| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
f \left (y^{2}+x^{2}\right ) \left (1+{y^{\prime }}^{2}\right )-\left (-y+y^{\prime } x \right )^{2}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
85.346 |
|
| \begin{align*}
\left (y^{2}+x^{2}\right ) f \left (\frac {x}{\sqrt {y^{2}+x^{2}}}\right ) \left (1+{y^{\prime }}^{2}\right )-\left (-y+y^{\prime } x \right )^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
7.771 |
|
| \begin{align*}
\left (y^{2}+x^{2}\right ) f \left (\frac {y}{\sqrt {y^{2}+x^{2}}}\right ) \left (1+{y^{\prime }}^{2}\right )-\left (-y+y^{\prime } x \right )^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
38.090 |
|
| \begin{align*}
{y^{\prime }}^{3}-\left (y-a \right )^{2} \left (y-b \right )^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.405 |
|
| \begin{align*}
{y^{\prime }}^{3}-f \left (x \right ) \left (a y^{2}+b y+c \right )^{2}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
6.810 |
|
| \begin{align*}
{y^{\prime }}^{3}+y^{\prime }-y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
96.434 |
|
| \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*}
{y^{\prime }}^{3}-a x y^{\prime }+x^{3}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.957 |
|
| \begin{align*}
{y^{\prime }}^{3}-2 y^{\prime } y+y^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
61.135 |
|
| \begin{align*}
{y^{\prime }}^{2}-a x y y^{\prime }+2 a y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.443 |
|
| \begin{align*}
{y^{\prime }}^{3}-\left (x^{2}+y x +y^{2}\right ) {y^{\prime }}^{2}+\left (x y^{3}+y^{2} x^{2}+x^{3} y\right ) y^{\prime }-x^{3} y^{3}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.428 |
|
| \begin{align*}
{y^{\prime }}^{3}-x y^{4} y^{\prime }-y^{5}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.368 |
|
| \begin{align*}
{y^{\prime }}^{3}+a {y^{\prime }}^{2}+b y+a b x&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
29.757 |
|
| \begin{align*}
{y^{\prime }}^{3}+x {y^{\prime }}^{2}-y&=0 \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
7.970 |
|
| \begin{align*}
{y^{\prime }}^{3}-y {y^{\prime }}^{2}+y^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
22.083 |
|
| \begin{align*}
{y^{\prime }}^{2}-\left (y^{4}+x y^{2}+x^{2}\right ) {y^{\prime }}^{2}+\left (x y^{6}+x^{2} y^{4}+x^{3} y^{2}\right ) y^{\prime }-x^{3} y^{6}&=0 \\
\end{align*} | [‘y=_G(x,y’)‘] | ✗ | ✗ | ✗ | ✗ | 91.522 |
|
| \begin{align*}
a {y^{\prime }}^{3}+b {y^{\prime }}^{2}+c y^{\prime }-y-d&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
0.633 |
|
| \begin{align*}
x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+a&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
2.675 |
|
| \begin{align*}
4 x {y^{\prime }}^{3}-6 y {y^{\prime }}^{2}-x +3 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.477 |
|
| \begin{align*}
8 x {y^{\prime }}^{3}-12 y {y^{\prime }}^{2}+9 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.431 |
|
| \begin{align*}
\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 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.056 |
|
| \begin{align*}
x^{3} {y^{\prime }}^{3}-3 x^{2} y {y^{\prime }}^{2}+\left (3 x y^{2}+x^{6}\right ) y^{\prime }-y^{3}-2 x^{5} y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✗ |
✗ |
✓ |
✗ |
165.026 |
|
| \begin{align*}
2 \left (y^{\prime } x +y\right )^{3}-y^{\prime } y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
221.238 |
|
| \begin{align*}
{y^{\prime }}^{3} \sin \left (x \right )-\left (y \sin \left (x \right )-\cos \left (x \right )^{2}\right ) {y^{\prime }}^{2}-\left (y \cos \left (x \right )^{2}+\sin \left (x \right )\right ) y^{\prime }+y \sin \left (x \right )&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
3.074 |
|
| \begin{align*}
2 y {y^{\prime }}^{3}-y {y^{\prime }}^{2}+2 y^{\prime } x -x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.901 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{3}+2 y^{\prime } x -y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.733 |
