| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime }&=\frac {x^{2}}{2}+\frac {y^{2}}{2}-1 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
49.588 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=y-2 x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.034 |
|
| \begin{align*}
y y^{\prime }+x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.293 |
|
| \begin{align*}
x y^{\prime }&=2 y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.468 |
|
| \begin{align*}
x y^{\prime }+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.148 |
|
| \begin{align*}
y^{\prime }+1&=2 \left (-x +y\right ) \left (y^{\prime }-1\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.418 |
|
| \begin{align*}
\left (1+y^{2}\right ) y^{\prime }+x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.746 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.177 |
|
| \begin{align*}
y^{\prime }&=\frac {y-3 x}{x +3 y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.222 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x +y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.907 |
|
| \begin{align*}
x^{2}+y^{2} y^{\prime }&=1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.113 |
|
| \begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime }&=4 x \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
1.757 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }+y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.802 |
|
| \begin{align*}
\sqrt {1+y^{2}}&=x y y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.031 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }+2 x y^{2}&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.161 |
|
| \begin{align*}
\cot \left (x \right ) y^{\prime }+y&=2 \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.824 |
|
| \begin{align*}
y^{\prime }&=3 y^{{2}/{3}} \\
y \left (2\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.529 |
|
| \begin{align*}
x y^{\prime }+y&=y^{2} \\
y \left (1\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.440 |
|
| \begin{align*}
2 x^{2} y y^{\prime }+y^{2}&=2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.301 |
|
| \begin{align*}
y^{\prime }-x y^{2}&=2 y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.710 |
|
| \begin{align*}
{\mathrm e}^{-s} \left (1+s^{\prime }\right )&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.966 |
|
| \begin{align*}
z^{\prime }&=10^{x +z} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.804 |
|
| \begin{align*}
x x^{\prime }+t&=1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.460 |
|
| \begin{align*}
y^{\prime }&=\cos \left (x -y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.441 |
|
| \begin{align*}
y^{\prime }-y&=2 x -3 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.070 |
|
| \begin{align*}
\left (x +2 y\right ) y^{\prime }&=1 \\
y \left (0\right ) &= -1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
7.999 |
|
| \begin{align*}
y^{\prime }&=\sqrt {4 x +2 y-1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.986 |
|
| \begin{align*}
x^{2} y^{\prime }-2 \cos \left (2 y\right )&=1 \\
y \left (\infty \right ) &= \frac {9 \pi }{4} \\
\end{align*} |
[_separable] |
✗ |
✓ |
✗ |
✓ |
26.970 |
|
| \begin{align*}
3 y^{2} y^{\prime }+16 x&=2 x y^{3} \\
y \left (\infty \right ) &= y_{0} \\
\end{align*} |
[_separable] |
✗ |
✓ |
✗ |
✗ |
19.071 |
|
| \begin{align*}
y^{\prime }&=\left (\frac {1+y^{2}}{x^{4}+1}\right )^{{1}/{3}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
3.185 |
|
| \begin{align*}
y^{\prime }&=\sqrt {\frac {\ln \left (y+1\right )}{\sin \left (x \right )}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
10.690 |
|
| \begin{align*}
x +2 y-x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.779 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }+x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.902 |
|
| \begin{align*}
y^{2}-2 y x +x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.074 |
|
| \begin{align*}
2 x^{3} y^{\prime }&=\left (2 x^{2}-y^{2}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
138.127 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}&=x y y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
10.556 |
|
| \begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime }&=2 y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
16.550 |
|
| \begin{align*}
x y^{\prime }-y&=x \tan \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
9.446 |
|
| \begin{align*}
x y^{\prime }&=y-{\mathrm e}^{\frac {y}{x}} x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
41.047 |
|
| \begin{align*}
x y^{\prime }-y&=\left (x +y\right ) \ln \left (\frac {x +y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.814 |
|
| \begin{align*}
x y^{\prime }&=y \cos \left (\ln \left (\frac {y}{x}\right )\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✗ |
✓ |
✓ |
863.770 |
|
| \begin{align*}
y+\sqrt {y x}&=x y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
8.526 |
|
| \begin{align*}
x y^{\prime }&=y+\sqrt {x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
23.101 |
|
| \begin{align*}
2 x -4 y+1+\left (-3+x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
20.234 |
|
| \begin{align*}
2 x +y+1-\left (4 x +2 y-3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.005 |
|
| \begin{align*}
x -y-1+\left (y-x +2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.279 |
|
| \begin{align*}
\left (x +4 y\right ) y^{\prime }&=2 x +3 y-5 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
33.993 |
|
| \begin{align*}
y+2&=\left (2 x +y-4\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.506 |
|
| \begin{align*}
y^{\prime }&=\frac {2 \left (y+2\right )^{2}}{\left (x +y-1\right )^{2}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
✓ |
✓ |
✗ |
4.654 |
|
| \begin{align*}
\left (y^{\prime }+1\right ) \ln \left (\frac {x +y}{x +3}\right )&=\frac {x +y}{x +3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
34.667 |
|
| \begin{align*}
y^{\prime }&=\frac {y+2}{x +1}+\tan \left (\frac {y-2 x}{x +1}\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
8.752 |
|
| \begin{align*}
x^{3} \left (y^{\prime }-x \right )&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
