| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
\left (3 x^{3}+6 x^{2} y-3 x y^{2}+20 y^{3}\right ) y^{\prime }+4 x^{3}+9 x^{2} y+6 x y^{2}-y^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
31.115 |
|
| \begin{align*}
\left (x^{3}+a y^{3}\right ) y^{\prime }&=x^{2} y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.907 |
|
| \begin{align*}
x y^{3} y^{\prime }&=\left (-x^{2}+1\right ) \left (1+y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.157 |
|
| \begin{align*}
x \left (x -y^{3}\right ) y^{\prime }&=\left (3 x +y^{3}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
14.823 |
|
| \begin{align*}
x \left (2 x^{3}+y^{3}\right ) y^{\prime }&=\left (2 x^{3}-x^{2} y+y^{3}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
393.883 |
|
| \begin{align*}
x \left (2 x^{3}-y^{3}\right ) y^{\prime }&=\left (x^{3}-2 y^{3}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
129.951 |
|
| \begin{align*}
x \left (x^{3}+3 x^{2} y+y^{3}\right ) y^{\prime }&=\left (3 x^{2}+y^{2}\right ) y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
35.264 |
|
| \begin{align*}
x \left (x^{3}-2 y^{3}\right ) y^{\prime }&=\left (2 x^{3}-y^{3}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
115.331 |
|
| \begin{align*}
x \left (x^{4}-2 y^{3}\right ) y^{\prime }+\left (2 x^{4}+y^{3}\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
16.693 |
|
| \begin{align*}
x \left (x +y+2 y^{3}\right ) y^{\prime }&=y \left (x -y\right ) \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
3.694 |
|
| \begin{align*}
\left (5 x -y-7 x y^{3}\right ) y^{\prime }+5 y-y^{4}&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✗ |
3.559 |
|
| \begin{align*}
x \left (1-2 x y^{3}\right ) y^{\prime }+\left (1-2 x^{3} y\right ) y&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
3.305 |
|
| \begin{align*}
x \left (2-x y^{2}-2 x y^{3}\right ) y^{\prime }+1+2 y&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
4.838 |
|
| \begin{align*}
\left (2-10 x^{2} y^{3}+3 y^{2}\right ) y^{\prime }&=x \left (1+5 y^{4}\right ) \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
3.268 |
|
| \begin{align*}
x \left (a +y^{3} b x \right ) y^{\prime }+\left (a +c \,x^{3} y\right ) y&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
3.504 |
|
| \begin{align*}
x \left (1-2 x^{2} y^{3}\right ) y^{\prime }+\left (1-2 x^{3} y^{2}\right ) y&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
3.101 |
|
| \begin{align*}
x \left (-y x +1\right ) \left (1-y^{2} x^{2}\right ) y^{\prime }+\left (y x +1\right ) \left (1+y^{2} x^{2}\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
0.705 |
|
| \begin{align*}
\left (x^{2}-y^{4}\right ) y^{\prime }&=y x \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
7.797 |
|
| \begin{align*}
\left (x^{3}-y^{4}\right ) y^{\prime }&=3 x^{2} y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
15.378 |
|
| \begin{align*}
\left (a^{2} x^{2}+\left (x^{2}+y^{2}\right )^{2}\right ) y^{\prime }&=a^{2} x y \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
8.076 |
|
| \begin{align*}
2 \left (x -y^{4}\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
7.016 |
|
| \begin{align*}
\left (4 x -x y^{3}-2 y^{4}\right ) y^{\prime }&=\left (2+y^{3}\right ) y \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
4.195 |
|
| \begin{align*}
\left (a \,x^{3}+\left (a x +b y\right )^{3}\right ) y y^{\prime }+x \left (\left (a x +b y\right )^{3}+y^{3} b \right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
52.038 |
|
| \begin{align*}
\left (x +2 y+2 x^{2} y^{3}+y^{4} x \right ) y^{\prime }+\left (1+y^{4}\right ) y&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
5.080 |
|
| \begin{align*}
2 x \left (x^{3}+y^{4}\right ) y^{\prime }&=\left (x^{3}+2 y^{4}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
8.789 |
|
| \begin{align*}
x \left (1-x^{2} y^{4}\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
7.791 |
|
| \begin{align*}
\left (x^{2}-y^{5}\right ) y^{\prime }&=2 y x \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
14.281 |
|
| \begin{align*}
x \left (x^{3}+y^{5}\right ) y^{\prime }&=\left (x^{3}-y^{5}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
12.989 |
|
| \begin{align*}
x^{3} \left (1+5 x^{3} y^{7}\right ) y^{\prime }+\left (3 x^{5} y^{5}-1\right ) y^{3}&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
3.343 |
|
| \begin{align*}
\left (1+a \left (x +y\right )\right )^{n} y^{\prime }+a \left (x +y\right )^{n}&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.647 |
|
| \begin{align*}
x \left (a +x y^{n}\right ) y^{\prime }+b y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
16.895 |
|
| \begin{align*}
f \left (x \right ) y^{m} y^{\prime }+g \left (x \right ) y^{m +1}+h \left (x \right ) y^{n}&=0 \\
