| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime \prime \prime }+y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.059 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }+y^{\prime }+y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.056 |
|
| \begin{align*}
y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.064 |
|
| \begin{align*}
y^{\left (5\right )}+y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.065 |
|
| \begin{align*}
2 y^{\prime \prime \prime \prime }+11 y^{\prime \prime \prime }+21 y^{\prime \prime }+16 y^{\prime }+4 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.056 |
|
| \begin{align*}
y^{\left (6\right )}+y^{\left (5\right )}+y^{\prime \prime \prime \prime }+y^{\prime \prime }+y^{\prime }+4 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.095 |
|
| \begin{align*}
2 y^{\prime \prime \prime \prime }+9 y^{\prime \prime \prime }+32 y^{\prime \prime }+54 y^{\prime }+20 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.054 |
|
| \begin{align*}
6 y^{\prime \prime \prime \prime }+29 y^{\prime \prime \prime }+45 y^{\prime \prime }+24 y^{\prime }+20 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.081 |
|
| \begin{align*}
y^{\left (5\right )}+y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.075 |
|
| \begin{align*}
y^{\left (6\right )}+y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+4 y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.080 |
|
| \begin{align*}
y^{\left (5\right )}+2 y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }+2 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.066 |
|
| \begin{align*}
x^{\prime }+3 x&={\mathrm e}^{-2 t} \\
x \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.262 |
|
| \begin{align*}
x^{\prime }-3 x&=3 t^{3}+3 t^{2}+2 t +1 \\
x \left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.194 |
|
| \begin{align*}
x^{\prime }-x&=\cos \left (t \right )-\sin \left (t \right ) \\
x \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.240 |
|
| \begin{align*}
x^{\prime }+x&=2 \sin \left (t \right ) \\
x \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.261 |
|
| \begin{align*}
x^{\prime }+6 x&=t \,{\mathrm e}^{-3 t} \\
x \left (0\right ) &= -{\frac {1}{2}} \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.379 |
|
| \begin{align*}
x^{\prime \prime }+4 x^{\prime }+3 x&=1 \\
x \left (0\right ) &= 3 \\
x^{\prime }\left (0\right ) &= -2 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.153 |
|
| \begin{align*}
x^{\prime \prime }-2 x^{\prime }+2 x&=1 \\
x \left (0\right ) &= {\frac {1}{2}} \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.091 |
|
| \begin{align*}
x^{\prime \prime }-5 x^{\prime }+6 x&=12 \\
x \left (0\right ) &= 2 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.092 |
|
| \begin{align*}
x^{\prime \prime }+3 x^{\prime }-1&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= {\frac {1}{3}} \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.100 |
|
| \begin{align*}
x^{\prime \prime }-2 x^{\prime }+1&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= {\frac {1}{2}} \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.092 |
|
| \begin{align*}
x^{\prime \prime }+3 x^{\prime }+2 x&=2 t^{2}+1 \\
x \left (0\right ) &= 4 \\
x^{\prime }\left (0\right ) &= -3 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.106 |
|
| \begin{align*}
x^{\prime \prime }-2 x^{\prime }-3 x&=3 t^{2}+7 t +3 \\
x \left (0\right ) &= -1 \\
x^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.122 |
|
| \begin{align*}
x^{\prime \prime }-7 x^{\prime }&=-14 t -5 \\
x \left (0\right ) &= 2 \\
x^{\prime }\left (0\right ) &= 8 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.132 |
|
| \begin{align*}
x^{\prime \prime }+2 x^{\prime }&=6 t^{2}+6 t -3 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= -{\frac {3}{2}} \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.128 |
|
| \begin{align*}
