| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
x_{1}^{\prime }&=-2 x_{1}+x_{2}+x_{3} \\
x_{2}^{\prime }&=-2 x_{2}+x_{3} \\
x_{3}^{\prime }&=x_{2}-2 x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.020 |
|
| \begin{align*}
x_{1}^{\prime }&=a x_{1}+5 x_{3} \\
x_{2}^{\prime }&=-x_{2}-2 x_{3} \\
x_{3}^{\prime }&=-3 x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.080 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2}+x_{3} \\
x_{2}^{\prime }&=x_{1}-2 x_{2}-x_{3} \\
x_{3}^{\prime }&=x_{2}-x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✗ |
13.416 |
|
| \begin{align*}
x_{1}^{\prime }&=a x_{1} \\
x_{2}^{\prime }&=a x_{2}+x_{3} \\
x_{3}^{\prime }&=x_{2}+a x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.937 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{2}+x_{4} \\
x_{2}^{\prime }&=-x_{2}+x_{3} \\
x_{3}^{\prime }&=x_{2}+x_{3} \\
x_{4}^{\prime }&=x_{1}-x_{4} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
2.960 |
|
| \begin{align*}
x^{\prime \prime \prime }+a x^{\prime \prime }+b x^{\prime }+c x&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.386 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{2} \\
x_{2}^{\prime }&=x_{3} \\
x_{3}^{\prime }&=-a x_{3}-b x_{2}-c x_{1} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✗ |
22.684 |
|
| \begin{align*}
x^{\prime \prime \prime }+x&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.090 |
|
| \begin{align*}
x^{\prime \prime \prime }-x&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.108 |
|
| \begin{align*}
x^{\prime \prime \prime }+5 x^{\prime \prime }+9 x^{\prime }+5 x&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.145 |
|
| \begin{align*}
x^{\prime \prime \prime \prime }+x^{\prime \prime \prime }-x^{\prime }-x&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.154 |
|
| \begin{align*}
x^{\prime \prime \prime \prime }+8 x^{\prime \prime \prime }+23 x^{\prime \prime }+2 x^{\prime }+12 x&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.184 |
|
| \begin{align*}
x^{\prime }&=\lambda x-x^{5} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
6.067 |
|
| \begin{align*}
x^{\prime }&=\lambda x-x^{3}-x^{5} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
3.012 |
|
| \begin{align*}
x_{1}^{\prime }&=-x_{1} \\
x_{2}^{\prime }&=-2 x_{2} \\
x_{3}^{\prime }&=x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.777 |
|
| \begin{align*}
x^{\prime }&=-x+y+y^{2} \\
y^{\prime }&=-2 y-x^{2} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
✗ |
0.211 |
|
| \begin{align*}
x^{\prime }&=-x^{3} \\
y^{\prime }&=-y^{3} \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.105 |
|
| \begin{align*}
x^{\prime \prime }-x^{3}&=0 \\
x \left (0\right ) &= 0 \\
x \left (b \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
5.944 |
|
| \begin{align*}
x^{\prime \prime }+4 x^{3}&=0 \\
x \left (a \right ) &= 0 \\
x \left (b \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
5.383 |
|
| \begin{align*}
x^{\prime \prime }+6 x^{5}&=0 \\
x \left (0\right ) &= 0 \\
x \left (b \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✗ |
✗ |
8.881 |
|
| \begin{align*}
x^{\prime \prime }+\lambda x-x^{3}&=0 \\
x \left (0\right ) &= 0 \\
x \left (1\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✗ |
✗ |
8.837 |
|
| \begin{align*}
x^{\prime \prime }+4 x^{3}&=0 \\
x \left (0\right ) &= 0 \\
x \left (b \right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✗ |
✓ |
✗ |
✗ |
48.170 |
|
| \begin{align*}
x^{\prime \prime }+4 x^{3}&=0 \\
x \left (0\right ) &= 0 \\
x \left (b \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
5.211 |
|
| \begin{align*}
-x^{\prime \prime }&=1-x-x^{2} \\
x \left (a \right ) &= 0 \\
x \left (b \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✗ |
✗ |
✗ |
✗ |
93.271 |
|
| \begin{align*}
-x^{\prime \prime }+x&={\mathrm e}^{-x} \\
x \left (a \right ) &= 0 \\
x \left (b \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✗ |
✗ |
✗ |
✗ |
67.083 |
|
| \begin{align*}
-x^{\prime \prime }+x&={\mathrm e}^{-x^{2}} \\
x \left (a \right ) &= 0 \\
x \left (b \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✗ |
✗ |
✗ |
✗ |
59.008 |
|
| \begin{align*}
-x^{\prime \prime }&=\frac {1}{\sqrt {x^{2}+1}}-x \\
x \left (a \right ) &= 0 \\
x \left (b \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✗ |
