| # |
ODE |
CAS classification |
Solved |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y&=y^{\prime } x -\frac {{y^{\prime }}^{2}}{4} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.210 |
|
| \begin{align*}
y^{\prime }&=-1-\frac {x}{2}+\frac {\sqrt {x^{2}+4 x +4 y}}{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
2.625 |
|
| \begin{align*}
y&=y^{\prime } x +{y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.293 |
|
| \begin{align*}
y&=y^{\prime } x +\frac {1}{y^{\prime }} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.807 |
|
| \begin{align*}
y&=y^{\prime } x -\sqrt {y^{\prime }} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
1.688 |
|
| \begin{align*}
y&=y^{\prime } x +\ln \left (y^{\prime }\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
4.648 |
|
| \begin{align*}
y&=y^{\prime } x +\frac {3}{{y^{\prime }}^{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
1.147 |
|
| \begin{align*}
y&=y^{\prime } x -{y^{\prime }}^{{2}/{3}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
1.621 |
|
| \begin{align*}
y&=y^{\prime } x +{\mathrm e}^{y^{\prime }} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
3.743 |
|
| \begin{align*}
\left (y-y^{\prime } x \right )^{2}&=1+{y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.406 |
|
| \begin{align*}
x {y^{\prime }}^{2}-y^{\prime } y-2&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.790 |
|
| \begin{align*}
\left (y-y^{\prime } x \right )^{2}&=1+{y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.230 |
|
| \begin{align*}
x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+1&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.693 |
|
| \begin{align*}
y&=y^{\prime } x +{y^{\prime }}^{3} \\
\end{align*} | [[_1st_order, _with_linear_symmetries], _Clairaut] | ✓ | ✓ | ✓ | ✗ | 0.329 |
|
| \begin{align*}
2 {y^{\prime }}^{2} \left (y-y^{\prime } x \right )&=1 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.580 |
|
| \begin{align*}
{y^{\prime }}^{2}+y^{\prime } x -y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.227 |
|
| \begin{align*}
{y^{\prime }}^{2}-y^{\prime } x +y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.223 |
|
| \begin{align*}
{y^{\prime }}^{2}+\left (1-x \right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.229 |
|
| \begin{align*}
{y^{\prime }}^{2}-\left (x +1\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.235 |
|
| \begin{align*}
{y^{\prime }}^{2}-\left (-x +2\right ) y^{\prime }+1-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.260 |
|
| \begin{align*}
{y^{\prime }}^{2}+\left (x +a \right ) y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.253 |
|
| \begin{align*}
{y^{\prime }}^{2}-2 y^{\prime } x +2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.236 |
|
| \begin{align*}
{y^{\prime }}^{2}-4 \left (x +1\right ) y^{\prime }+4 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.238 |
|
| \begin{align*}
{y^{\prime }}^{2}-a x y^{\prime }+a y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.276 |
|
| \begin{align*}
{y^{\prime }}^{2}+\left (b x +a \right ) y^{\prime }+c&=b y \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.282 |
|
| \begin{align*}
2 {y^{\prime }}^{2}-\left (1-x \right ) y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.235 |
|
| \begin{align*}
x {y^{\prime }}^{2}-y^{\prime } y+a&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.688 |
|
| \begin{align*}
x {y^{\prime }}^{2}+\left (-y+a \right ) y^{\prime }+b&=0 \\
\end{align*} | [[_1st_order, _with_linear_symmetries], _rational, _Clairaut] | ✓ | ✓ | ✓ | ✗ | 0.269 |
|
| \begin{align*}
x {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }+1-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
0.289 |
|
| \begin{align*}
x {y^{\prime }}^{2}+\left (a +x -y\right ) y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
0.315 |
|
| \begin{align*}
x {y^{\prime }}^{2}+\left (a +b x -y\right ) y^{\prime }-b y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
0.336 |
|
| \begin{align*}
\left (x +1\right ) {y^{\prime }}^{2}-\left (x +y\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
