| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime \prime } x +y&=x \,{\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.202 |
|
| \begin{align*}
y^{\prime }+y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.006 |
|
| \begin{align*}
y^{\prime }-y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.332 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.372 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime }&=2 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
3.535 |
|
| \begin{align*}
y^{\prime \prime }-\tan \left (x \right ) y^{\prime }-\frac {\tan \left (x \right ) y}{x}&=\frac {y^{3}}{x^{3}} \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
✗ |
3.233 |
|
| \begin{align*}
y^{\prime \prime \prime }-5 y^{\prime \prime }+6 y^{\prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.113 |
|
| \begin{align*}
m s^{\prime \prime }&=\frac {g \,t^{2}}{2} \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.669 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\frac {y-y^{\prime }}{x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.509 |
|
| \begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.353 |
|
| \begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.452 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
6.766 |
|
| \begin{align*}
y^{\prime }-2 y&={\mathrm e}^{x} \left (1-x \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.626 |
|
| \begin{align*}
y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.050 |
|
| \begin{align*}
y y^{\prime }-y^{2}&=x^{2} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.279 |
|
| \begin{align*}
y^{\prime \prime }+y&=\cos \left (x \right )^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.890 |
|
| \begin{align*}
y^{\prime \prime }&=y^{\prime } \left (y^{\prime }+y\right ) \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
0.690 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+y^{2}}{2 y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
37.003 |
|
| \begin{align*}
y^{\prime }&=-\frac {x^{2}+y^{2}}{2 y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
26.205 |
|
| \begin{align*}
y^{\prime }+y x&=3 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.501 |
|
| \begin{align*}
y^{\prime } x +y&=3 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✗ |
✗ |
✗ |
✓ |
211.237 |
|
| \begin{align*}
y^{\prime }&=\frac {x -y}{x +y} \\
y \left (0\right ) &= -1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
121.122 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
6.670 |
|
| \begin{align*}
y^{\prime }&=y^{{2}/{3}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
37.008 |
|
| \begin{align*}
y^{\prime }&=\frac {x -y}{x +y} \\
y \left (1\right ) &= -1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
46.670 |
|
| \begin{align*}
y^{\prime } x +\frac {y}{3+2 x}&=\ln \left (x -2\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.919 |
|
| \begin{align*}
x^{\prime }&=\frac {a x^{{5}/{6}}}{\left (-B t +b \right )^{{3}/{2}}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
95.754 |
|
| \begin{align*}
-y+y^{\prime } x&=1 \\
y \left (2\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.619 |
|
| \begin{align*}
y^{\prime }-y x&=-x^{2}+1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
34.923 |
|
| \begin{align*}
y^{\prime } x +y^{2}&=1 \\
y \left (-2\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
39.527 |
|
| \begin{align*}
y^{\prime }&=-x +y \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.685 |
|
| \begin{align*}
y^{\prime }&=y x \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.755 |
|
| \begin{align*}
y^{\prime }&=x^{2}+y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_Riccati, _special]] |
✗ |
✓ |
✓ |
✗ |
93.716 |
|
| \begin{align*}
y^{\prime } x +\left (x +1\right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.697 |
|
| \begin{align*}
x^{2}+y^{2}-2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
30.672 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
6.104 |
|
| \begin{align*}
y^{\prime } x +y&=3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.395 |
|
| \begin{align*}
y^{\prime }+y x&=3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.597 |
|
| \begin{align*}
p^{\prime }&=a p-b p^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
23.677 |
|
| \begin{align*}
y^{\prime } x -\frac {y}{\ln \left (x \right )}&=x y^{2} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.296 |
|
| \begin{align*}
y y^{\prime }&=y+x^{2} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
✗ |
77.502 |
|
| \begin{align*}
y^{\prime }&=x -y x -y+1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.714 |
|
| \begin{align*}
\left (x^{2}+4\right ) y^{\prime }+3 y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.558 |
|
| \begin{align*}
\cos \left (x \right ) \sin \left (y\right ) y^{\prime }-\cos \left (x \right ) \cos \left (y\right )-\cos \left (x \right )&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.109 |
|
| \begin{align*}
y y^{\prime }&=x^{3} y^{2}+x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.267 |
|
| \begin{align*}
y^{4}+\left (x^{2}-3 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✗ |
✗ |
8.655 |
|
| \begin{align*}
\left (1+y^{2}\right ) \cos \left (x \right )&=2 \left (1+\sin \left (x \right )^{2}\right ) y y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.616 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (b_{2} x +b_{1} \right )}{x \left (a_{1} +a_{2} y\right )} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.794 |
|
| \begin{align*}
x^{\prime }&=k \left (a -x\right ) \left (b -x\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
38.564 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (a -x \right ) y}{d \,x^{2}+c x +b} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
27.312 |
|
| \begin{align*}
y^{\prime } x +y&=3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.133 |