|
| \begin{align*}
16 y^{2} {y^{\prime }}^{3}+2 y^{\prime } x -y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.796 |
|
| \begin{align*}
x y^{2} {y^{\prime }}^{3}-y^{3} {y^{\prime }}^{2}+x \left (x^{2}+1\right ) y^{\prime }-x^{2} y&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✓ |
✗ |
229.186 |
|
| \begin{align*}
x^{7} y^{2} {y^{\prime }}^{3}-\left (3 x^{6} y^{3}-1\right ) {y^{\prime }}^{2}+3 x^{5} y^{4} y^{\prime }-x^{4} y^{5}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
4.191 |
|
| \begin{align*}
{y^{\prime }}^{4}-\left (y-a \right )^{3} \left (y-b \right )^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.191 |
|
| \begin{align*}
{y^{\prime }}^{4}+3 \left (x -1\right ) {y^{\prime }}^{2}-3 \left (-1+2 y\right ) y^{\prime }+3 x&=0 \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
33.868 |
|
| \begin{align*}
{y^{\prime }}^{4}-4 y \left (y^{\prime } x -2 y\right )^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
155.454 |
|
| \begin{align*}
{y^{\prime }}^{6}-\left (y-a \right )^{4} \left (y-b \right )^{3}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.345 |
|
| \begin{align*}
x^{2} \left (1+{y^{\prime }}^{2}\right )^{3}-a^{2}&=0 \\
\end{align*} | [_quadrature] | ✓ | ✓ | ✓ | ✓ | 0.845 |
|
| \begin{align*}
{y^{\prime }}^{r}-a y^{s}-b \,x^{\frac {r s}{r -s}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
4.959 |
|
| \begin{align*}
{y^{\prime }}^{n}-f \left (x \right )^{n} \left (y-a \right )^{n +1} \left (y-b \right )^{n -1}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
23.066 |
|
| \begin{align*}
{y^{\prime }}^{n}-f \left (x \right ) g \left (y\right )&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.342 |
|
| \begin{align*}
a {y^{\prime }}^{m}+b {y^{\prime }}^{n}-y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
4.270 |
|
| \begin{align*}
x^{n -1} {y^{\prime }}^{n}-n x y^{\prime }+y&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✓ |
✗ |
11.902 |
|
| \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*}
\sqrt {1+{y^{\prime }}^{2}}+x {y^{\prime }}^{2}+y&=0 \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.838 |
|
| \begin{align*}
x \left (y^{\prime }+\sqrt {1+{y^{\prime }}^{2}}\right )-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
25.505 |
|
| \begin{align*}
a x \sqrt {1+{y^{\prime }}^{2}}+y^{\prime } x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
79.075 |
|
| \begin{align*}
y \sqrt {1+{y^{\prime }}^{2}}-a y y^{\prime }-a x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✗ |
✓ |
✓ |
✗ |
0.094 |
|
| \begin{align*}
a y \sqrt {1+{y^{\prime }}^{2}}-2 x y^{\prime } y+y^{2}-x^{2}&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✓ |
✗ |
248.086 |
|
| \begin{align*}
f \left (y^{2}+x^{2}\right ) \sqrt {1+{y^{\prime }}^{2}}-y^{\prime } x +y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
105.477 |
|
| \begin{align*}
a \left (1+{y^{\prime }}^{3}\right )^{{1}/{3}}+b x y^{\prime }-y&=0 \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.421 |
|
| \begin{align*}
\ln \left (y^{\prime }\right )+y^{\prime } x +a y+b&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.855 |
|
| \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*}
y \ln \left (y^{\prime }\right )+y^{\prime }-y \ln \left (y\right )-y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.069 |
|
| \begin{align*}
\sin \left (y^{\prime }\right )+y^{\prime }-x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
0.386 |
|
| \begin{align*}
a \cos \left (y^{\prime }\right )+b y^{\prime }+x&=0 \\
\end{align*} | [_quadrature] | ✓ | ✓ | ✓ | ✗ | 0.380 |
|
| \begin{align*}
{y^{\prime }}^{2} \sin \left (y^{\prime }\right )-y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
2.637 |
|