0.309 |
|
| \begin{align*}
\left (a -x \right ) {y^{\prime }}^{2}+y^{\prime } y-b&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.298 |
|
| \begin{align*}
\left (1+3 x \right ) {y^{\prime }}^{2}-3 \left (y+2\right ) y^{\prime }+9&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.306 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}-\left (2 y x +1\right ) y^{\prime }+1+y^{2}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.229 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}-\left (a +2 y x \right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.467 |
|
| \begin{align*}
\left (a^{2}+x^{2}\right ) {y^{\prime }}^{2}-2 x y^{\prime } y+b +y^{2}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.377 |
|
| \begin{align*}
{y^{\prime }}^{3}+a x y^{\prime }-a y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.397 |
|
| \begin{align*}
{y^{\prime }}^{3}-\left (b x +a \right ) y^{\prime }+b y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.487 |
|
| \begin{align*}
{y^{\prime }}^{3}-{y^{\prime }}^{2}+y^{\prime } x -y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.494 |
|
| \begin{align*}
x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+a&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.618 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{3}-2 x y {y^{\prime }}^{2}+y^{2} y^{\prime }+1&=0 \\
\end{align*} | [[_1st_order, _with_linear_symmetries], _Clairaut] | ✓ | ✓ | ✓ | ✗ | 1.196 |
|
| \begin{align*}
2 \sqrt {a y^{\prime }}+y^{\prime } x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
2.158 |
|
| \begin{align*}
\sqrt {a^{2}+b^{2} {y^{\prime }}^{2}}+y^{\prime } x -y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
2.255 |
|
| \begin{align*}
a \sqrt {1+{y^{\prime }}^{2}}+y^{\prime } x -y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.759 |
|
| \begin{align*}
a \left (1+{y^{\prime }}^{3}\right )^{{1}/{3}}+y^{\prime } x -y&=0 \\
\end{align*} |
[_Clairaut] |
✓ |
✓ |
✓ |
✗ |
17.441 |
|
| \begin{align*}
\cos \left (y^{\prime }\right )+y^{\prime } x&=y \\
\end{align*} |
[_Clairaut] |
✓ |
✓ |
✓ |
✗ |
1.312 |
|
| \begin{align*}
\left (1+{y^{\prime }}^{2}\right ) \sin \left (-y+y^{\prime } x \right )^{2}&=1 \\
\end{align*} |
[_Clairaut] |
✓ |
✓ |
✓ |
✗ |
2.237 |
|
| \begin{align*}
\ln \left (y^{\prime }\right )+y^{\prime } x +a&=y \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
2.721 |
|
| \begin{align*}
\ln \left (y^{\prime }\right )+a \left (-y+y^{\prime } x \right )&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
2.839 |
|
| \begin{align*}
y^{\prime } \ln \left (y^{\prime }\right )-\left (x +1\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
2.167 |
|
| \begin{align*}
y^{\prime } \ln \left (y^{\prime }+\sqrt {1+{y^{\prime }}^{2}}\right )-\sqrt {1+{y^{\prime }}^{2}}-y^{\prime } x +y&=0 \\
\end{align*} |
[_Clairaut] |
✓ |
✓ |
✓ |
✗ |
12.283 |
|
| \begin{align*}
y&=y^{\prime } x +\frac {a y^{\prime }}{\sqrt {1+{y^{\prime }}^{2}}} \\
\end{align*} |
[_Clairaut] |
✓ |
✓ |
✓ |
✗ |
6.210 |
|
| \begin{align*}
y&=y^{\prime } x +y^{\prime }-{y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.208 |
|
| \begin{align*}
y&=y^{\prime } x +\sqrt {b^{2}-a^{2} {y^{\prime }}^{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
2.769 |
|
| \begin{align*}
y&=y^{\prime } x +2 {y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.261 |
|
| \begin{align*}
x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+2&=0 \\
\end{align*} | [[_1st_order, _with_linear_symmetries], _Clairaut] | ✓ | ✓ | ✓ | ✗ | 0.862 |
|
| \begin{align*}
y&=y^{\prime } x +{y^{\prime }}^{4} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
3.150 |
|
| \begin{align*}
{y^{\prime }}^{2}-y^{\prime } x +y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.263 |
|
| \begin{align*}
y&=y^{\prime } x -2 {y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.282 |
|
| \begin{align*}
{y^{\prime }}^{2}-y^{\prime } x +y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.231 |
|
| \begin{align*}
{y^{\prime }}^{2}-y^{\prime } x +y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.207 |
|
| \begin{align*}