\end{align*} |
[_Bernoulli] |
✗ |
✓ |
✓ |
✗ |
10.613 |
|
| \begin{align*}
y^{\prime } \sqrt {b^{2}+y^{2}}&=\sqrt {a^{2}+x^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.917 |
|
| \begin{align*}
y^{\prime } \sqrt {b^{2}-y^{2}}&=\sqrt {a^{2}-x^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.688 |
|
| \begin{align*}
\left (1+\sqrt {x +y}\right ) y^{\prime }+1&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.444 |
|
| \begin{align*}
y^{\prime } \sqrt {y x}+x -y&=\sqrt {y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
37.233 |
|
| \begin{align*}
\left (x -2 \sqrt {y x}\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
30.827 |
|
| \begin{align*}
\left (y+\sqrt {1+y^{2}}\right ) \left (x^{2}+1\right )^{{3}/{2}} y^{\prime }&=1+y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.655 |
|
| \begin{align*}
\left (y+\sqrt {1+y^{2}}\right ) \left (x^{2}+1\right )^{{3}/{2}} y^{\prime }&=1+y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.936 |
|
| \begin{align*}
\left (x -\sqrt {x^{2}+y^{2}}\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
29.894 |
|
| \begin{align*}
x \left (1-\sqrt {x^{2}-y^{2}}\right ) y^{\prime }&=y \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✗ |
4.625 |
|
| \begin{align*}
x \left (x +\sqrt {x^{2}+y^{2}}\right ) y^{\prime }+y \sqrt {x^{2}+y^{2}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
98.226 |
|
| \begin{align*}
x y \left (x +\sqrt {x^{2}-y^{2}}\right ) y^{\prime }&=x y^{2}-\left (x^{2}-y^{2}\right )^{{3}/{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
17.226 |
|
| \begin{align*}
\left (x \sqrt {1+x^{2}+y^{2}}-y \left (x^{2}+y^{2}\right )\right ) y^{\prime }&=\left (x^{2}+y^{2}\right ) x +y \sqrt {1+x^{2}+y^{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
7.107 |
|
| \begin{align*}
y^{\prime } \cos \left (y\right ) \left (\cos \left (y\right )-\sin \left (A \right ) \sin \left (x \right )\right )+\cos \left (x \right ) \left (\cos \left (x \right )-\sin \left (A \right ) \sin \left (y\right )\right )&=0 \\
\end{align*} |
unknown |
✓ |
✓ |
✓ |
✗ |
32.168 |
|
| \begin{align*}
\left (a \cos \left (a y+b x \right )-b \sin \left (a x +b y\right )\right ) y^{\prime }+b \cos \left (a y+b x \right )-a \sin \left (a x +b y\right )&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
4.157 |
|
| \begin{align*}
\left (x +\sec \left (y\right ) \cos \left (x \right )\right ) y^{\prime }+\tan \left (y\right )-y \sin \left (x \right ) \sec \left (y\right )&=0 \\
\end{align*} |
[NONE] |
✓ |
✓ |
✓ |
✗ |
43.583 |
|
| \begin{align*}
\left (1+\left (x +y\right ) \tan \left (y\right )\right ) y^{\prime }+1&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
4.211 |
|
| \begin{align*}
x \left (x -y \tan \left (\frac {y}{x}\right )\right ) y^{\prime }+\left (x +y \tan \left (\frac {y}{x}\right )\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
44.986 |
|
| \begin{align*}
\left ({\mathrm e}^{x}+x \,{\mathrm e}^{y}\right ) y^{\prime }+{\mathrm e}^{x} y+{\mathrm e}^{y}&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
3.280 |
|
| \begin{align*}
\left (1-2 x -\ln \left (y\right )\right ) y^{\prime }+2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.448 |
|
| \begin{align*}
\left (\sinh \left (x \right )+x \cosh \left (y\right )\right ) y^{\prime }+y \cosh \left (x \right )+\sinh \left (y\right )&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
31.337 |
|
| \begin{align*}
y^{\prime } \left (1+\sinh \left (x \right )\right ) \sinh \left (y\right )+\cosh \left (x \right ) \left (\cosh \left (y\right )-1\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.170 |
|
| \begin{align*}
{y^{\prime }}^{2}&=x^{n} a \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.716 |
|
| \begin{align*}
{y^{\prime }}^{2}&=y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.425 |
|
| \begin{align*}
{y^{\prime }}^{2}&=x -y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.160 |
|
| \begin{align*}
{y^{\prime }}^{2}&=y+x^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
26.244 |
|
| \begin{align*}
{y^{\prime }}^{2}+x^{2}&=4 y \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
17.007 |
|
| \begin{align*}
{y^{\prime }}^{2}+3 x^{2}&=8 y \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
34.604 |
|
| \begin{align*}
{y^{\prime }}^{2}+a \,x^{2}+b y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✗ |
✓ |
✗ |
43.559 |
|
| \begin{align*}
{y^{\prime }}^{2}&=1+y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.334 |
|
| \begin{align*}
{y^{\prime }}^{2}&=1-y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.781 |
|
| \begin{align*}
{y^{\prime }}^{2}&=a^{2}-y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.116 |
