| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
2 x y \cos \left (x^{2}\right )-2 y x +1+\left (\sin \left (x^{2}\right )-x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.239 |
|
| \begin{align*}
2 x -3 y+\left (-3 x +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
28.841 |
|
| \begin{align*}
x y^{2}+y-x +x \left (y x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
11.410 |
|
| \begin{align*}
3 \left (x^{2}-1\right ) y+\left (x^{3}+8 y-3 x \right ) y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.043 |
|
| \begin{align*}
\frac {1}{\left (-y x +1\right )^{2}}+\left (y^{2}+\frac {x^{2}}{\left (-y x +1\right )^{2}}\right ) y^{\prime }&=0 \\
y \left (4\right ) &= 1 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✗ |
✗ |
7.152 |
|
| \begin{align*}
y \,{\mathrm e}^{y x}-2 y^{3}+\left (x \,{\mathrm e}^{y x}-6 x y^{2}-2 y\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
6.270 |
|
| \begin{align*}
y \left (2 y x +1\right )-y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.782 |
|
| \begin{align*}
y \left (y^{3}-x \right )+x \left (y^{3}+x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
11.479 |
|
| \begin{align*}
x^{3} y^{3}+1+x^{4} y^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.411 |
|
| \begin{align*}
s \left (2+s^{2} t \right )+2 t s^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.951 |
|
| \begin{align*}
y \left (x^{4}-y^{2}\right )+x \left (x^{4}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
9.690 |
|
| \begin{align*}
y \left (1+y^{2}\right )+x \left (-1+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.691 |
|
| \begin{align*}
\left (x^{3}-y^{5}\right ) y-x \left (x^{3}+y^{5}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
10.487 |
|
| \begin{align*}
\left (1+x^{2}-y^{2}\right ) y-x \left (x^{2}-y^{2}-1\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
10.340 |
|
| \begin{align*}
x^{3}+x y^{2}+y+\left (x^{2} y+y^{3}+x \right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
3.976 |
|
| \begin{align*}
y \left (x^{2}+y^{2}-1\right )+x \left (1+x^{2}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
3.798 |
|
| \begin{align*}
x^{3}+x y^{2}-y+\left (x^{2} y+y^{3}+x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✗ |
4.851 |
|
| \begin{align*}
y \left (x^{3} {\mathrm e}^{y x}-y\right )+x \left (y+x^{3} {\mathrm e}^{y x}\right ) y^{\prime }&=0 \\
\end{align*} |
[NONE] |
✓ |
✓ |
✓ |
✗ |
5.158 |
|
| \begin{align*}
x y \left (1+y^{2}\right )+\left (y^{2} x^{2}-2\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
4.791 |
|
| \begin{align*}
y^{2} \left (-x^{2}+1\right )+x \left (y^{2} x^{2}+2 x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
✗ |
19.808 |
|
| \begin{align*}
y \left (y^{2} x^{2}-1\right )+x \left (x^{2} y+2 x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✗ |
✗ |
✗ |
✗ |
109.472 |
|
| \begin{align*}
x^{4} y^{\prime }&=-x^{3} y-\csc \left (y x \right ) \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
5.476 |
|
| \begin{align*}
1+y \tan \left (y x \right )+x \tan \left (y x \right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
5.366 |
|
| \begin{align*}
y \left (y^{2} x^{2}-m \right )+x \left (y^{2} x^{2}+n \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
10.863 |
|
| \begin{align*}
x \left (x^{2}-y^{2}-x \right )-y \left (x^{2}-y^{2}\right ) y^{\prime }&=0 \\
y \left (2\right ) &= 0 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
4.556 |
|
| \begin{align*}
y \left (y+x^{2}\right )+x \left (x^{2}-2 y\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
26.062 |
|
| \begin{align*}
y \left (x^{3} y^{3}+2 x^{2}-y\right )+x^{3} \left (x y^{3}-2\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✗ |
✗ |
8.353 |
|
| \begin{align*}
y \left (2-3 y x \right )-y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.938 |
|
| \begin{align*}
y \left (y^{2}+2 x \right )+x \left (y^{2}-x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
13.780 |
|
| \begin{align*}
y+2 \left (y^{4}-x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
8.487 |
|
| \begin{align*}
y \left (3 x^{3}-x +y\right )+x^{2} \left (-x^{2}+1\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.503 |
|
| \begin{align*}
2 x^{5} y^{\prime }&=y \left (3 x^{4}+y^{2}\right ) \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
34.098 |
|
| \begin{align*}
x^{n} y^{n +1}+a y+\left (x^{n +1} y^{n}+b x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