✗ |
✗ |
✗ |
62.753 |
|
| \begin{align*}
-x^{\prime \prime }&=2 x-x^{2} \\
x \left (0\right ) &= 0 \\
x \left (\pi \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✗ |
✓ |
✗ |
✗ |
28.095 |
|
| \begin{align*}
-x^{\prime \prime }&=\arctan \left (x\right ) \\
x \left (0\right ) &= 0 \\
x \left (b \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✗ |
✓ |
✗ |
✗ |
616.861 |
|
| \begin{align*}
y^{\prime }&=y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.946 |
|
| \begin{align*}
y^{\prime }&=6 y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.509 |
|
| \begin{align*}
y^{\prime }&=-5 y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.504 |
|
| \begin{align*}
y^{\prime }&=f \left (x \right ) g \left (y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.983 |
|
| \begin{align*}
-y+y^{\prime } x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.730 |
|
| \begin{align*}
y^{\prime }-k y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.840 |
|
| \begin{align*}
x +y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
16.225 |
|
| \begin{align*}
y^{\prime } x +y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.518 |
|
| \begin{align*}
y^{\prime } x -2 y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.655 |
|
| \begin{align*}
\sqrt {x}\, y^{\prime }+1&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.470 |
|
| \begin{align*}
2 x \left (1+y\right )-y y^{\prime }&=0 \\
y \left (0\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.720 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.256 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.480 |
|
| \begin{align*}
-2+2 y+x^{2} \sin \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.618 |
|
| \begin{align*}
y^{\prime }&=\frac {x +1}{1+y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.362 |
|
| \begin{align*}
y^{\prime }&=\frac {a x +b}{y^{n}+d} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.984 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{y} \\
y \left (0\right ) &= a_{0} \\
\end{align*} |
[_separable] |
✓ |
✗ |
✓ |
✓ |
17.300 |
|
| \begin{align*}
y^{\prime }&=x^{2} y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.545 |
|
| \begin{align*}
y^{\prime }&=\frac {1+y^{2}}{x^{2}+1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.125 |
|
| \begin{align*}
\cos \left (x \right ) x +\left (1-6 y^{5}\right ) y^{\prime }&=0 \\
y \left (\pi \right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.341 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y^{3}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.138 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y^{2} \sqrt {x^{2}+1}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
5.282 |
|
| \begin{align*}
y^{\prime }&=2 y x \\
y \left (0\right ) &= 5 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.171 |
|
| \begin{align*}
x y^{2}-x +\left (y+x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.849 |
|
| \begin{align*}
y^{\prime }&=x^{2} y^{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.990 |
|
| \begin{align*}
y^{\prime }&=\frac {y \ln \left (x \right )}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.424 |
|
| \begin{align*}
y^{\prime }&=x^{2} y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.435 |
|
| \begin{align*}
{\mathrm e}^{x}-y y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.938 |
|
| \begin{align*}
2 x -6 y+3-\left (1+x -3 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.029 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
16.401 |
|
| \begin{align*}
2 x +3 y-1+\left (2 x -3 y+2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
49.819 |
|
| \begin{align*}
x +2 y-4-\left (-5+2 x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
45.250 |
|
| \begin{align*}
x +2 y-1+3 \left (x +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
17.702 |
|
| \begin{align*}
{\mathrm e}^{-y} \left (1+y^{\prime }\right )&=x \,{\mathrm e}^{x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
7.280 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y}{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.243 |
|
| \begin{align*}
x -y+\left (x -4 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
78.959 |
|
| \begin{align*}