y&=y^{\prime } x +k {y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.284 |
|
| \begin{align*}
x {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }+1-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
0.319 |
|
| \begin{align*}
y^{\prime } \left (y^{\prime } x -y+k \right )+a&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.313 |
|
| \begin{align*}
x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+1&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.685 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{3}-2 x y {y^{\prime }}^{2}+y^{2} y^{\prime }+1&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
1.755 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}-\left (2 y x +1\right ) y^{\prime }+1+y^{2}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.411 |
|
| \begin{align*}
\left (1+y^{\prime }\right )^{2} \left (y-y^{\prime } x \right )&=1 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
0.720 |
|
| \begin{align*}
{y^{\prime }}^{3}-{y^{\prime }}^{2}+y^{\prime } x -y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.603 |
|
| \begin{align*}
x {y^{\prime }}^{2}+\left (k -x -y\right ) y^{\prime }+y&=0 \\
\end{align*} | [[_1st_order, _with_linear_symmetries], _rational, _dAlembert] | ✓ | ✓ | ✓ | ✗ | 0.369 |
|
| \begin{align*}
\frac {{y^{\prime }}^{2}}{4}-y^{\prime } x +y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.154 |
|
| \begin{align*}
f^{\prime } x -f&=\frac {{f^{\prime }}^{2} \left (1-{f^{\prime }}^{\lambda }\right )^{2}}{\lambda ^{2}} \\
\end{align*} |
[_Clairaut] |
✓ |
✓ |
✓ |
✗ |
3.583 |
|
| \begin{align*}
{y^{\prime }}^{2}+\left (x -2\right ) y^{\prime }-y+1&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.326 |
|
| \begin{align*}
{y^{\prime }}^{2}+\left (x +a \right ) y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.339 |
|
| \begin{align*}
{y^{\prime }}^{2}-\left (x +1\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.293 |
|
| \begin{align*}
{y^{\prime }}^{2}+\left (a x +b \right ) y^{\prime }-a y+c&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.372 |
|
| \begin{align*}
2 {y^{\prime }}^{2}+\left (x -1\right ) y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.302 |
|
| \begin{align*}
x {y^{\prime }}^{2}-y^{\prime } y+a&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.841 |
|
| \begin{align*}
\left (x +1\right ) {y^{\prime }}^{2}-\left (x +y\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
0.398 |
|
| \begin{align*}
\left (1+3 x \right ) {y^{\prime }}^{2}-3 \left (y+2\right ) y^{\prime }+9&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.389 |
|
| \begin{align*}
\left (3 x +5\right ) {y^{\prime }}^{2}-\left (x +3 y\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
0.415 |
|
| \begin{align*}
a x {y^{\prime }}^{2}+\left (b x -a y+c \right ) y^{\prime }-b y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
0.532 |
|
| \begin{align*}
a x {y^{\prime }}^{2}-\left (a y+b x -a -b \right ) y^{\prime }+b y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
0.544 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}-\left (a +2 y x \right ) y^{\prime }+y^{2}&=0 \\
\end{align*} | [[_homogeneous, ‘class G‘], _rational, _Clairaut] | ✓ | ✓ | ✓ | ✓ | 2.181 |
|
| \begin{align*}
\left (x^{2}+1\right ) {y^{\prime }}^{2}-2 x y^{\prime } y+y^{2}-1&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.401 |
|
| \begin{align*}
\left (x^{2}+a \right ) {y^{\prime }}^{2}-2 x y^{\prime } y+y^{2}+b&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.543 |
|
| \begin{align*}
{y^{\prime }}^{3}+y^{\prime } x -y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
1.460 |
|
| \begin{align*}
{y^{\prime }}^{3}-\left (x +5\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
1.674 |
|
| \begin{align*}
x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+a&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
2.675 |
|
| \begin{align*}
\sqrt {1+{y^{\prime }}^{2}}+y^{\prime } x -y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
3.016 |
|
| \begin{align*}
\ln \left (y^{\prime }\right )+a \left (-y+y^{\prime } x \right )&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
