| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
\left (2 x -1\right ) y^{\prime \prime }-3 y^{\prime }&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
0.592 |
|
| \begin{align*}
\left (2 x^{2}+1\right ) y^{\prime \prime }+3 x y^{\prime }-6 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.697 |
|
| \begin{align*}
\left (x^{2}-2 x \right ) y^{\prime \prime }+\left (1+3 x \right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.273 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}-3 x \right ) y^{\prime }+\left (x +4\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.030 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\left (x +2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.128 |
|
| \begin{align*}
y^{\prime }-y^{2}-x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✓ |
0.434 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 x y^{\prime }-3 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.921 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (-n^{2}+x^{2}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Bessel] |
✓ |
✓ |
✓ |
✗ |
1.243 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.407 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }&=0 \\
y \left (0\right ) &= -2 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.299 |
|
| \begin{align*}
y^{\prime \prime }-4 y&=0 \\
y \left (0\right ) &= 6 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.288 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.332 |
|
| \begin{align*}
y^{\prime \prime }+n^{2} y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= k \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.351 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y&=2 \,{\mathrm e}^{-t} \\
y \left (0\right ) &= {\frac {3}{2}} \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.394 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=5 \cos \left (2 t \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.470 |
|
| \begin{align*}
y^{\prime \prime }+y&=\sin \left (2 t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.467 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-4 y^{\prime \prime }&=0 \\
y \left (0\right ) &= 5 \\
y^{\prime }\left (0\right ) &= 2 \\
y^{\prime \prime }\left (0\right ) &= 8 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.500 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }-2 y^{\prime }+y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 1 \\
y^{\prime \prime }\left (0\right ) &= -3 \\
y^{\prime \prime \prime }\left (0\right ) &= -5 \\
\end{align*}
Using Laplace transform method. |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.143 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 3 \\
y^{\prime \prime }\left (0\right ) &= -4 \\
y^{\prime \prime \prime }\left (0\right ) &= 12 \\
\end{align*}
Using Laplace transform method. |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.520 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=t \sin \left (t \right ) \\
y \left (0\right ) &= {\frac {7}{9}} \\
y^{\prime }\left (0\right ) &= -{\frac {5}{2}} \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.563 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=x \sin \left (x \right ) \\
y \left (0\right ) &= {\frac {7}{9}} \\
y \left (\frac {\pi }{2}\right ) &= \frac {\pi }{6}-1 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.928 |
|
| \begin{align*}
y^{\prime \prime }+3 y&=0 \\
y \left (0\right ) &= -2 \\
y \left (1\right ) &= \left (1-3 \,{\mathrm e}^{3}\right ) {\mathrm e}^{-3} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
27.915 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y+8 \,{\mathrm e}^{-x}+3 x&=0 \\
y \left (0\right ) &= -{\frac {2}{3}} \\
y \left (1\right ) &= 2 \,{\mathrm e}^{-1}+\frac {1}{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.734 |
|
| \begin{align*}
x^{\prime }+y^{\prime }-y&=0 \\
y^{\prime }+2 y+z^{\prime }+2 z&=2 \\
x+z^{\prime }-z&=0 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
z \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.382 |
|
| \begin{align*}
x^{\prime \prime }&=1 \\
x^{\prime }+x+y^{\prime \prime }-9 y+z^{\prime }+z&=0 \\
5 x+z^{\prime \prime }-4 z&=2 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
z \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
z^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.049 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}&=x^{2} y y^{\prime }-x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.346 |
|
| \begin{align*}
2 x +\frac {1}{y}+\left (\frac {1}{y}-\frac {x}{y^{2}}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
21.909 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}&=x y y^{\prime } \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
51.662 |
|
| \begin{align*}
\left (x^{3}+3\right ) y^{\prime }+2 y x +5 x^{2}&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
50.286 |
|
| \begin{align*}
x y^{2}&=-x y^{\prime }+y \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.069 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.460 |
|
| \begin{align*}
k^{2} y^{\prime \prime }+2 k y^{\prime }+\left (k^{2}+1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.224 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=\frac {{\mathrm e}^{-2 x}}{x^{2}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.767 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=\sin \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.382 |
|
| \begin{align*}
x^{\prime \prime }+2 x^{\prime }+2 x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.481 |
|
| \begin{align*}
x y^{\prime \prime }+y^{\prime }&=16 x^{3} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.725 |
|
| \begin{align*}
y^{\prime \prime \prime }-7 y^{\prime \prime }+12 y^{\prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.083 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+13 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.511 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }&=3 x +x \,{\mathrm e}^{x} \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.242 |
|
| \begin{align*}
y^{\prime }-3 z&=5 \\
y-z^{\prime }-x&=3-2 t \\
z+x^{\prime }&=-1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.372 |
|
| \begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=\frac {{\mathrm e}^{x}}{x^{3}} \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 0 \\
y^{\prime \prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.463 |
|
| \begin{align*}
y^{\prime \prime }+x y^{\prime }-2 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.604 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }-8 x y^{\prime }+20 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| \begin{align*}