|
| \begin{align*}
y^{\prime } x +y&=3 x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
14.026 |
|
| \begin{align*}
x^{2}+y^{2}-2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
52.785 |
|
| \begin{align*}
y^{\prime } x +\left (x +1\right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.495 |
|
| \begin{align*}
-y+y^{\prime } x&=2 x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.686 |
|
| \begin{align*}
y^{2} y^{\prime }+\tan \left (x \right ) y&=\sin \left (x \right )^{3} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
✗ |
117.594 |
|
| \begin{align*}
y^{\prime }-\frac {3 y}{x -1}&=\left (x -1\right )^{4} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
9.611 |
|
| \begin{align*}
y^{\prime } x +6 y&=1+3 x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
10.596 |
|
| \begin{align*}
y^{\prime }+\frac {y}{\sin \left (x \right )}-y^{2}&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.440 |
|
| \begin{align*}
{\mathrm e}^{x}+x^{3} y^{\prime }+4 x^{2} y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.556 |
|
| \begin{align*}
y^{\prime } x +y&=x^{5} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
9.497 |
|
| \begin{align*}
y^{\prime }-\frac {x}{x^{2}+1}&=-\frac {x y}{x^{2}+1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.774 |
|
| \begin{align*}
y y^{\prime }-7 y&=6 x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
45.294 |
|
| \begin{align*}
x +y y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
38.060 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x}&=-\frac {1}{2 y} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
23.658 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=-2 x y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.249 |
|
| \begin{align*}
y^{\prime }-2 y x&=4 x \sqrt {y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
15.075 |
|
| \begin{align*}
y^{\prime } x -\frac {y}{2 \ln \left (x \right )}&=y^{2} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.955 |
|
| \begin{align*}
y^{\prime }-y x&=\left (-x^{2}+1\right ) {\mathrm e}^{\frac {x^{2}}{2}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.273 |
|
| \begin{align*}
y^{\prime } x +y&=2 x \\
y \left (2\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
75.254 |
|
| \begin{align*}
y^{\prime } x -\frac {y}{\ln \left (x \right )}&=0 \\
y \left ({\mathrm e}\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.494 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+2 y x&=-2 x \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.794 |
|
| \begin{align*}
\left (1-x \right ) y^{\prime }+y x&=x \left (x -1\right )^{2} \\
y \left (5\right ) &= 24 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
25.842 |
|
| \begin{align*}
\left (x -1\right ) y^{\prime }-3 y&=\left (x -1\right )^{5} \\
y \left (-1\right ) &= 16 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
9.143 |
|
| \begin{align*}
y^{\prime }-2 y x&=x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.832 |
|
| \begin{align*}
y^{\prime }&=\left (1-y\right ) \left (\frac {1}{t}-\frac {1}{10}+\frac {y}{10}\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
7.469 |
|
| \begin{align*}
y^{\prime }&=\left (1-y\right ) \left (-\frac {1}{t \ln \left (t \right )}-\frac {3}{100}+\frac {3 y}{100}\right ) \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✓ |
13.338 |
|
| \begin{align*}
x -y+\left (y-x +2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
18.254 |
|
| \begin{align*}
x +y+\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
54.160 |
|
| \begin{align*}
y^{\prime }&=\frac {y-x +1}{3-x +y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
18.333 |
|
| \begin{align*}
x^{2}+y^{2}-2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
44.546 |
|
| \begin{align*}
x^{2}+y^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
30.153 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
7.622 |
|
| \begin{align*}
y \,{\mathrm e}^{y x}+\left (x \,{\mathrm e}^{y x}+1\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
8.117 |
|
| \begin{align*}
\cos \left (y\right )+\sin \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.024 |
|
| \begin{align*}
y+\cos \left (x \right )+\left (x +\sin \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
6.981 |
|
| \begin{align*}
3 x^{2} y+y^{2}-\left (-x^{3}-2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
55.911 |
|
| \begin{align*}
{\mathrm e}^{x} \cos \left (y\right )-x^{2}+\left ({\mathrm e}^{y} \sin \left (x \right )+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
✗ |
90.727 |
|
| \begin{align*}
2 x -y \sin \left (y x \right )+\left (6 y^{2}-x \sin \left (y x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
7.018 |
|
| \begin{align*}
x -y+\left (y-x +2\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.987 |
|
| \begin{align*}
x +y+\left (x -y\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
126.908 |
|
| \begin{align*}
x^{2}+y^{2}+2 y y^{\prime } x&=0 \\
y \left (1\right ) &= -1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
34.082 |
|
| \begin{align*}
y^{\prime }&=\frac {y-x +1}{3-x +y} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.809 |
|
| \begin{align*}
-y^{\prime } x +y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.405 |
|
| \begin{align*}
x^{2}-2 y+y^{\prime } x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.142 |
|
| \begin{align*}
y+\left (2 x -y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
56.596 |
|
| \begin{align*}
y-2 x -y^{\prime } x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
8.882 |
|
| \begin{align*}
y-\left (x -2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
46.280 |
|
| \begin{align*}
x^{4}+y^{4}-x y^{3} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
114.076 |
|
| \begin{align*}
x^{2}-y^{2}+x +2 y y^{\prime } x&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.718 |
|