7.471 |
|
| \begin{align*}
\left (1+{y^{\prime }}^{2}\right ) \sin \left (-y+y^{\prime } x \right )^{2}-1&=0 \\
\end{align*} |
[_Clairaut] |
✓ |
✓ |
✓ |
✗ |
4.771 |
|
| \begin{align*}
\left (-y+y^{\prime } x \right )^{2}&=1+{y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.252 |
|
| \begin{align*}
y^{\prime } y&=\left (-b +x \right ) {y^{\prime }}^{2}+a \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.234 |
|
| \begin{align*}
\left (x^{2}+1\right ) {y^{\prime }}^{2}-2 x y^{\prime } y+y^{2}-1&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.212 |
|
| \begin{align*}
y&=y^{\prime } x +\frac {1}{y^{\prime }} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.377 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}-2 \left (y x -2\right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.417 |
|
| \begin{align*}
y&=y^{\prime } x +{y^{\prime }}^{2} \\
y \left (2\right ) &= -1 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.213 |
|
| \begin{align*}
y&=y^{\prime } x +{y^{\prime }}^{2} \\
y \left (1\right ) &= -1 \\
\end{align*} | [[_1st_order, _with_linear_symmetries], _Clairaut] | ✓ | ✓ | ✓ | ✗ | 0.170 |
|
| \begin{align*}
{y^{\prime }}^{2}+\left (x +a \right ) y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.199 |
|
| \begin{align*}
{y^{\prime }}^{2}-y^{\prime }-y^{\prime } x +y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.193 |
|
| \begin{align*}
y&=y^{\prime } x +\sqrt {1-{y^{\prime }}^{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
1.428 |
|
| \begin{align*}
y&=y^{\prime } x +\frac {1}{y^{\prime }} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.509 |
|
| \begin{align*}
y&=y^{\prime } x -\frac {1}{{y^{\prime }}^{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.585 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \\
y \left (6\right ) &= -9 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
3.496 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
3.283 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \\
y \left (1\right ) &= -{\frac {1}{4}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
3.576 |
|
| \begin{align*}
y^{\prime }+2 x&=2 \sqrt {y+x^{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
2.420 |
|
| \begin{align*}
t y^{\prime }-{y^{\prime }}^{3}&=y \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.432 |
|
| \begin{align*}
t y^{\prime }-y-2 \left (-y+t y^{\prime }\right )^{2}&=y^{\prime }+1 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.464 |
|
| \begin{align*}
t y^{\prime }-y-1&={y^{\prime }}^{2}-y^{\prime } \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.246 |
|
| \begin{align*}
1+y-t y^{\prime }&=\ln \left (y^{\prime }\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
3.855 |
|
| \begin{align*}
1+2 y-2 t y^{\prime }&=\frac {1}{{y^{\prime }}^{2}} \\
\end{align*} | [[_1st_order, _with_linear_symmetries], _Clairaut] | ✓ | ✓ | ✓ | ✗ | 0.919 |
|
| \begin{align*}
y&=t y^{\prime }+3 {y^{\prime }}^{4} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
2.931 |
|
| \begin{align*}
y-t y^{\prime }&=-2 {y^{\prime }}^{3} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.428 |
|
| \begin{align*}
y-t y^{\prime }&=-4 {y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.252 |
|
| \begin{align*}
y&=y^{\prime } x +\frac {a}{{y^{\prime }}^{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.513 |
|
| \begin{align*}
y&=y^{\prime } x +{y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.158 |
|
| \begin{align*}
x {y^{\prime }}^{2}-y^{\prime } y-y^{\prime }+1&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.194 |
|
| \begin{align*}
y&=y^{\prime } x +a \sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.692 |
|
| \begin{align*}
x&=\frac {y}{y^{\prime }}+\frac {1}{{y^{\prime }}^{2}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.365 |
|
| \begin{align*}
y&=y^{\prime } x +\sqrt {a^{2} {y^{\prime }}^{2}+b^{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
2.138 |
|
| \begin{align*}
y^{\prime }&=-\frac {t}{2}+\frac {\sqrt {t^{2}+4 y}}{2} \\
