| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
\cot \left (x \right ) y^{\prime }+y&=\tan \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.180 |
|
| \begin{align*}
\tan \left (x \right ) y^{\prime }+y&=\cot \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.147 |
|
| \begin{align*}
\tan \left (x \right ) y^{\prime }&=y-\cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.709 |
|
| \begin{align*}
y^{\prime }+\cos \left (x \right ) y&=\sin \left (2 x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.072 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime }+y&=\sin \left (2 x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.041 |
|
| \begin{align*}
y^{\prime }+\sin \left (x \right ) y&=\sin \left (2 x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
2.066 |
|
| \begin{align*}
\sin \left (x \right ) y^{\prime }+y&=\sin \left (2 x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
2.958 |
|
| \begin{align*}
\sqrt {x^{2}+1}\, y^{\prime }+y&=2 x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.044 |
|
| \begin{align*}
\sqrt {x^{2}+1}\, y^{\prime }-y&=2 \sqrt {x^{2}+1} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.364 |
|
| \begin{align*}
\sqrt {\left (a +x \right ) \left (x +b \right )}\, \left (2 y^{\prime }-3\right )+y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
4.353 |
|
| \begin{align*}
\sqrt {\left (a +x \right ) \left (x +b \right )}\, y^{\prime }+y&=\sqrt {a +x}-\sqrt {x +b} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
4.977 |
|
| \begin{align*}
3 y^{2} y^{\prime }&=2 x -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.040 |
|
| \begin{align*}
y^{\prime }&=6 x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.895 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{y} \sin \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.705 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x -y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.403 |
|
| \begin{align*}
y^{\prime }&=x \sec \left (y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.559 |
|
| \begin{align*}
y^{\prime }&=3 \cos \left (y\right )^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.500 |
|
| \begin{align*}
y^{\prime } x&=y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.709 |
|
| \begin{align*}
\left (1-x \right ) y^{\prime }&=y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.634 |
|
| \begin{align*}
y^{\prime }&=\frac {4 x y}{x^{2}+1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.827 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y}{x^{2}-1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.832 |
|
| \begin{align*}
x^{2} y^{\prime }-y^{2}&=0 \\
y \left (1\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.309 |
|
| \begin{align*}
y^{\prime }+2 y x&=0 \\
y \left (0\right ) &= 5 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.976 |
|
| \begin{align*}
\cot \left (x \right ) y^{\prime }&=y \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.290 |
|
| \begin{align*}
y^{\prime }&=x \,{\mathrm e}^{-2 y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.484 |
|
| \begin{align*}
y^{\prime }-2 y x&=2 x \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.867 |
|
| \begin{align*}
y^{\prime } x&=y x +y \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.220 |
|
| \begin{align*}
\left (x^{3}+1\right ) y^{\prime }&=3 x^{2} \tan \left (x \right ) \\
y \left (0\right ) &= \frac {\pi }{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.604 |
|
| \begin{align*}
x \cos \left (y\right ) y^{\prime }&=1+\sin \left (y\right ) \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.417 |
|
| \begin{align*}
y^{\prime } x&=2 y \left (-1+y\right ) \\
y \left (\frac {1}{2}\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.005 |
|
| \begin{align*}
2 y^{\prime } x&=1-y^{2} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.997 |
|
| \begin{align*}
\left (1-x \right ) y^{\prime }&=y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.098 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }&=\left (x^{2}+1\right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.389 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x} \left (1+y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.843 |
|
| \begin{align*}
{\mathrm e}^{y} y^{\prime }+2 x&=2 x \,{\mathrm e}^{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.038 |
