| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 19201 |
\begin{align*}
\cos \left (x \right ) y^{\prime }&=1-y-\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.632 |
|
| 19202 |
\begin{align*}
2 y^{\prime } x +y^{3} {\mathrm e}^{-2 x}&=2 y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.633 |
|
| 19203 |
\begin{align*}
y-2 x^{3} \tan \left (\frac {y}{x}\right )-y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.633 |
|
| 19204 |
\begin{align*}
2 y^{\prime } x&=y \left (1+y^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.633 |
|
| 19205 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+y x&=2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.634 |
|
| 19206 |
\begin{align*}
y^{\prime }&=\frac {-{\mathrm e}^{x}+3 x^{2}}{2 y-11} \\
y \left (0\right ) &= 11 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.634 |
|
| 19207 |
\begin{align*}
-y+y^{\prime } x&=x \\
y \left (1\right ) &= 7 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.635 |
|
| 19208 |
\begin{align*}
y^{\prime \prime }+a y^{\prime }+b \left (-b \,x^{2 n}-a \,x^{n}+n \,x^{n -1}\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
2.635 |
|
| 19209 |
\begin{align*}
x y^{\prime } y&=a +b y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.636 |
|
| 19210 |
\begin{align*}
y x +{\mathrm e}^{x} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.636 |
|
| 19211 |
\begin{align*}
{y^{\prime }}^{2} \sin \left (y^{\prime }\right )-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.637 |
|
| 19212 |
\begin{align*}
t^{2} x^{\prime \prime }+a t x^{\prime }+x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.637 |
|
| 19213 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime } x +\left (3 x^{2}+2 n -1\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.638 |
|
| 19214 |
\begin{align*}
y^{\prime }+\left (4 y-\frac {8}{y^{3}}\right ) x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.638 |
|
| 19215 |
\begin{align*}
y^{\prime }&=t \left (3-y\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.639 |
|
| 19216 |
\begin{align*}
x^{2} y^{\prime }&=2 x^{2}+y^{2}+4 y x \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.639 |
|
| 19217 |
\begin{align*}
\left (y^{2}-a^{2} x^{2}\right ) {y^{\prime }}^{2}+2 x y^{\prime } y+\left (-a^{2}+1\right ) x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.639 |
|
| 19218 | \begin{align*}
y^{\prime }-2 y x&=2 x \\
y \left (0\right ) &= 1 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 2.641 |
|
| 19219 |
\begin{align*}
x y^{2}+x -2 y+3+\left (x^{2} y-2 y-2 x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.641 |
|
| 19220 |
\begin{align*}
y^{\prime \prime }-\left (\frac {2 f^{\prime }\left (x \right )}{f \left (x \right )}+\frac {g^{\prime \prime }\left (x \right )}{g^{\prime }\left (x \right )}-\frac {g^{\prime }\left (x \right )}{g \left (x \right )}\right ) y^{\prime }+\left (\frac {f^{\prime }\left (x \right ) \left (\frac {2 f^{\prime }\left (x \right )}{f \left (x \right )}+\frac {g^{\prime \prime }\left (x \right )}{g^{\prime }\left (x \right )}-\frac {g^{\prime }\left (x \right )}{g \left (x \right )}\right )}{f \left (x \right )}-\frac {f^{\prime \prime }\left (x \right )}{f \left (x \right )}-\frac {v^{2} {g^{\prime }\left (x \right )}^{2}}{g \left (x \right )^{2}}+{g^{\prime }\left (x \right )}^{2}\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.641 |
|
| 19221 |
\begin{align*}
y^{\prime } \cos \left (y\right )&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.642 |
|
| 19222 |
\begin{align*}
2 \cos \left (x \right ) \sin \left (x \right ) \sin \left (y\right )+\cos \left (y\right ) \sin \left (x \right )^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.643 |
|
| 19223 |
\begin{align*}
y^{\prime }&=\frac {1+y}{x -1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.644 |
|
| 19224 |
\begin{align*}
y^{\prime }+\frac {2 y}{x}&=6 \sqrt {x^{2}+1}\, \sqrt {y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.645 |
|
| 19225 |
\begin{align*}