x^{\prime \prime }+6 x^{\prime }&=t \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= -{\frac {1}{36}} \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.115 |
|
| \begin{align*}
x^{\prime \prime }+x&=2 \,{\mathrm e}^{t} \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.126 |
|
| \begin{align*}
7 x^{\prime \prime }+14 x^{\prime }&=\left (t -\frac {1}{4}\right ) {\mathrm e}^{-2 t} \\
x \left (0\right ) &= 2 \\
x^{\prime }\left (0\right ) &= -{\frac {1}{56}} \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.142 |
|
| \begin{align*}
x^{\prime \prime }-4 x^{\prime }+4 x&=\left (t -1\right ) {\mathrm e}^{2 t} \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.135 |
|
| \begin{align*}
4 x^{\prime \prime }-4 x^{\prime }+x&={\mathrm e}^{\frac {t}{2}} \\
x \left (0\right ) &= -2 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.135 |
|
| \begin{align*}
x^{\prime \prime }+3 x^{\prime }+2 x&={\mathrm e}^{-t}+{\mathrm e}^{-2 t} \\
x \left (0\right ) &= 2 \\
x^{\prime }\left (0\right ) &= -3 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.149 |
|
| \begin{align*}
x^{\prime \prime }-x^{\prime }-6 x&=6 \,{\mathrm e}^{3 t}+2 \,{\mathrm e}^{-2 t} \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= {\frac {4}{5}} \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.163 |
|
| \begin{align*}
x^{\prime \prime }+4 x^{\prime }+4 x&=t^{2} {\mathrm e}^{-2 t} \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.105 |
|
| \begin{align*}
x^{\prime \prime }-x^{\prime }&=2 \sin \left (t \right ) \\
x \left (0\right ) &= 2 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.154 |
|
| \begin{align*}
x^{\prime \prime }+9 x&=18 \cos \left (3 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 9 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.171 |
|
| \begin{align*}
x^{\prime \prime }+4 x&=4 \cos \left (2 t \right )-\frac {\sin \left (2 t \right )}{2} \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= {\frac {1}{8}} \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.168 |
|
| \begin{align*}
x^{\prime \prime }+2 x^{\prime }+3 x&=\cos \left (t \right ) t \\
x \left (0\right ) &= -{\frac {1}{4}} \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.175 |
|
| \begin{align*}
x^{\prime \prime }-2 x^{\prime }+10 x&=\cos \left (3 t \right ) \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= {\frac {18}{37}} \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.210 |
|
| \begin{align*}
x^{\prime \prime }-4 x^{\prime }+5 x&=2 \,{\mathrm e}^{2 t} \left (\sin \left (t \right )+\cos \left (t \right )\right ) \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.204 |
|
| \begin{align*}
x^{\prime \prime \prime }-x^{\prime \prime }&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 3 \\
x^{\prime \prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.151 |
|
| \begin{align*}
x^{\prime \prime \prime }-x&=2 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= \frac {1}{2}+\frac {\sqrt {3}}{2} \\
x^{\prime \prime }\left (0\right ) &= \frac {1}{2}-\frac {\sqrt {3}}{2} \\
\end{align*}
Using Laplace transform method. |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.276 |
|
| \begin{align*}
x^{\prime \prime \prime }+x^{\prime \prime }-2 x&={\mathrm e}^{t} t \\
x \left (0\right ) &= 2 \\
x^{\prime }\left (0\right ) &= {\frac {21}{25}} \\
x^{\prime \prime }\left (0\right ) &= -{\frac {28}{25}} \\
\end{align*}
Using Laplace transform method. |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.261 |
|
| \begin{align*}
x^{\prime \prime }+4 x^{\prime }&=8 \sqrt {2}\, \sin \left (t +\frac {\pi }{4}\right ) \\
x \left (0\right ) &= -{\frac {40}{17}} \\
x^{\prime }\left (0\right ) &= {\frac {24}{17}} \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.170 |
|
| \begin{align*}
x^{\prime \prime }+4 x^{\prime }&=8 \sqrt {2}\, \sin \left (2 t +\frac {\pi }{4}\right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= -2 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.172 |