46.605 |
|
| \begin{align*}
x^{n +1} y^{n}+a y+\left (x^{n} y^{n +1}+a x \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✓ |
✗ |
✓ |
✗ |
32.827 |
|
| \begin{align*}
x^{4}+2 y-y^{\prime } x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.407 |
|
| \begin{align*}
3 y x +3 y-4+\left (x +1\right )^{2} y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.677 |
|
| \begin{align*}
y^{\prime }&=\csc \left (x \right )-\cot \left (x \right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.879 |
|
| \begin{align*}
t x^{\prime }&=6 \,{\mathrm e}^{2 t} t +x \left (2 t -1\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.169 |
|
| \begin{align*}
y^{\prime }&=x -3 y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.354 |
|
| \begin{align*}
\left (3 x -1\right ) y^{\prime }&=6 y-10 \left (3 x -1\right )^{{1}/{3}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.839 |
|
| \begin{align*}
y-2+\left (3 x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
170.167 |
|
| \begin{align*}
2 y x +x^{2}+x^{4}-\left (x^{2}+1\right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.854 |
|
| \begin{align*}
y^{\prime }&=-2 y x +x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.293 |
|
| \begin{align*}
y-\cos \left (x \right )^{2}+\cos \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.161 |
|
| \begin{align*}
y^{\prime }&=x -2 y \cot \left (2 x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.898 |
|
| \begin{align*}
y-x +x y \cot \left (x \right )+y^{\prime } x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.486 |
|
| \begin{align*}
y^{\prime }-m y&=c \,{\mathrm e}^{x m} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.301 |
|
| \begin{align*}
y^{\prime }-m_{2} y&=c \,{\mathrm e}^{m_{1} x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.282 |
|
| \begin{align*}
v+\left (2 x +1-v x \right ) v^{\prime }&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
15.355 |
|
| \begin{align*}
x \left (x^{2}+1\right ) y^{\prime }+2 y&=\left (x^{2}+1\right )^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.944 |
|
| \begin{align*}
2 x \left (-x^{2}+y\right )+y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.404 |
|
| \begin{align*}
1+y x -\left (x^{2}+1\right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
9.764 |
|
| \begin{align*}
2 y&=\left (x^{2}-1\right ) \left (1-y^{\prime }\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.707 |
|
| \begin{align*}
1-\left (1+2 x \tan \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
3.208 |
|
| \begin{align*}
\left (\cos \left (x \right )+1\right ) y^{\prime }&=\sin \left (x \right ) \left (\sin \left (x \right )+\cos \left (x \right ) \sin \left (x \right )-y\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.680 |
|
| \begin{align*}
y^{\prime }&=1+3 \tan \left (x \right ) y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.740 |
|
| \begin{align*}
\left (a^{2}+x^{2}\right ) y^{\prime }&=2 x \left (\left (a^{2}+x^{2}\right )^{2}+3 y\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.423 |
|
| \begin{align*}
\left (a +x \right ) y^{\prime }&=b x -n y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.987 |
|
| \begin{align*}
\left (a +x \right ) y^{\prime }&=b x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.625 |
|
| \begin{align*}
\left (a +x \right ) y^{\prime }&=b x +y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.999 |
|
| \begin{align*}
\left (3+2 x \right ) y^{\prime }&=y+\sqrt {3+2 x} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.704 |
|
| \begin{align*}
y^{\prime }&=x^{3}-2 y x \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.142 |
|
| \begin{align*}
L i^{\prime }+R i&=e \\
i \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.938 |
|
| \begin{align*}
L i^{\prime }+R i&=e \sin \left (w t \right ) \\
i \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.247 |
|
| \begin{align*}
y^{\prime }&=4 x -2 y \\
y \left (0\right ) &= -1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.748 |
|
| \begin{align*}
y^{\prime }&=4 x -2 y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.511 |
|
| \begin{align*}
\left (t^{2}+1\right ) s^{\prime }+2 t \left (s t^{2}-3 \left (t^{2}+1\right )^{2}\right )&=0 \\
s \left (0\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.410 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x +y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.118 |