2 x {y^{\prime }}^{2}+\left (2 x -y\right ) y^{\prime }+1-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.646 |
|
| 19226 |
\begin{align*}
y^{\prime }+y&=\sin \left (x \right ) \\
y \left (\pi \right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.646 |
|
| 19227 |
\begin{align*}
y^{\prime }&=x \sqrt {x^{2}+9} \\
y \left (-4\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.647 |
|
| 19228 |
\begin{align*}
y^{\prime }&=\frac {x^{2}+{\mathrm e}^{-x}}{y^{2}-{\mathrm e}^{y}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.647 |
|
| 19229 |
\begin{align*}
y^{\prime }&=\frac {\cos \left (x -y\right )}{\sin \left (x \right ) \sin \left (y\right )}-1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.648 |
|
| 19230 |
\begin{align*}
x^{3}+x y^{2}-y+\left (x^{2} y+y^{3}+x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.648 |
|
| 19231 |
\begin{align*}
y^{\prime }&=\cos \left (y\right ) \cos \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.649 |
|
| 19232 |
\begin{align*}
y \cos \left (t \right )+\left (2 y+\sin \left (t \right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.649 |
|
| 19233 |
\begin{align*}
y^{\prime }&=\sqrt {a +b y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.650 |
|
| 19234 |
\begin{align*}
y^{\prime } x +b x +\left (2+a x y\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.650 |
|
| 19235 |
\begin{align*}
y x^{\prime }+2 x&=5 y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.650 |
|
| 19236 |
\begin{align*}
y^{\prime \prime \prime }&=y^{\prime } \left (1+y^{\prime }\right ) \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
2.651 |
|
| 19237 | \begin{align*}
x^{\prime \prime }-\omega ^{2} x&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 2.651 |
|
| 19238 |
\begin{align*}
y^{\prime }&=\frac {x -2 y+1}{2 x -4 y} \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.651 |
|
| 19239 |
\begin{align*}
y-\left (x +x y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.652 |
|
| 19240 |
\begin{align*}
\left (b x +a \right ) y+8 y^{\prime }+16 y^{\prime \prime } x&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.652 |
|
| 19241 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+n \left (n -1\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
2.652 |
|
| 19242 |
\begin{align*}
y^{\prime \prime }+8 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.653 |
|
| 19243 |
\begin{align*}
y^{\prime } x -2 x^{4}-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.654 |
|
| 19244 |
\begin{align*}
{y^{\prime }}^{3}+f \left (x \right ) \left (y-a \right )^{2} \left (y-b \right )^{2} \left (y-c \right )^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.654 |
|
| 19245 |
\begin{align*}
\left (t^{2}+1\right ) y^{\prime }&=t y-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.655 |
|
| 19246 |
\begin{align*}
x^{2} {y^{\prime }}^{2}+y^{2}-y^{4}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.655 |
|
| 19247 |
\begin{align*}
4 y y^{\prime \prime }-3 {y^{\prime }}^{2}-12 y^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.655 |
|
| 19248 |
\begin{align*}
x^{\prime \prime }+4 x^{3}&=0 \\
x \left (a \right ) &= 0 \\
x \left (b \right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.655 |
|
| 19249 |
\begin{align*}
x^{2} u^{\prime \prime }-3 x u^{\prime }+13 u&=0 \\
u \left (1\right ) &= -1 \\
u^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.656 |
|
| 19250 |
\begin{align*}
\ln \left (y\right ) x +y x +\left (y \ln \left (x \right )+y x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.657 |
|
| 19251 |
\begin{align*}
x^{2} y^{\prime }&=y \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.658 |
|
| 19252 |
\begin{align*}
y^{\prime \prime } x +\left (2 x +3\right ) y^{\prime }+8 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.658 |
|
| 19253 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.658 |
|
| 19254 |
\begin{align*}
y^{\prime }&=2 x \left (\pi +y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.658 |
|
| 19255 |
\begin{align*}
