| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime }&=y-x^{2}+2 x \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.276 |
|
| \begin{align*}
y^{\prime }&=\frac {x -1}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.318 |
|
| \begin{align*}
y^{\prime }&=-\frac {y}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.619 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.283 |
|
| \begin{align*}
y^{\prime }&=\frac {y x}{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.390 |
|
| \begin{align*}
y^{\prime }&=x^{2}+y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
7.013 |
|
| \begin{align*}
y^{\prime }&=1+x y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
16.259 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x +1}-y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.208 |
|
| \begin{align*}
1+y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.927 |
|
| \begin{align*}
x y y^{\prime }+1+y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.523 |
|
| \begin{align*}
\left (y^{2}+x y^{2}\right ) y^{\prime }+x^{2}-x^{2} y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.982 |
|
| \begin{align*}
1+y^{2}&=x y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.199 |
|
| \begin{align*}
y y^{\prime } \sqrt {x^{2}+1}+x \sqrt {1+y^{2}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.672 |
|
| \begin{align*}
x \sqrt {1-y^{2}}+y \sqrt {-x^{2}+1}\, y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.687 |
|
| \begin{align*}
{\mathrm e}^{-y} \left (y^{\prime }+1\right )&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.058 |
|
| \begin{align*}
\ln \left (y\right ) y+x y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.901 |
|
| \begin{align*}
y^{\prime }&=a^{x +y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.707 |
|
| \begin{align*}
{\mathrm e}^{y} \left (x^{2}+1\right ) y^{\prime }-2 x \left (1+{\mathrm e}^{y}\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.813 |
|
| \begin{align*}
\left (1+{\mathrm e}^{x}\right ) y y^{\prime }&={\mathrm e}^{y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.408 |
|
| \begin{align*}
\left (1+y^{2}\right ) {\mathrm e}^{2 x}-\left (1+y^{2}\right ) {\mathrm e}^{y} y^{\prime }-\left (y+1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.449 |
|
| \begin{align*}
x y^{2}-y^{2}+x -1+\left (x^{2} y-2 y x +x^{2}+2 y-2 x +2\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.793 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x -y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.730 |
|
| \begin{align*}
y^{\prime }&=a x +b y+c \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.182 |
|
| \begin{align*}
\left (x +y\right )^{2} y^{\prime }&=a^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.751 |
|
| \begin{align*}
x -y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.328 |
|
| \begin{align*}
1+y^{2}&=\left (y-\sqrt {1+y^{2}}\right ) \left (x^{2}+1\right )^{{3}/{2}} y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.992 |
|
| \begin{align*}
x y^{2} \left (x y^{\prime }+y\right )&=a^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.040 |
|
| \begin{align*}
x^{2} y^{2}+1+2 x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✓ |
2.877 |
|
| \begin{align*}
\left (x^{3} y^{3}+x^{2} y^{2}+y x +1\right ) y+\left (x^{3} y^{3}-x^{2} y^{2}-y x +1\right ) x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
0.634 |
|
| \begin{align*}
x^{2} y^{3}+y+x -2+\left (x +x^{3} y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
2.320 |
|
| \begin{align*}
x^{6}-2 x^{5}+2 x^{4}-y^{3}+4 x^{2} y+\left (x y^{2}-4 x^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational] |
✓ |
✓ |
✓ |
✗ |
3.895 |
|
| \begin{align*}
y^{\prime }+1&=\frac {\left (x +y\right )^{m}}{\left (x +y\right )^{n}+\left (x +y\right )^{p}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.855 |
|
| \begin{align*}
\ln \left (x \right )+y^{3}-3 x y^{2} y^{\prime }&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.169 |
|
| \begin{align*}
y x +2 x y \ln \left (y\right )^{2}+\ln \left (y\right ) y+\left (2 x^{2} \ln \left (y\right )+x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
3.426 |
|
| \begin{align*}
-x y^{\prime }+y&=a \left (1+x^{2} y^{\prime }\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.124 |
|
| \begin{align*}
a^{2}+y^{2}+2 x \sqrt {a x -x^{2}}\, y^{\prime }&=0 \\