|
| \begin{align*}
y^{\prime } x +x +y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
8.049 |
|
| \begin{align*}
y^{2}-x \left (2 x +3 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
78.461 |
|
| \begin{align*}
x^{2}+1+x^{2} y^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.411 |
|
| \begin{align*}
x^{3}+y^{3}+y^{2} \left (3 x +k y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
80.871 |
|
| \begin{align*}
y^{\prime } x&=y^{2} x^{2}+2 y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.577 |
|
| \begin{align*}
y^{\prime }-\cos \left (x \right )&=\tan \left (y\right )^{2} \cos \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.307 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime }&=1-y-\sin \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.958 |
|
| \begin{align*}
\sin \left (\theta \right ) r^{\prime }&=-1-2 r \cos \left (\theta \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.684 |
|
| \begin{align*}
y \left (x +3 y\right )+x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
28.701 |
|
| \begin{align*}
y^{\prime }&=\sec \left (x \right )^{2} \sec \left (y\right )^{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
4.484 |
|
| \begin{align*}
\left (2 x^{3}-x^{2} y+y^{3}\right ) y-x \left (2 x^{3}+y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
408.589 |
|
| \begin{align*}
y^{\prime } x&=y \left (2 y x +1\right ) \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.980 |
|
| \begin{align*}
y x +\sqrt {x^{2}+1}\, y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.412 |
|
| \begin{align*}
x -y \cos \left (\frac {y}{x}\right )+x y^{\prime } \cot \left (\frac {y}{x}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
57.214 |
|
| \begin{align*}
y \left (x^{2}+y^{2}\right )+x \left (3 x^{2}-5 y^{2}\right ) y^{\prime }&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
59.665 |
|
| \begin{align*}
y^{\prime }+a y&=b \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.392 |
|
| \begin{align*}
x -y-\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
36.536 |
|
| \begin{align*}
x^{\prime }&=\cos \left (x\right ) \cos \left (t \right )^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
4.846 |
|
| \begin{align*}
\left (x \cos \left (y\right )+\cos \left (x \right )\right ) y^{\prime }-\sin \left (x \right ) y+\sin \left (y\right )&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
31.822 |
|
| \begin{align*}
1+4 y x -4 x^{2} y+\left (-x^{3}+x^{2}\right ) y^{\prime }&=0 \\
y \left (2\right ) &= {\frac {1}{4}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.778 |
|
| \begin{align*}
3-2 y x -\left (x^{2}+\frac {1}{y^{2}}+\frac {1}{y}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
5.594 |
|
| \begin{align*}
3 \left (-1+y\right ) x +y+2+y^{\prime } x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.733 |
|
| \begin{align*}
x y \left (1-y^{\prime }\right )&=x^{2} y^{\prime }+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
29.896 |
|
| \begin{align*}
a^{2} \left (y^{\prime }-1\right )&=x^{2} y^{\prime }+y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.368 |
|
| \begin{align*}
y-\sin \left (x \right )^{2}+\sin \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
5.366 |
|
| \begin{align*}
x -y+\left (3 x +y\right ) y^{\prime }&=0 \\
y \left (2\right ) &= -1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
27.152 |
|
| \begin{align*}
y&=\left (2 x +1\right ) \left (1-y^{\prime }\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
17.398 |
|
| \begin{align*}
y^{\prime } \sqrt {-x^{2}+1}+\sqrt {1-y^{2}}&=0 \\
y \left (0\right ) &= \frac {\sqrt {3}}{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
21.372 |
|
| \begin{align*}
y^{\prime } \sqrt {-x^{2}+1}+\sqrt {1-y^{2}}&=0 \\
y \left (0\right ) &= -\frac {\sqrt {3}}{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
24.860 |
|
| \begin{align*}
\sqrt {1-y^{2}}-y^{\prime } \sqrt {-x^{2}+1}&=0 \\
y \left (0\right ) &= \frac {\sqrt {3}}{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
21.044 |
|
| \begin{align*}
\sqrt {1-y^{2}}-y^{\prime } \sqrt {-x^{2}+1}&=0 \\
y \left (0\right ) &= -\frac {\sqrt {3}}{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
19.474 |
|
| \begin{align*}
v-\left ({\mathrm e}^{v}+2 u v-2 u \right ) v^{\prime }&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✗ |
4.790 |
|