3.253 |
|
| \begin{align*}
2 x^{2} y^{\prime }&=y^{3}+y x \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.151 |
|
| \begin{align*}
2 x y^{\prime }+\left (x^{2} y^{4}+1\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.886 |
|
| \begin{align*}
y+x \left (1+2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
23.783 |
|
| \begin{align*}
2 y^{\prime }+x&=4 \sqrt {y} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Chini] |
✓ |
✓ |
✓ |
✗ |
5.768 |
|
| \begin{align*}
y^{\prime }&=y^{2}-\frac {2}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✓ |
5.911 |
|
| \begin{align*}
2 x y^{\prime }+y&=y^{2} \sqrt {x -x^{2} y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
8.512 |
|
| \begin{align*}
\frac {2 x y y^{\prime }}{3}&=\sqrt {x^{6}-y^{4}}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
17.480 |
|
| \begin{align*}
2 y+\left (x^{2} y+1\right ) x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
16.661 |
|
| \begin{align*}
x y^{\prime }-2 y&=2 x^{4} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.343 |
|
| \begin{align*}
\left (2 x +1\right ) y^{\prime }&=4 x +2 y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.897 |
|
| \begin{align*}
y^{\prime }+y \tan \left (x \right )&=\sec \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.593 |
|
| \begin{align*}
x \left (y^{\prime }-y\right )&={\mathrm e}^{x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.826 |
|
| \begin{align*}
x^{2} y^{\prime }+y x +1&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.379 |
|
| \begin{align*}
y&=x \left (y^{\prime }-x \cos \left (x \right )\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.769 |
|
| \begin{align*}
y^{\prime }&=2 x \left (x^{2}+y\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.652 |
|
| \begin{align*}
\left (x y^{\prime }-1\right ) \ln \left (x \right )&=2 y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.369 |
|
| \begin{align*}
x y^{\prime }+\left (x +1\right ) y&=3 x^{2} {\mathrm e}^{-x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.153 |
|
| \begin{align*}
\left (x +y^{2}\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
2.286 |
|
| \begin{align*}
\left (2 \,{\mathrm e}^{y}-x \right ) y^{\prime }&=1 \\
\end{align*} |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.608 |
|
| \begin{align*}
\left (\sin \left (y\right )^{2}+x \cot \left (y\right )\right ) y^{\prime }&=1 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✗ |
2.444 |
|
| \begin{align*}
\left (2 x +y\right ) y^{\prime }&=y+4 \ln \left (y\right ) y^{\prime } \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.982 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{3 x -y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
3.349 |
|
| \begin{align*}
\left (1-2 y x \right ) y^{\prime }&=y \left (-1+y\right ) \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
5.463 |
|
| \begin{align*}
2 y+y^{\prime }&=y^{2} {\mathrm e}^{x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.178 |
|
| \begin{align*}
\left (x +1\right ) \left (y^{\prime }+y^{2}\right )&=-y \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.639 |
|
| \begin{align*}
y^{\prime }&=y^{4} \cos \left (x \right )+y \tan \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.320 |
|
| \begin{align*}
x y^{2} y^{\prime }&=x^{2}+y^{3} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.778 |
|
| \begin{align*}
x y y^{\prime }&=x +y^{2} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.394 |
|
| \begin{align*}
x y^{\prime }-2 x^{2} \sqrt {y}&=4 y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.726 |
|
| \begin{align*}
x y^{\prime }+2 y+x^{5} y^{3} {\mathrm e}^{x}&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.951 |
|
| \begin{align*}
2 y^{\prime }-\frac {x}{y}&=\frac {x y}{x^{2}-1} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.331 |
|
| \begin{align*}
y^{\prime } x^{3} \sin \left (y\right )&=x y^{\prime }-2 y \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
1.960 |
|
| \begin{align*}
\left (2 x^{2} y \ln \left (y\right )-x \right ) y^{\prime }&=y \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
3.086 |
|
| \begin{align*}
x&=\left (x^{2}-2 y+1\right ) y^{\prime } \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
1.877 |
|
| \begin{align*}
\left (x +1\right ) \left (y y^{\prime }-1\right )&=y^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.611 |
|
| \begin{align*}
x \left ({\mathrm e}^{y}-y^{\prime }\right )&=2 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.834 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime } \sin \left (y\right )+2 x \cos \left (y\right )&=-2 x^{3}+2 x \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✓ |
3.731 |
|
| \begin{align*}
x^{2} y^{\prime }+y x +x^{2} y^{2}&=4 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.691 |
|
| \begin{align*}
3 y^{\prime }+y^{2}+\frac {2}{x^{2}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✓ |
3.141 |
|
| \begin{align*}
x y^{\prime }-\left (2 x +1\right ) y+y^{2}&=-x^{2} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
1.292 |
|
| \begin{align*}
y^{\prime }-2 y x +y^{2}&=-x^{2}+5 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
6.125 |
|
| \begin{align*}
y^{\prime }+2 y \,{\mathrm e}^{x}-y^{2}&={\mathrm e}^{x}+{\mathrm e}^{2 x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
10.431 |
|
| \begin{align*}
y^{\prime } \sin \left (2 x \right )&=2 y+2 \cos \left (x \right ) \\
y \left (\frac {\pi }{2}\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✗ |
✓ |
✗ |
14.400 |
|
| \begin{align*}
x^{\prime }+x&=f \left (t \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.580 |
|
| \begin{align*}
x^{\prime }+a \left (t \right ) x&=f \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.749 |
|
| \begin{align*}
x^{\prime }+a \left (t \right ) x&=f \left (t \right ) \\
x \left (0\right ) &= b \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.806 |
|
| \begin{align*}
x y^{\prime }-\left (2 x^{2}+1\right ) y&=x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.529 |
|
| \begin{align*}
2 y x +\left (x^{2}-y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
54.755 |
|