|
| \begin{align*}
y \,{\mathrm e}^{2 x} y^{\prime }+2 x&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.212 |
|
| \begin{align*}
y y^{\prime } x&=\sqrt {y^{2}-9} \\
y \left ({\mathrm e}^{4}\right ) &= 5 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
4.898 |
|
| \begin{align*}
\left (x +y-1\right ) y^{\prime }&=x -y+1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.794 |
|
| \begin{align*}
y y^{\prime } x&=2 x^{2}-y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.118 |
|
| \begin{align*}
x^{2}-y^{2}+y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.875 |
|
| \begin{align*}
x^{2} y^{\prime }-2 y x -2 y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.823 |
|
| \begin{align*}
x^{2} y^{\prime }&=3 \left (x^{2}+y^{2}\right ) \arctan \left (\frac {y}{x}\right )+y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
8.901 |
|
| \begin{align*}
x \sin \left (\frac {y}{x}\right ) y^{\prime }&=y \sin \left (\frac {y}{x}\right )+x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.464 |
|
| \begin{align*}
y^{\prime } x&=y+2 \,{\mathrm e}^{-\frac {y}{x}} \\
\end{align*} |
[[_homogeneous, ‘class D‘]] |
✓ |
✓ |
✓ |
✓ |
2.962 |
|
| \begin{align*}
y^{\prime }&=\left (x +y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
1.286 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x -y+1\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.122 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y+4}{x -y-6} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.815 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y+4}{x +y-6} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.453 |
|
| \begin{align*}
\left (x +\frac {2}{y}\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
4.982 |
|
| \begin{align*}
\sin \left (x \right ) \tan \left (y\right )+1+\cos \left (x \right ) \sec \left (y\right )^{2} y^{\prime }&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✗ |
✓ |
✗ |
68.421 |
|
| \begin{align*}
y-x^{3}+\left (y^{3}+x \right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
1.684 |
|
| \begin{align*}
2 y^{2}-4 x +5&=\left (4-2 y+4 y x \right ) y^{\prime } \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
✗ |
16.155 |
|
| \begin{align*}
y+y \cos \left (y x \right )+\left (x +x \cos \left (y x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.102 |
|
| \begin{align*}
\cos \left (x \right ) \cos \left (y\right )^{2}+2 \sin \left (x \right ) \sin \left (y\right ) \cos \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.303 |
|
| \begin{align*}
\left (\sin \left (x \right ) \sin \left (y\right )-x \,{\mathrm e}^{y}\right ) y^{\prime }&={\mathrm e}^{y}+\cos \left (x \right ) \cos \left (y\right ) \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
38.158 |
|
| \begin{align*}
-\frac {\sin \left (\frac {x}{y}\right )}{y}+\frac {x \sin \left (\frac {x}{y}\right ) y^{\prime }}{y^{2}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.378 |
|
| \begin{align*}
1+y+\left (1-x \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.960 |
|
| \begin{align*}
2 x y^{3}+\cos \left (x \right ) y+\left (3 y^{2} x^{2}+\sin \left (x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
66.661 |
|
| \begin{align*}
1&=\frac {y}{1-y^{2} x^{2}}+\frac {x y^{\prime }}{1-y^{2} x^{2}} \\
\end{align*} |
[_exact, _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.621 |
|
| \begin{align*}
\left (3 x^{2}-y^{2}\right ) y^{\prime }-2 y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.756 |
|
| \begin{align*}
y x -1+\left (x^{2}-y x \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
1.680 |
|
| \begin{align*}
\left (x +3 y^{4} x^{3}\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
3.800 |
|
| \begin{align*}
\left (x -1-y^{2}\right ) y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✓ |
1.917 |
|
| \begin{align*}
y-\left (x +x y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.062 |
|
| \begin{align*}
y^{\prime } x&=x^{5}+x^{3} y^{2}+y \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
2.212 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }&=-x +y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.306 |
|
| \begin{align*}
y^{\prime } x&=y+x^{2}+9 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
1.239 |
|
| \begin{align*}
y^{\prime } x -3 y&=x^{4} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.186 |
|
| \begin{align*}