x^{2}-y x +y^{2}-y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
39.950 |
|
| \begin{align*}
y+x y^{2}+\left (x -x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
85.339 |
|
| \begin{align*}
x^{2}-2 y^{2}+y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✗ |
63.085 |
|
| \begin{align*}
y x +\left (x^{2}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
19.509 |
|
| \begin{align*}
y+y^{\prime } x +\frac {y^{3} \left (-y^{\prime } x +y\right )}{x}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
18.477 |
|
| \begin{align*}
\left (x -4\right ) y^{4}-x^{3} \left (y^{2}-3\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
5.864 |
|
| \begin{align*}
1+y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.296 |
|
| \begin{align*}
x \sin \left (y\right )+\left (x^{2}+1\right ) \cos \left (y\right ) y^{\prime }&=0 \\
y \left (1\right ) &= \frac {\pi }{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.516 |
|
| \begin{align*}
y^{\prime }-y x&=x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.300 |
|
| \begin{align*}
y^{\prime }&=-\frac {{\mathrm e}^{y}}{x \,{\mathrm e}^{y}+2 y} \\
\end{align*} |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
✓ |
✓ |
6.842 |
|
| \begin{align*}
\left (x +y^{2}\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
✓ |
✓ |
✓ |
11.324 |
|
| \begin{align*}
y^{\prime }+\frac {2 x \sin \left (y\right )+y^{3} {\mathrm e}^{x}}{\cos \left (y\right ) x^{2}+3 y^{2} {\mathrm e}^{x}}&=0 \\
\end{align*} |
[NONE] |
✓ |
✓ |
✓ |
✗ |
7.618 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }+3 x +y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
35.460 |
|
| \begin{align*}
3 x \left (y x -2\right )+\left (x^{3}+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
8.022 |
|
| \begin{align*}
3 x^{2}+6 x y^{2}+\left (6 x^{2} y+4 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
4.613 |
|
| \begin{align*}
y^{\prime }&=2 x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.727 |
|
| \begin{align*}
\left (x +y^{2}\right ) y^{\prime }-x^{2}+y&=0 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
4.354 |
|
| \begin{align*}
3 x^{2}+4 y x +\left (2 x^{2}+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
7.914 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x y \,{\mathrm e}^{\frac {2 x}{y}}}{y^{2}+y^{2} {\mathrm e}^{\frac {2 x}{y}}+2 x^{2} {\mathrm e}^{\frac {2 x}{y}}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
48.901 |
|
| \begin{align*}
y^{2}-x^{2}-2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
62.915 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{3}-2 x^{3}}{x y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
19.104 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y^{4}+x^{4}}{x y^{3}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
115.515 |
|
| \begin{align*}
y^{\prime }&=\sqrt {1-\frac {y^{2}}{x^{2}}}+\frac {y}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
69.369 |
|
| \begin{align*}
2 y y^{\prime } x&=y^{2}-x^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
52.372 |
|
| \begin{align*}
x +y-\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.322 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x y}{y^{2}-x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.706 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y^{4}+x^{4}}{x y^{3}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
112.200 |
|
| \begin{align*}
x^{2}-3 y^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
76.170 |
|
| \begin{align*}
y y^{\prime } x +x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
21.731 |
|
| \begin{align*}
-y+y^{\prime } x&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
22.054 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x y}{x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
23.677 |
|
| \begin{align*}
y+\sqrt {x^{2}+y^{2}}-y^{\prime } x&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
22.587 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+y^{2}}{y x} \\
y \left (1\right ) &= -2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✗ |
24.345 |
|
| \begin{align*}
y-x y^{2}+y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.574 |
|
| \begin{align*}
y^{\prime }+\tan \left (\theta \right ) y&=\cos \left (\theta \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.618 |
|