y \left (a \right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
6.431 |
|
| \begin{align*}
y^{\prime }+\sin \left (\frac {x}{2}+\frac {y}{2}\right )&=\sin \left (\frac {x}{2}-\frac {y}{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.744 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
2.325 |
|
| \begin{align*}
y^{\prime }&=y^{a} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✗ |
6.056 |
|
| \begin{align*}
y^{\prime }+y \tan \left (x \right )&=x \tan \left (x \right )+1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.468 |
|
| \begin{align*}
\cos \left (y^{\prime }\right )&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.644 |
|
| \begin{align*}
{\mathrm e}^{y^{\prime }}&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.404 |
|
| \begin{align*}
\sin \left (y^{\prime }\right )&=x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.241 |
|
| \begin{align*}
\ln \left (y^{\prime }\right )&=x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.312 |
|
| \begin{align*}
\tan \left (y^{\prime }\right )&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.438 |
|
| \begin{align*}
{\mathrm e}^{y^{\prime }}&=x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.217 |
|
| \begin{align*}
\tan \left (y^{\prime }\right )&=x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.273 |
|
| \begin{align*}
x^{2} \cos \left (y\right ) y^{\prime }+1&=0 \\
y \left (\infty \right ) &= 2 \pi \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✗ |
3.743 |
|
| \begin{align*}
x^{2} y^{\prime }+\cos \left (2 y\right )&=1 \\
y \left (\infty \right ) &= \frac {5 \pi }{4} \\
\end{align*} |
[_separable] |
✗ |
✓ |
✗ |
✗ |
9.183 |
|
| \begin{align*}
x^{3} y^{\prime }-\cos \left (y\right )&=1 \\
y \left (\infty \right ) &= 5 \pi \\
\end{align*} |
[_separable] |
✓ |
✗ |
✗ |
✗ |
9.174 |
|
| \begin{align*}
2 \left (x^{2}+1\right ) y^{\prime }-\cos \left (2 y\right )^{2}&=0 \\
y \left (-\infty \right ) &= \frac {7 \pi }{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✗ |
4.450 |
|
| \begin{align*}
{\mathrm e}^{y}&={\mathrm e}^{4 y} y^{\prime }+1 \\
y \left (\infty \right ) &= y_{0} \\
\end{align*} |
[_quadrature] |
✓ |
✗ |
✗ |
✗ |
2.366 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }&=-1+y \\
y \left (\infty \right ) &= y_{0} \\
\end{align*} |
[_separable] |
✗ |
✓ |
✗ |
✓ |
6.156 |
|
| \begin{align*}
y^{\prime }&=2 x \left (\pi +y\right ) \\
y \left (\infty \right ) &= y_{0} \\
\end{align*} |
[_separable] |
✗ |
✓ |
✗ |
✓ |
7.970 |
|
| \begin{align*}
x^{2} y^{\prime }+\sin \left (2 y\right )&=1 \\
y \left (\infty \right ) &= \frac {11 \pi }{4} \\
\end{align*} |
[_separable] |
✗ |
✓ |
✗ |
✓ |
20.300 |
|
| \begin{align*}
4 x -3 y+\left (-3 x +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.563 |
|
| \begin{align*}
x y^{\prime }&=y+\sqrt {y^{2}-x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
7.069 |
|
| \begin{align*}
4 x^{2}-y x +y^{2}+y^{\prime } \left (x^{2}-y x +4 y^{2}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
12.755 |
|
| \begin{align*}
4 x^{2}+y x -3 y^{2}+y^{\prime } \left (-5 x^{2}+2 y x +y^{2}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
18.140 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x y}{3 x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
7.879 |
|
| \begin{align*}
2 x \left (x^{2}+y^{2}\right ) y^{\prime }&=\left (2 x^{2}+y^{2}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
9.559 |
|
| \begin{align*}
x y^{\prime }&=\sqrt {y^{2}-x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
17.296 |
|
| \begin{align*}
a \,x^{2}+2 b x y+c y^{2}+y^{\prime } \left (b \,x^{2}+2 c x y+f y^{2}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
124.392 |
|
| \begin{align*}
\left (y^{4}-3 x^{2}\right ) y^{\prime }&=-y x \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
6.483 |
|
| \begin{align*}
y^{3}+2 \left (x^{2}-x y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
4.953 |
|
| \begin{align*}
\left (-x y^{\prime }+y\right )^{2}&=x^{2}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.296 |
|
| \begin{align*}
3 x +y-2+\left (x -1\right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.775 |
|
| \begin{align*}
2 x +2 y-1+\left (x +y-2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.709 |
|
| \begin{align*}
3 y-7 x +7-\left (3 x -7 y-3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