y^{\prime }+y&=\frac {1}{{\mathrm e}^{2 x}+1} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.985 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+2 y x&=\cot \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.993 |
|
| \begin{align*}
y^{\prime }+y&=2 x \,{\mathrm e}^{-x}+x^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.655 |
|
| \begin{align*}
y^{\prime }+\cot \left (x \right ) y&=2 x \csc \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.802 |
|
| \begin{align*}
2 y-x^{3}&=y^{\prime } x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.163 |
|
| \begin{align*}
\left (-y x +1\right ) y^{\prime }&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
4.477 |
|
| \begin{align*}
2 x +3 y+1+\left (2 y-3 x +5\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.230 |
|
| \begin{align*}
y^{\prime } x&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
11.802 |
|
| \begin{align*}
y^{2}&=\left (x^{3}-y x \right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
4.266 |
|
| \begin{align*}
x^{2} y^{3}+y&=\left (x^{3} y^{2}-x \right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
3.735 |
|
| \begin{align*}
y^{\prime } x +y&=\cos \left (x \right ) x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.666 |
|
| \begin{align*}
\left (y x -x^{2}\right ) y^{\prime }&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
8.500 |
|
| \begin{align*}
\left ({\mathrm e}^{x}-3 y^{2} x^{2}\right ) y^{\prime }+{\mathrm e}^{x} y&=2 x y^{3} \\
\end{align*} |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
2.909 |
|
| \begin{align*}
y+x^{2}&=y^{\prime } x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.247 |
|
| \begin{align*}
y^{\prime } x +y&=\cos \left (x \right ) x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.932 |
|
| \begin{align*}
6 x +4 y+3+\left (3 x +2 y+2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.822 |
|
| \begin{align*}
\cos \left (x +y\right )-x \sin \left (x +y\right )&=x \sin \left (x +y\right ) y^{\prime } \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _exact] |
✓ |
✓ |
✓ |
✓ |
3.336 |
|
| \begin{align*}
y^{2} {\mathrm e}^{y x}+\cos \left (x \right )+\left ({\mathrm e}^{y x}+x y \,{\mathrm e}^{y x}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
61.951 |
|
| \begin{align*}
y^{\prime } \ln \left (x -y\right )&=1+\ln \left (x -y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.682 |
|
| \begin{align*}
y^{\prime }+2 y x&={\mathrm e}^{-x^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.218 |
|
| \begin{align*}
y^{2}-3 y x -2 x^{2}&=\left (x^{2}-y x \right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
6.060 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+2 y x&=4 x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.264 |
|
| \begin{align*}
{\mathrm e}^{x} \sin \left (y\right )-y \sin \left (y x \right )+\left ({\mathrm e}^{x} \cos \left (y\right )-x \sin \left (y x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
5.330 |
|
| \begin{align*}
\left (x \,{\mathrm e}^{y}+y-x^{2}\right ) y^{\prime }&=2 y x -{\mathrm e}^{y}-x \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
2.479 |
|
| \begin{align*}
{\mathrm e}^{x} \left (x +1\right )&=\left (x \,{\mathrm e}^{x}-{\mathrm e}^{y} y\right ) y^{\prime } \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✓ |
2.382 |
|
| \begin{align*}
x^{2} y^{\prime }+2 y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.360 |
|
| \begin{align*}
x +y+\left (x -y\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.967 |
|
| \begin{align*}
\ln \left (x \right ) y^{\prime }+\frac {x +y}{x}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.725 |
|
| \begin{align*}
\cos \left (y\right )-x \sin \left (y\right ) y^{\prime }&=\sec \left (x \right )^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✗ |
✗ |
71.793 |
|
| \begin{align*}
y \sin \left (\frac {x}{y}\right )+x \cos \left (\frac {x}{y}\right )-1+\left (x \sin \left (\frac {x}{y}\right )-\frac {x^{2} \cos \left (\frac {x}{y}\right )}{y}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
3.811 |
|
| \begin{align*}
\frac {x}{x^{2}+y^{2}}+\frac {y}{x^{2}}+\left (\frac {y}{x^{2}+y^{2}}-\frac {1}{x}\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.347 |
|
| \begin{align*}
x^{2} \left (1+y^{2}\right ) y^{\prime }+y^{2} \left (x^{2}+1\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.283 |
|