|
| \begin{align*}
x^{\prime }+y&=0 \\
x+y^{\prime }&=0 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.186 |
|
| \begin{align*}
x^{\prime }+x-2 y&=0 \\
y^{\prime }+x+4 y&=0 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.177 |
|
| \begin{align*}
x^{\prime }&=-y \\
y^{\prime }&=2 x+2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.190 |
|
| \begin{align*}
x^{\prime }+2 y&=3 t \\
y^{\prime }-2 x&=4 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.184 |
|
| \begin{align*}
x^{\prime }+x&=y+{\mathrm e}^{t} \\
y+y^{\prime }&=x+{\mathrm e}^{t} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.152 |
|
| \begin{align*}
x^{\prime }+y^{\prime }&=y+{\mathrm e}^{t} \\
2 x^{\prime }+y^{\prime }+2 y&=\cos \left (t \right ) \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.205 |
|
| \begin{align*}
x^{\prime }&=y-z \\
y^{\prime }&=x+y \\
z^{\prime }&=x+z \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 2 \\
z \left (0\right ) &= 3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.188 |
|
| \begin{align*}
x^{\prime }&=4 y+z \\
y^{\prime }&=z \\
z^{\prime }&=4 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 5 \\
y \left (0\right ) &= 0 \\
z \left (0\right ) &= 4 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.168 |
|
| \begin{align*}
x^{\prime }+2 y^{\prime }+x+y+z&=0 \\
x^{\prime }+y^{\prime }+x+z&=0 \\
z^{\prime }+2 y^{\prime }-y&=0 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 1 \\
z \left (0\right ) &= -4 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.190 |
|
| \begin{align*}
2 y y^{\prime }&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.495 |
|
| \begin{align*}
y^{\prime }+y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.069 |
|
| \begin{align*}
y^{\prime }&=-\frac {2 y+{\mathrm e}^{x}}{2 x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.980 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x y}{-x^{2}+2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.578 |
|
| \begin{align*}
x y^{\prime }&=x -y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.671 |
|
| \begin{align*}
y^{\prime }+y&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.740 |
|
| \begin{align*}
3 y^{\prime }&=\frac {4 x}{y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.126 |
|
| \begin{align*}
x y^{\prime }+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.890 |
|
| \begin{align*}
\cos \left (y\right ) y^{\prime }&=\sin \left (x +y\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
✗ |
6.092 |
|
| \begin{align*}
{\mathrm e}^{x +y} y^{\prime }&=3 x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.048 |
|
| \begin{align*}
x y^{\prime }+y&=y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.525 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (x +1\right )^{2}-2 y}{2 y} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
✗ |
9.193 |
|
| \begin{align*}
x \sin \left (y\right ) y^{\prime }&=\cos \left (y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.161 |
|
| \begin{align*}
\frac {x y^{\prime }}{y}&=\frac {2 y^{2}+1}{x +1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.945 |
|
| \begin{align*}
y^{\prime }+y&={\mathrm e}^{x}-\sin \left (y\right ) \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✗ |
✗ |
✗ |
✗ |
3.159 |
|
| \begin{align*}
\left (\cos \left (x +y\right )+\sin \left (x -y\right )\right ) y^{\prime }&=\cos \left (2 x \right ) \\
\end{align*} |
[_separable] |
✗ |
✓ |
✓ |
✗ |
21.828 |
|
| \begin{align*}
x y^{2} y^{\prime }&=y+1 \\
y \left (3 \,{\mathrm e}^{2}\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.253 |
|
| \begin{align*}
y^{\prime }&=3 x^{2} \left (y+2\right ) \\
y \left (2\right ) &= 8 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.835 |
|
| \begin{align*}
\ln \left (y^{x}\right ) y^{\prime }&=3 x^{2} y \\
y \left (2\right ) &= {\mathrm e}^{3} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✓ |
✗ |
4.895 |
|
