1 |
[_Clairaut] |
✓ |
✓ |
60.916 |
|
|
\[ {}y = x y^{\prime }+y^{\prime }-{y^{\prime }}^{2} \] |
2 |
2 |
2 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.26 |
|
|
\[ {}y = x y^{\prime }+\sqrt {b^{2}-a^{2} {y^{\prime }}^{2}} \] |
2 |
3 |
1 |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
4.908 |
|
|
\[ {}y = x y^{\prime }+{y^{\prime }}^{4} \] |
4 |
4 |
4 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
1.519 |
|
|
\[ {}{y^{\prime }}^{2}-x y^{\prime }+y = 0 \] |
2 |
2 |
2 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.297 |
|
|
\[ {}x {y^{\prime }}^{5}-y {y^{\prime }}^{4}+\left (x^{2}+1\right ) {y^{\prime }}^{3}-2 x y {y^{\prime }}^{2}+\left (x +y^{2}\right ) y^{\prime }-y = 0 \] |
5 |
3 |
6 |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
✓ |
0.808 |
|
|
\[ {}y = x y^{\prime }-2 {y^{\prime }}^{2} \] |
2 |
2 |
2 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.317 |
|
|
\[ {}{y^{\prime }}^{2}-x y^{\prime }+y = 0 \] |
2 |
2 |
2 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.262 |
|
|
\[ {}{y^{\prime }}^{2}-x y^{\prime }+y = 0 \] |
2 |
2 |
2 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.292 |
|
|
\[ {}y = x y^{\prime }+k {y^{\prime }}^{2} \] |
2 |
2 |
2 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.302 |
|
|
\[ {}{y^{\prime }}^{2} x +\left (x -y\right ) y^{\prime }+1-y = 0 \] |
2 |
3 |
3 |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
✓ |
0.401 |
|
|
\[ {}y^{\prime } \left (x y^{\prime }-y+k \right )+a = 0 \] |
2 |
3 |
3 |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
0.422 |
|
|
\[ {}x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+1 = 0 \] |
3 |
4 |
4 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
1.012 |
|
|
\[ {}x^{2} {y^{\prime }}^{3}-2 x y {y^{\prime }}^{2}+y^{2} y^{\prime }+1 = 0 \] |
3 |
8 |
5 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
9.514 |
|
|
\[ {}x^{2} {y^{\prime }}^{2}-\left (1+2 x y\right ) y^{\prime }+1+y^{2} = 0 \] |
2 |
4 |
3 |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
1.059 |
|
|
\[ {}\left (y^{\prime }+1\right )^{2} \left (y-x y^{\prime }\right ) = 1 \] |
3 |
4 |
4 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
2.13 |
|
|
\[ {}{y^{\prime }}^{3}-{y^{\prime }}^{2}+x y^{\prime }-y = 0 \] |
3 |
3 |
3 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
1.22 |
|
|
\[ {}{y^{\prime }}^{2} x +\left (k -x -y\right ) y^{\prime }+y = 0 \] |
2 |
3 |
3 |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
✓ |
0.583 |
|
|
\[ {}\frac {{y^{\prime }}^{2}}{4}-x y^{\prime }+y = 0 \] |
2 |
2 |
2 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.258 |
|
|
\[ {}x f^{\prime }-f = \frac {{f^{\prime }}^{2} \left (1-{f^{\prime }}^{\lambda }\right )^{2}}{\lambda ^{2}} \] |
0 |
2 |
3 |
[_Clairaut] |
✓ |
✓ |
41.631 |
|
|
\[ {}{y^{\prime }}^{2}+\left (-2+x \right ) y^{\prime }-y+1 = 0 \] |
2 |
2 |
2 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.513 |
|
|
\[ {}{y^{\prime }}^{2}+\left (x +a \right ) y^{\prime }-y = 0 \] |
2 |
2 |
2 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.466 |
|
|
\[ {}{y^{\prime }}^{2}-\left (1+x \right ) y^{\prime }+y = 0 \] |
2 |
2 |
2 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.458 |
|
|
\[ {}{y^{\prime }}^{2}+\left (x a +b \right ) y^{\prime }-a y+c = 0 \] |
2 |
2 |
2 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.502 |
|
|
\[ {}2 {y^{\prime }}^{2}+\left (-1+x \right ) y^{\prime }-y = 0 \] |
2 |
2 |
2 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.484 |
|
|
\[ {}{y^{\prime }}^{2} x -y y^{\prime }+a = 0 \] |
2 |
3 |
3 |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
✓ |
0.625 |
|
|
\[ {}\left (1+x \right ) {y^{\prime }}^{2}-\left (x +y\right ) y^{\prime }+y = 0 \] |
2 |
3 |
3 |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
✓ |
0.747 |
|
|
\[ {}\left (1+3 x \right ) {y^{\prime }}^{2}-3 \left (y+2\right ) y^{\prime }+9 = 0 \] |
2 |
3 |
3 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.732 |
|
|
\[ {}\left (3 x +5\right ) {y^{\prime }}^{2}-\left (x +3 y\right ) y^{\prime }+y = 0 \] |
2 |
3 |
3 |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
✓ |
0.777 |
|
|
\[ {}a x {y^{\prime }}^{2}+\left (b x -a y+c \right ) y^{\prime }-b y = 0 \] |
2 |
3 |
3 |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
✓ |
0.829 |
|
|
\[ {}a x {y^{\prime }}^{2}-\left (a y+b x -a -b \right ) y^{\prime }+b y = 0 \] |
2 |
3 |
3 |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
✓ |
0.886 |
|
|
\[ {}x^{2} {y^{\prime }}^{2}-\left (a +2 x y\right ) y^{\prime }+y^{2} = 0 \] |
2 |
4 |
3 |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
✓ |
1.856 |
|
|
\[ {}\left (x^{2}+1\right ) {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2}-1 = 0 \] |