y \left (2\right ) &= -1 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
3.499 |
|
| \begin{align*}
y&=y^{\prime } x +y^{\prime }-{y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.196 |
|
| \begin{align*}
{y^{\prime }}^{2} \left (x^{2}-1\right )-2 x y^{\prime } y+y^{2}-1&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.239 |
|
| \begin{align*}
y^{\prime }&=-x +\sqrt {x^{2}+2 y} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
3.449 |
|
| \begin{align*}
y^{\prime }&=-x -\sqrt {x^{2}+2 y} \\
\end{align*} | [[_1st_order, _with_linear_symmetries], _Clairaut] | ✓ | ✓ | ✓ | ✓ | 3.352 |
|
| \begin{align*}
y&=y^{\prime } x +y^{\prime }-{y^{\prime }}^{3} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
1.966 |
|
| \begin{align*}
y&=y^{\prime } x -{y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.822 |
|
| \begin{align*}
{y^{\prime }}^{2}+y^{\prime } x -y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.766 |
|
| \begin{align*}
y&=y^{\prime } x +\arcsin \left (y^{\prime }\right ) \\
\end{align*} |
[_Clairaut] |
✓ |
✓ |
✓ |
✗ |
2.891 |
|
| \begin{align*}
y&=y^{\prime } \left (-b +x \right )+\frac {a}{y^{\prime }} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
1.074 |
|
| \begin{align*}
y&=y^{\prime } x +\frac {m}{y^{\prime }} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.420 |
|
| \begin{align*}
y&=y^{\prime } x +a \sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.660 |
|
| \begin{align*}
{y^{\prime }}^{2}+y^{\prime } x -y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.163 |
|
| \begin{align*}
y^{2}-2 x y^{\prime } y+{y^{\prime }}^{2} \left (x^{2}-1\right )&=m^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✗ |
✗ |
0.242 |
|
| \begin{align*}
y&=y^{\prime } x +\sqrt {b^{2}+a^{2} y^{\prime }} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
1.293 |
|
| \begin{align*}
y&=y^{\prime } x -{y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.167 |
|
| \begin{align*}
\left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}-2 x y^{\prime } y+y^{2}-b^{2}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.400 |
|
| \begin{align*}
y&=y^{\prime } x +\frac {a}{y^{\prime }} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.563 |
|
| \begin{align*}
y&=y^{\prime } x +y^{\prime }-{y^{\prime }}^{3} \\
\end{align*} | [[_1st_order, _with_linear_symmetries], _Clairaut] | ✓ | ✓ | ✓ | ✗ | 0.463 |
|
| \begin{align*}
y&=y^{\prime } x +a y^{\prime } \left (1-y^{\prime }\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.250 |
|
| \begin{align*}
y&=y^{\prime } x +\sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
1.555 |
|
| \begin{align*}
y&=y^{\prime } x +\sqrt {b^{2}-a^{2} {y^{\prime }}^{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
2.719 |
|
| \begin{align*}
\left (y-y^{\prime } x \right ) \left (y^{\prime }-1\right )&=y^{\prime } \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
0.259 |
|
| \begin{align*}
x {y^{\prime }}^{2}-y^{\prime } y+a&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.505 |
|
| \begin{align*}
y&=y^{\prime } \left (-b +x \right )+\frac {a}{y^{\prime }} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.272 |
|
| \begin{align*}
y&=y^{\prime } x +{y^{\prime }}^{3} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.370 |
|
| \begin{align*}
\left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}-2 x y^{\prime } y+y^{2}+a^{4}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.746 |
|
| \begin{align*}
\left (x^{2}+1\right ) {y^{\prime }}^{2}-2 x y^{\prime } y+y^{2}&=1 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.317 |
|
| \begin{align*}
y^{2}-2 x y^{\prime } y+{y^{\prime }}^{2} \left (x^{2}-1\right )&=m \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.316 |
|
| \begin{align*}
y&=y^{\prime } x -{y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.202 |
|
| \begin{align*}
\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}+2 x y^{\prime } y+b^{2}-y^{2}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.487 |
|
| \begin{align*}
y&=y^{\prime } x +\frac {1}{y^{\prime }} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.809 |
|
| \begin{align*}