|
| \begin{align*}
{y^{\prime }}^{2}&=y^{2} a^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.496 |
|
| \begin{align*}
{y^{\prime }}^{2}&=a +b y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.782 |
|
| \begin{align*}
{y^{\prime }}^{2}&=y^{2} x^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.542 |
|
| \begin{align*}
{y^{\prime }}^{2}&=\left (-1+y\right ) y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
7.813 |
|
| \begin{align*}
{y^{\prime }}^{2}&=\left (y-a \right ) \left (y-b \right ) \left (y-c \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
176.541 |
|
| \begin{align*}
{y^{\prime }}^{2}&=a^{2} y^{n} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
17.640 |
|
| \begin{align*}
{y^{\prime }}^{2}&=a^{2} \left (1-\ln \left (y\right )^{2}\right ) y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.856 |
|
| \begin{align*}
{y^{\prime }}^{2}+f \left (x \right ) \left (y-a \right ) \left (y-b \right )&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
3.778 |
|
| \begin{align*}
{y^{\prime }}^{2}+f \left (x \right ) \left (y-a \right )^{2} \left (y-b \right )&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.298 |
|
| \begin{align*}
{y^{\prime }}^{2}+f \left (x \right ) \left (y-a \right ) \left (y-b \right ) \left (y-c \right )&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
3.103 |
|
| \begin{align*}
{y^{\prime }}^{2}+f \left (x \right ) \left (y-a \right )^{2} \left (y-b \right ) \left (y-c \right )&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
3.431 |
|
| \begin{align*}
{y^{\prime }}^{2}&=f \left (x \right )^{2} \left (y-a \right ) \left (y-b \right ) \left (y-c \right )^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.083 |
|
| \begin{align*}
{y^{\prime }}^{2}&=f \left (x \right )^{2} \left (y-u \left (x \right )\right )^{2} \left (y-a \right ) \left (y-b \right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
✗ |
19.012 |
|
| \begin{align*}
{y^{\prime }}^{2}+2 y^{\prime }+x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.411 |
|
| \begin{align*}
{y^{\prime }}^{2}-2 y^{\prime }+a \left (x -y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.801 |
|
| \begin{align*}
{y^{\prime }}^{2}-2 y^{\prime }-y^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
31.834 |
|
| \begin{align*}
{y^{\prime }}^{2}-5 y^{\prime }+6&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.337 |
|
| \begin{align*}
{y^{\prime }}^{2}-7 y^{\prime }+12&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.336 |
|
| \begin{align*}
{y^{\prime }}^{2}+a y^{\prime }+b&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.884 |
|
| \begin{align*}
{y^{\prime }}^{2}+a y^{\prime }+b x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.542 |
|
| \begin{align*}
{y^{\prime }}^{2}+a y^{\prime }+b y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.583 |
|
| \begin{align*}
{y^{\prime }}^{2}+y^{\prime } x +1&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.066 |
|
| \begin{align*}
{y^{\prime }}^{2}+y^{\prime } x -y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.560 |
|
| \begin{align*}
{y^{\prime }}^{2}-y^{\prime } x +y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| \begin{align*}
{y^{\prime }}^{2}-y^{\prime } x -y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.244 |
|
| \begin{align*}
{y^{\prime }}^{2}+y^{\prime } x +x -y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.838 |
|
| \begin{align*}
{y^{\prime }}^{2}+\left (1-x \right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.568 |
|
| \begin{align*}
{y^{\prime }}^{2}-\left (x +1\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.564 |
|
| \begin{align*}
{y^{\prime }}^{2}-\left (2-x \right ) y^{\prime }+1-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.584 |
|
| \begin{align*}
{y^{\prime }}^{2}+\left (a +x \right ) y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.617 |
|
| \begin{align*}
{y^{\prime }}^{2}-2 y^{\prime } x +1&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.036 |
|
| \begin{align*}
{y^{\prime }}^{2}+2 y^{\prime } x -3 x^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.402 |
|
| \begin{align*}
{y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.850 |
|
| \begin{align*}
{y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.734 |
|
| \begin{align*}
{y^{\prime }}^{2}-2 y^{\prime } x +2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.564 |
|
| \begin{align*}
{y^{\prime }}^{2}-\left (2 x +1\right ) y^{\prime }-x \left (1-x \right )&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.044 |
|
| \begin{align*}
{y^{\prime }}^{2}+2 \left (1-x \right ) y^{\prime }-2 x +2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.801 |
|