| \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 (1+{y^{\prime }}^{2}\right ) \left (\arctan \left (y^{\prime }\right )+a x \right )+y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
1.422 |
|
| \begin{align*}
a \,x^{n} f \left (y^{\prime }\right )+y^{\prime } x -y&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✓ |
✗ |
4.008 |
|
| \begin{align*}
f \left (x {y^{\prime }}^{2}\right )+2 y^{\prime } x -y&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✓ |
✗ |
1.120 |
|
| \begin{align*}
f \left (x -\frac {3 {y^{\prime }}^{2}}{2}\right )+{y^{\prime }}^{3}-y&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
✓ |
✓ |
✗ |
4.970 |
|
| \begin{align*}
y^{\prime }&=F \left (\frac {y}{x +a}\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.568 |
|
| \begin{align*}
y^{\prime }&=2 x +F \left (y-x^{2}\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.578 |
|
| \begin{align*}
y^{\prime }&=-\frac {a x}{2}+F \left (y+\frac {a \,x^{2}}{4}+\frac {b x}{2}\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
4.000 |
|
| \begin{align*}
y^{\prime }&=F \left (y \,{\mathrm e}^{-b x}\right ) {\mathrm e}^{b x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
3.203 |
|
| \begin{align*}
y^{\prime }&=\frac {1+2 F \left (\frac {4 x^{2} y+1}{4 x^{2}}\right ) x}{2 x^{3}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
✓ |
✓ |
✗ |
6.225 |
|
| \begin{align*}
y^{\prime }&=\frac {1+F \left (\frac {a x y+1}{a x}\right ) a \,x^{2}}{a \,x^{2}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
✓ |
✓ |
✗ |
6.687 |
|
| \begin{align*}
y^{\prime }&=-\frac {\left (a \,x^{2}-2 F \left (y+\frac {a \,x^{4}}{8}\right )\right ) x}{2} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
✓ |
✓ |
✗ |
6.510 |
|
| \begin{align*}
y^{\prime }&=\frac {2 a}{y+2 F \left (y^{2}-4 a x \right ) a} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
3.946 |
|
| \begin{align*}
y^{\prime }&=F \left (\ln \left (\ln \left (y\right )\right )-\ln \left (x \right )\right ) y \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
✓ |
✓ |
✗ |
13.441 |
|
| \begin{align*}
y^{\prime }&=\frac {F \left (\frac {y}{\sqrt {x^{2}+1}}\right ) x}{\sqrt {x^{2}+1}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
✓ |
✓ |
✗ |
8.806 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (x^{{3}/{2}}+2 F \left (y-\frac {x^{3}}{6}\right )\right ) \sqrt {x}}{2} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
✓ |
✓ |
✗ |
8.437 |
|
| \begin{align*}
y^{\prime }&=\frac {x +F \left (-\left (x -y\right ) \left (x +y\right )\right )}{y} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
3.712 |
|
| \begin{align*}
y^{\prime }&=\frac {F \left (-\frac {-1+y \ln \left (x \right )}{y}\right ) y^{2}}{x} \\
\end{align*} | [[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] | ✓ | ✓ | ✓ | ✗ | 6.180 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{-y+F \left (y^{2}+x^{2}\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
3.657 |
|
| \begin{align*}
y^{\prime }&=\frac {F \left (\frac {a y^{2}+b \,x^{2}}{a}\right ) x}{\sqrt {a}\, y} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
✓ |
✓ |
✗ |
7.451 |
|
| \begin{align*}
y^{\prime }&=\frac {6 x^{3}+5 \sqrt {x}+5 F \left (y-\frac {2 x^{3}}{5}-2 \sqrt {x}\right )}{5 x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
✓ |
✓ |
✗ |
9.167 |
|
| \begin{align*}
y^{\prime }&=\frac {F \left (y^{{3}/{2}}-\frac {3 \,{\mathrm e}^{x}}{2}\right ) {\mathrm e}^{x}}{\sqrt {y}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
✓ |
✓ |
✗ |
10.490 |
|
| \begin{align*}
y^{\prime }&=\frac {F \left (-\frac {-y^{2}+b}{x^{2}}\right ) x}{y} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
✓ |
✓ |
✗ |
6.798 |
|
| \begin{align*}
y^{\prime }&=\frac {F \left (\frac {x y^{2}+1}{x}\right )}{y x^{2}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
✓ |
✓ |
✗ |
8.038 |
|
| \begin{align*}
y^{\prime }&=\frac {-2 x^{2}+x +F \left (y+x^{2}-x \right )}{x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