y&=y^{\prime } x -\sqrt {y^{\prime }-1} \\
\end{align*} | [[_1st_order, _with_linear_symmetries], _Clairaut] | ✓ | ✓ | ✓ | ✗ | 0.986 |
|
| \begin{align*}
y&=y^{\prime } x +{y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.233 |
|
| \begin{align*}
x&=t x^{\prime }-{x^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.244 |
|
| \begin{align*}
x&=t x^{\prime }-{\mathrm e}^{x^{\prime }} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
4.741 |
|
| \begin{align*}
x&=t x^{\prime }-\ln \left (x^{\prime }\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
6.402 |
|
| \begin{align*}
x&=t x^{\prime }+\frac {1}{x^{\prime }} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.900 |
|
| \begin{align*}
\left (-y+y^{\prime } x \right )^{2}-{y^{\prime }}^{2}-1&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.412 |
|
| \begin{align*}
{y^{\prime }}^{2} \left (x^{2}-1\right )-2 x y^{\prime } y+y^{2}-1&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.346 |
|
| \begin{align*}
y&=y^{\prime } x +{y^{\prime }}^{3} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.470 |
|
| \begin{align*}
{y^{\prime }}^{2}+y^{\prime } x -y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.545 |
|
| \begin{align*}
y^{2}-2 x y^{\prime } y+x^{2} {y^{\prime }}^{2}-{y^{\prime }}^{3}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
28.741 |
|
| \begin{align*}
{y^{\prime }}^{2}+y&=y^{\prime } x +1 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.389 |
|
| \begin{align*}
\left (y-y^{\prime } x \right )^{2}&=y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✓ |
1.426 |
|
| \begin{align*}
y&=y^{\prime } x +\ln \left (y^{\prime }\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
30.557 |
|
| \begin{align*}
y+1-y^{\prime } x&=0 \\
\end{align*} | [_separable] | ✓ | ✓ | ✓ | ✓ | 1.666 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (\sqrt {y x +1}-1\right )^{2}}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
6.492 |
|
| \begin{align*}
y&=y^{\prime } x -{y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.263 |
|
| \begin{align*}
y&=y^{\prime } x +1+4 {y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.157 |
|
| \begin{align*}
y&=y^{\prime } x -\tan \left (y^{\prime }\right ) \\
\end{align*} |
[_Clairaut] |
✓ |
✓ |
✓ |
✗ |
1.409 |
|
| \begin{align*}
y&=y^{\prime } x +\sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✓ |
1.117 |
|
| \begin{align*}
-y+y^{\prime } x&=1 \\
y \left (2\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.053 |
|
| \begin{align*}
{y^{\prime }}^{2}-y^{\prime } x +y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.154 |
|
| \begin{align*}
{y^{\prime }}^{2}-y^{\prime } x +y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.121 |
|
| \begin{align*}
y&=y^{\prime } x +k {y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.173 |
|
| \begin{align*}
x {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }+1-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
0.210 |
|
| \begin{align*}
y^{\prime } \left (y^{\prime } x -y+k \right )+a&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.195 |
|
| \begin{align*}
x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+1&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.406 |
|
| \begin{align*}
y&=y^{\prime } x +{y^{\prime }}^{n} \\
\end{align*} |
[_Clairaut] |
✓ |
✓ |
✓ |
✗ |
1.486 |
|
| \begin{align*}
x {y^{\prime }}^{2}+\left (k -x -y\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
0.234 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{3}-2 x y {y^{\prime }}^{2}+y^{2} y^{\prime }+1&=0 \\
\end{align*} | [[_1st_order, _with_linear_symmetries], _Clairaut] | ✓ | ✓ | ✓ | ✗ | 1.058 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}-\left (2 y x +1\right ) y^{\prime }+1+y^{2}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.228 |
|
| \begin{align*}
\left (1+y^{\prime }\right )^{2} \left (y-y^{\prime } x \right )&=1 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
0.585 |
|
| \begin{align*}
{y^{\prime }}^{3}-{y^{\prime }}^{2}+y^{\prime } x -y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.462 |
|