2 |
4 |
4 |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
0.944 |
|
|
\[ {}\left (x^{2}+a \right ) {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2}+b = 0 \] |
2 |
5 |
4 |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
3.489 |
|
|
\[ {}{y^{\prime }}^{3}+x y^{\prime }-y = 0 \] |
3 |
3 |
3 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.293 |
|
|
\[ {}{y^{\prime }}^{3}-\left (x +5\right ) y^{\prime }+y = 0 \] |
3 |
3 |
3 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.324 |
|
|
\[ {}x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+a = 0 \] |
3 |
4 |
4 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.572 |
|
|
\[ {}\sqrt {1+{y^{\prime }}^{2}}+x y^{\prime }-y = 0 \] |
2 |
2 |
1 |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
1.257 |
|
|
\[ {}\ln \left (y^{\prime }\right )+a \left (-y+x y^{\prime }\right ) = 0 \] |
0 |
2 |
2 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.636 |
|
|
\[ {}\left (1+{y^{\prime }}^{2}\right ) \sin \left (-y+x y^{\prime }\right )^{2}-1 = 0 \] |
0 |
6 |
6 |
[_Clairaut] |
✓ |
✓ |
2.947 |
|
|
\[ {}\left (-y+x y^{\prime }\right )^{2} = 1+{y^{\prime }}^{2} \] |
2 |
4 |
4 |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
0.709 |
|
|
\[ {}y y^{\prime } = \left (x -b \right ) {y^{\prime }}^{2}+a \] |
2 |
3 |
3 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.422 |
|
|
\[ {}\left (x^{2}+1\right ) {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2}-1 = 0 \] |
2 |
4 |
4 |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
0.564 |
|
|
\[ {}y = x y^{\prime }+\frac {1}{y^{\prime }} \] |
2 |
3 |
3 |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
✓ |
0.363 |
|
|
\[ {}x^{2} {y^{\prime }}^{2}-2 \left (x y-2\right ) y^{\prime }+y^{2} = 0 \] |
2 |
4 |
3 |
[[_homogeneous, ‘class G‘], _Clairaut] |
✓ |
✓ |
0.776 |
|
|
\[ {}y = x y^{\prime }+{y^{\prime }}^{2} \] |
2 |
2 |
2 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.594 |
|
|
\[ {}y = x y^{\prime }+{y^{\prime }}^{2} \] |
2 |
2 |
3 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.797 |
|
|
\[ {}{y^{\prime }}^{2}+\left (x +a \right ) y^{\prime }-y = 0 \] |
2 |
2 |
2 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.456 |
|
|
\[ {}{y^{\prime }}^{2}-y^{\prime }-x y^{\prime }+y = 0 \] |
2 |
2 |
2 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.322 |
|
|
\[ {}y = x y^{\prime }+\sqrt {1-{y^{\prime }}^{2}} \] |
2 |
2 |
1 |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
1.396 |
|
|
\[ {}y = x y^{\prime }+\frac {1}{y^{\prime }} \] |
2 |
3 |
3 |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
✓ |
0.372 |
|
|
\[ {}y = x y^{\prime }-\frac {1}{{y^{\prime }}^{2}} \] |
3 |
4 |
4 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.758 |
|
|
\[ {}t y^{\prime }-{y^{\prime }}^{3} = y \] |
3 |
3 |
3 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.749 |
|
|
\[ {}t y^{\prime }-y-2 \left (t y^{\prime }-y\right )^{2} = y^{\prime }+1 \] |
2 |
4 |
3 |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
1.021 |
|
|
\[ {}t y^{\prime }-y-1 = {y^{\prime }}^{2}-y^{\prime } \] |
2 |
2 |
2 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.456 |
|
|
\[ {}1+y-t y^{\prime } = \ln \left (y^{\prime }\right ) \] |
0 |
2 |
2 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
1.332 |
|
|
\[ {}1-2 t y^{\prime }+2 y = \frac {1}{{y^{\prime }}^{2}} \] |
3 |
4 |
4 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
1.589 |
|
|
\[ {}y = t y^{\prime }+3 {y^{\prime }}^{4} \] |
4 |
4 |
4 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
2.53 |
|
|
\[ {}y-t y^{\prime } = -2 {y^{\prime }}^{3} \] |
3 |
3 |
3 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.726 |
|
|
\[ {}y-t y^{\prime } = -4 {y^{\prime }}^{2} \] |
2 |
2 |
2 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.48 |
|
|
\[ {}y = x y^{\prime }+\frac {a}{{y^{\prime }}^{2}} \] |
3 |
4 |
4 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.572 |
|
|
\[ {}y = x y^{\prime }+{y^{\prime }}^{2} \] |
2 |
2 |
2 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.279 |
|
|
\[ {}{y^{\prime }}^{2} x -y y^{\prime }-y^{\prime }+1 = 0 \] |
2 |
3 |
3 |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
0.306 |
|
|
\[ {}y = x y^{\prime }+a \sqrt {1+{y^{\prime }}^{2}} \] |
2 |
3 |
1 |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
1.637 |
|
|
\[ {}x = \frac {y}{y^{\prime }}+\frac {1}{{y^{\prime }}^{2}} \] |
2 |
3 |
3 |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
✓ |
0.299 |
|
|
\[ {}y = x y^{\prime }+\sqrt {a^{2} {y^{\prime }}^{2}+b^{2}} \] |
2 |
3 |
1 |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
2.647 |
|
|
|
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