4.996 |
|
| \begin{align*}
y^{\prime }&=\frac {2 a}{x^{2} \left (-y+2 F \left (\frac {x y^{2}-4 a}{x}\right ) a \right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
6.724 |
|
| \begin{align*}
y^{\prime }&=\frac {y+F \left (\frac {y}{x}\right )}{x -1} \\
\end{align*} |
[[_homogeneous, ‘class D‘]] |
✓ |
✓ |
✓ |
✗ |
6.421 |
|
| \begin{align*}
y^{\prime }&=\frac {-x +F \left (y^{2}+x^{2}\right )}{y} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
3.562 |
|
| \begin{align*}
y^{\prime }&=\frac {F \left (-\frac {2 y \ln \left (x \right )-1}{y}\right ) y^{2}}{x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
6.245 |
|
| \begin{align*}
y^{\prime }&=\frac {F \left (-\left (x -y\right ) \left (x +y\right )\right ) x}{y} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
✓ |
✓ |
✗ |
6.636 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2} \left (2+F \left (\frac {x^{2}-y}{y x^{2}}\right ) x^{2}\right )}{x^{3}} \\
\end{align*} |
[NONE] |
✗ |
✓ |
✓ |
✗ |
7.505 |
|
| \begin{align*}
y^{\prime }&=\frac {2 F \left (y+\ln \left (2 x +1\right )\right ) x +F \left (y+\ln \left (2 x +1\right )\right )-2}{2 x +1} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
✓ |
✓ |
✗ |
7.312 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y^{3}}{1+2 F \left (\frac {1+4 x y^{2}}{y^{2}}\right ) y} \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✗ |
✓ |
✓ |
✗ |
6.554 |
|
| \begin{align*}
y^{\prime }&=-\frac {y^{2} \left (2 x -F \left (-\frac {y x -2}{2 y}\right )\right )}{4 x} \\
\end{align*} |
[NONE] |
✓ |
✓ |
✓ |
✗ |
7.010 |
|
| \begin{align*}
y^{\prime }&=-\left (-{\mathrm e}^{-x^{2}}+x^{2} {\mathrm e}^{-x^{2}}-F \left (y-\frac {x^{2} {\mathrm e}^{-x^{2}}}{2}\right )\right ) x \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
✓ |
✓ |
✗ |
8.158 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y+F \left (\frac {y}{x^{2}}\right ) x^{3}}{x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
3.266 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {y}}{\sqrt {y}+F \left (\frac {x -y}{\sqrt {y}}\right )} \\
\end{align*} | [[_1st_order, _with_linear_symmetries]] | ✓ | ✓ | ✓ | ✗ | 6.898 |
|
| \begin{align*}
y^{\prime }&=\frac {-3 x^{2} y+F \left (x^{3} y\right )}{x^{3}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
3.391 |
|
| \begin{align*}
y^{\prime }&=\frac {y+F \left (\frac {y}{x}\right ) x^{2}}{x} \\
\end{align*} |
[[_homogeneous, ‘class D‘]] |
✓ |
✓ |
✓ |
✗ |
3.533 |
|
| \begin{align*}
y^{\prime }&=\frac {-2 x -y+F \left (x \left (x +y\right )\right )}{x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
2.942 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (y \,{\mathrm e}^{-\frac {x^{2}}{4}} x +2 F \left (y \,{\mathrm e}^{-\frac {x^{2}}{4}}\right )\right ) {\mathrm e}^{\frac {x^{2}}{4}}}{2} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
5.960 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y+F \left (-\frac {-y+x \ln \left (x \right )}{x}\right ) x^{2}}{x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
3.065 |
|
| \begin{align*}
y^{\prime }&=\frac {x \left (a -1\right ) \left (a +1\right )}{y+F \left (\frac {y^{2}}{2}-\frac {a^{2} x^{2}}{2}+\frac {x^{2}}{2}\right ) a^{2}-F \left (\frac {y^{2}}{2}-\frac {a^{2} x^{2}}{2}+\frac {x^{2}}{2}\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
4.642 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x \left (-1+F \left (y x \right ) y\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
4.637 |
|
| \begin{align*}
y^{\prime }&=-\frac {-x^{2}+2 x^{3} y-F \left (\left (y x -1\right ) x \right )}{x^{4}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
5.048 |
|
| \begin{align*}
y^{\prime }&=\frac {F \left (\frac {\left (3+y\right ) {\mathrm e}^{\frac {3 x^{2}}{2}}}{3 y}\right ) x y^{2} {\mathrm e}^{3 x^{2}} {\mathrm e}^{-\frac {9 x^{2}}{2}}}{9} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
✓ |
✓ |
✗ |
8.726 |
|