y^{\prime }+y-x^{\prime }+x&=t \\
x^{\prime }+y^{\prime }+x-y&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.856 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=2 t -8 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.558 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.358 |
|
| \begin{align*}
y^{\prime \prime }+y&=2 \cos \left (t \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.468 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }-6 y^{\prime }&=6 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.477 |
|
| \begin{align*}
y^{\prime \prime \prime }-5 x y^{\prime }&=1+{\mathrm e}^{x} \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.585 |
|
| \begin{align*}
t y^{\prime \prime }+t^{2} y^{\prime }-\sin \left (t \right ) \sqrt {t}&=t^{2}-t +1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
2.304 |
|
| \begin{align*}
s^{2} t^{\prime \prime }+s t t^{\prime }&=s \\
\end{align*} |
[[_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
✓ |
✓ |
✗ |
2.386 |
|
| \begin{align*}
5 {b^{\prime \prime \prime \prime }}^{5}+7 {b^{\prime }}^{10}+b^{7}-b^{5}&=p \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
✗ |
0.309 |
|
| \begin{align*}
y y^{\prime \prime }&=1+y^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
3.728 |
|
| \begin{align*}
{y^{\prime \prime }}^{2}-3 y y^{\prime }+y x&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
✗ |
0.096 |
|
| \begin{align*}
x^{4} y^{\prime \prime \prime \prime }+x y^{\prime \prime \prime }&={\mathrm e}^{x} \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
0.893 |
|
| \begin{align*}
t^{2} s^{\prime \prime }-t s^{\prime }&=1-\sin \left (t \right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.332 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+x y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-x y^{\prime }+\sin \left (y\right )&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
✗ |
0.065 |
|
| \begin{align*}
{r^{\prime \prime }}^{2}+r^{\prime \prime }+y r^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✗ |
✗ |
✗ |
✗ |
127.533 |
|
| \begin{align*}
{y^{\prime \prime }}^{{3}/{2}}+y&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✗ |
✓ |
✓ |
✗ |
0.365 |
|
| \begin{align*}
b^{\left (7\right )}&=3 p \\
\end{align*} |
[[_high_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.223 |
|
| \begin{align*}
{b^{\prime }}^{7}&=3 p \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
8.191 |
|
| \begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.477 |
|
| \begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.675 |
|
| \begin{align*}
x y^{\prime \prime }+y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.533 |
|
| \begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.209 |
|
| \begin{align*}
y^{\prime }+y&=0 \\
y \left (3\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.730 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.931 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=0 \\
y \left (\frac {\pi }{8}\right ) &= 0 \\
y \left (\frac {\pi }{6}\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
3.651 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 1 \\
y \left (\frac {\pi }{2}\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
✗ |
46.419 |
|
| \begin{align*}
y^{\prime \prime }-y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
4.119 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.685 |
|
| \begin{align*}
y^{\prime }&=y \sin \left (x \right )+{\mathrm e}^{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
3.127 |
|
| \begin{align*}
y^{\prime }&=\sin \left (y\right ) x +{\mathrm e}^{x} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
✗ |
16.209 |
|
| \begin{align*}
y^{\prime }&=5 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.378 |
|
| \begin{align*}
y^{\prime }&=x +y^{2} \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
8.059 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y}{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.139 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.119 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x y \,{\mathrm e}^{\frac {y}{x}}}{x^{2}+y^{2} \sin \left (\frac {x}{y}\right )} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
35.874 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+y}{x^{3}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.469 |
|
| \begin{align*}
\sin \left (x \right )+y^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.453 |
|
| \begin{align*}
x y^{2}-x^{2} y^{2} y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.352 |
|
| \begin{align*}
1+y x +y y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✓ |
✓ |
✗ |
142.749 |
|
| \begin{align*}
3 x^{2} y+\left (y+x^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
20.576 |
|
| \begin{align*}
y x +y^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.425 |
|
| \begin{align*}
y^{\prime }&=2 \sqrt {{| y|}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
39.456 |
|
| \begin{align*}
y^{\prime }&=y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.540 |
|
| \begin{align*}
y^{\prime }&=y x +1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.494 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}}{y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
15.181 |
|
| \begin{align*}
y^{\prime }&=-\frac {2 y}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.689 |
|
| \begin{align*}
y^{\prime }&=\frac {x y^{2}}{x^{2} y+y^{3}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
14.697 |
|
| \begin{align*}
x -y^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.061 |
|
| \begin{align*}
y^{\prime }&=x^{3} y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.472 |
|
| \begin{align*}
y^{\prime }&=5 y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.199 |
|
| \begin{align*}
y^{\prime }&=\frac {x +1}{1+y^{4}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.655 |
|
| \begin{align*}
{\mathrm e}^{x}-y y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.832 |
|
| \begin{align*}
x \cos \left (x \right )+\left (1-6 y^{5}\right ) y^{\prime }&=0 \\
y \left (\pi \right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.171 |
|
| \begin{align*}
y y^{\prime }+x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.655 |
|
| \begin{align*}
\frac {1}{x}-\frac {y^{\prime }}{y}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.012 |
|
| \begin{align*}
\frac {1}{x}+y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.924 |
|
| \begin{align*}
x +\frac {y^{\prime }}{y}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.390 |
|