| \begin{align*}
2 y y^{\prime }&={\mathrm e}^{x -y^{2}} \\
y \left (4\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.651 |
|
| \begin{align*}
y y^{\prime }&=2 x \sec \left (3 y\right ) \\
y \left (\frac {2}{3}\right ) &= \frac {\pi }{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✓ |
9.985 |
|
| \begin{align*}
y^{\prime }-\frac {3 y}{x}&=2 x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.089 |
|
| \begin{align*}
y^{\prime }+y&=\frac {{\mathrm e}^{x}}{2}-\frac {{\mathrm e}^{-x}}{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
2.053 |
|
| \begin{align*}
2 y+y^{\prime }&=x \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.325 |
|
| \begin{align*}
y^{\prime }+y \sec \left (x \right )&=\cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.743 |
|
| \begin{align*}
y^{\prime }-2 y&=-8 x^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.237 |
|
| \begin{align*}
y^{\prime }+3 y&=5 \,{\mathrm e}^{2 x}-6 \\
y \left (0\right ) &= 2 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.575 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x -2}&=3 x \\
y \left (3\right ) &= 4 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.356 |
|
| \begin{align*}
y^{\prime }-y&=2 \,{\mathrm e}^{4 x} \\
y \left (0\right ) &= -3 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.729 |
|
| \begin{align*}
y^{\prime }+\frac {2 y}{x +1}&=3 \\
y \left (0\right ) &= 5 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.158 |
|
| \begin{align*}
y^{\prime }+\frac {5 y}{9 x}&=3 x^{3}+x \\
y \left (-1\right ) &= 4 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.932 |
|
| \begin{align*}
2 y^{2}+y \,{\mathrm e}^{y x}+\left (4 y x +x \,{\mathrm e}^{y x}+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
3.246 |
|
| \begin{align*}
4 y x +2 x +\left (2 x^{2}+3 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✗ |
2.027 |
|
| \begin{align*}
4 y x +2 x^{2}+y+\left (2 x^{2}+3 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
✗ |
1.516 |
|
| \begin{align*}
2 \cos \left (x +y\right )-2 x \sin \left (x +y\right )-2 x \sin \left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _exact] |
✓ |
✓ |
✓ |
✓ |
4.876 |
|
| \begin{align*}
\frac {1}{x}+y+\left (x +3 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
2.100 |
|
| \begin{align*}
2 y-y^{2} \sec \left (x y^{2}\right )^{2}+\left (2 x -2 x y \sec \left (x y^{2}\right )^{2}\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✗ |
✓ |
✗ |
4.299 |
|
| \begin{align*}
4 y^{4}-1+12 x y^{3} y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.802 |
|
| \begin{align*}
1+{\mathrm e}^{\frac {y}{x}}-\frac {y \,{\mathrm e}^{\frac {y}{x}}}{x}+{\mathrm e}^{\frac {y}{x}} y^{\prime }&=0 \\
y \left (1\right ) &= -5 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
19.619 |
|
| \begin{align*}
x \cos \left (x -2 y\right )+\sin \left (x -2 y\right )-2 x \cos \left (x -2 y\right ) y^{\prime }&=0 \\
y \left (\frac {\pi }{12}\right ) &= \frac {\pi }{8} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _exact] |
✓ |
✓ |
✓ |
✓ |
7.454 |
|
| \begin{align*}
{\mathrm e}^{y}+\left (x \,{\mathrm e}^{y}-1\right ) y^{\prime }&=0 \\
y \left (5\right ) &= 0 \\
\end{align*} |
[[_1st_order, _with_exponential_symmetries], _exact] |
✓ |
✓ |
✗ |
✗ |
1.965 |
|
| \begin{align*}
-x y^{\prime }+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.178 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.130 |
|
| \begin{align*}
y x +x^{2} y^{\prime }&=-\frac {1}{y^{{3}/{2}}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
60.450 |
|
| \begin{align*}
2 y^{2}-9 y x +\left (3 y x -6 x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
12.391 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}}{x^{2}}-\frac {y}{x}+1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
3.650 |
|
| \begin{align*}
\frac {1}{x}+y^{\prime }&=\frac {2}{x^{3} y^{{4}/{3}}} \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
✗ |
1.980 |
|