58.395 |
|
| \begin{align*}
y+y \sqrt {x^{2} y^{4}+1}+2 x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
4.914 |
|
| \begin{align*}
4 x y^{2}+\left (3 x^{2} y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
18.910 |
|
| \begin{align*}
x +y^{3}+\left (3 y^{5}-3 x y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
9.395 |
|
| \begin{align*}
2 x^{2} y+2 \sqrt {1+y^{2} x^{4}}+x^{3} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
6.624 |
|
| \begin{align*}
\cos \left (x \right ) y+\left (2 y-\sin \left (x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.667 |
|
| \begin{align*}
x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
14.622 |
|
| \begin{align*}
y^{3} y^{\prime }+3 x y^{2}+2 x^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.871 |
|
| \begin{align*}
\left (2 \sqrt {y x}-x \right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.074 |
|
| \begin{align*}
2 y+y^{\prime }&=x^{2}+2 x \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.099 |
|
| \begin{align*}
\left (x^{2}+2 x -1\right ) y^{\prime }-\left (x +1\right ) y&=x -1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.085 |
|
| \begin{align*}
x \ln \left (x \right ) y^{\prime }-y&=x^{3} \left (3 \ln \left (x \right )-1\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.652 |
|
| \begin{align*}
\left (a^{2}-x^{2}\right ) y^{\prime }+y x&=a^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.310 |
|
| \begin{align*}
2 x y^{\prime }-y&=3 x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.082 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }-\left (x +1\right )^{4}-2 y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.720 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{\sin \left (y\right ) x +2 \sin \left (2 y\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✗ |
2.536 |
|
| \begin{align*}
y^{\prime }-2 y x&=2 x \,{\mathrm e}^{x^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.447 |
|
| \begin{align*}
\left (x^{3}+1\right ) x y^{\prime }+\left (2 x^{3}-1\right ) y&=\frac {x^{3}-2}{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.137 |
|
| \begin{align*}
y^{\prime }+\cos \left (x \right ) y&=\sin \left (x \right ) \cos \left (x \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.515 |
|
| \begin{align*}
x \ln \left (x \right ) y^{\prime }-\left (1+\ln \left (x \right )\right ) y+\frac {\sqrt {x}\, \left (2+\ln \left (x \right )\right )}{2}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.204 |
|
| \begin{align*}
3 x y^{\prime }-2 y&=\frac {x^{3}}{y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.157 |
|
| \begin{align*}
8 x y^{\prime }-y&=-\frac {1}{y^{3} \sqrt {x +1}} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.224 |
|
| \begin{align*}
\left (x^{2} y^{3}+y x \right ) y^{\prime }&=1 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
2.170 |
|
| \begin{align*}
x^{2} y^{\prime }+2 x^{3} y&=y^{2} \left (x^{3}+1\right ) \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.162 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x y}{-y^{2}-a^{2}+x^{2}} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
5.010 |
|
| \begin{align*}
2 \sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y&=y^{3} \left (x \cos \left (x \right )-\sin \left (x \right )\right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.665 |
|
| \begin{align*}
y^{\prime }&=\frac {3 x^{2}}{1+x^{3}+y} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
2.457 |
|
| \begin{align*}
y^{\prime }+\frac {y \left (x +\frac {1}{2}\right )}{x^{2}+x +1}&=\frac {\left (-x^{2}+1\right ) y^{2}}{\left (x^{2}+x +1\right )^{{3}/{2}}} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
28.355 |
|
| \begin{align*}
3 y^{\prime }+\frac {y \left (a^{2}+x^{2}\right )}{x \left (-a^{2}+x^{2}\right )}&=\frac {x \left (-a^{2}+3 x^{2}\right )}{y^{2} \left (-a^{2}+x^{2}\right )} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.866 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=x^{2} y^{2}+y x \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.906 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x +1}&=-\frac {\left (x +1\right )^{3} y^{3}}{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.799 |
|
| \begin{align*}
\left (1+x^{2}+y^{2}\right ) y^{\prime }+y x&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
1.788 |
|