y^{\prime }-\frac {3 y}{x}+x^{3} y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.659 |
|
| 19256 | \begin{align*}
y^{\prime } y&=x y^{2}+x \\
y \left (0\right ) &= -2 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 2.660 |
|
| 19257 |
\begin{align*}
y^{\prime }&=t -1-y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.661 |
|
| 19258 |
\begin{align*}
y^{\prime }&=y \cos \left (t \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.661 |
|
| 19259 |
\begin{align*}
y^{\prime }-a \,x^{n} \left (1+y^{2}\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.663 |
|
| 19260 |
\begin{align*}
y^{\prime }&=\cos \left (x \right )^{2} \cos \left (2 y\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.664 |
|
| 19261 |
\begin{align*}
y^{\prime \prime } x -y^{\prime } x +y&=x^{3} \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
2.665 |
|
| 19262 |
\begin{align*}
y^{\prime }+\tan \left (x \right )&=\left (1-y\right ) \sec \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.666 |
|
| 19263 |
\begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y-5 x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.667 |
|
| 19264 |
\begin{align*}
y^{\prime }&=x \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.667 |
|
| 19265 |
\begin{align*}
3 x^{2} y+x^{3} y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.668 |
|
| 19266 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime }+2 y x&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.668 |
|
| 19267 |
\begin{align*}
y {y^{\prime }}^{2}+x^{3} y^{\prime }-x^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.669 |
|
| 19268 |
\begin{align*}
y^{\prime }+\frac {y}{x}&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.669 |
|
| 19269 |
\begin{align*}
y^{\prime } x +y^{2}+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.670 |
|
| 19270 |
\begin{align*}
\left (x^{2}-1\right ) y+x \left (x^{2}+1\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.670 |
|
| 19271 |
\begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}}&=\ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.670 |
|
| 19272 |
\begin{align*}
x \left (x^{2}-1\right ) y^{\prime }-\left (2 x^{2}-1\right ) y+a \,x^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.670 |
|
| 19273 |
\begin{align*}
y^{\prime }+y \cos \left (x \right )&=\frac {\sin \left (2 x \right )}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.670 |
|
| 19274 |
\begin{align*}
y^{4}+2 y+\left (x y^{3}+2 y^{4}-4 x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.670 |
|
| 19275 | \begin{align*}
x^{\prime \prime }&=x-x^{3} \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} | ✓ | ✓ | ✓ | ✗ | 2.670 |
|
| 19276 |
\begin{align*}
3 \left (x^{2}-y^{2}\right ) y^{\prime }+3 \,{\mathrm e}^{x}+6 \left (x +1\right ) x y-2 y^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.671 |
|
| 19277 |
\begin{align*}
a y+y^{\prime }+2 y^{\prime \prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.671 |
|
| 19278 |
\begin{align*}
y^{\prime }&=\frac {y x +2 y-x -2}{y x -3 y+x -3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.672 |
|
| 19279 |
\begin{align*}
y^{\prime }&=\sin \left (x -y\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.674 |
|
| 19280 |
\begin{align*}
{y^{\prime }}^{2}&=\frac {1}{x y^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.674 |
|
| 19281 |
\begin{align*}
m v^{\prime }&=-m g +k v^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.674 |
|
| 19282 |
\begin{align*}
y^{\prime }&=\frac {1+\sqrt {x -y}}{1-\sqrt {x -y}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.674 |
|
| 19283 |
\begin{align*}
x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+a&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.675 |
|
| 19284 |
\begin{align*}
y \,{\mathrm e}^{x} y^{\prime }&={\mathrm e}^{-y}+{\mathrm e}^{-2 x -y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.675 |
|
| 19285 |
\begin{align*}
y^{\prime } x -2 y&=\cos \left (x \right ) x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.677 |
|
| 19286 |
\begin{align*}
y^{\prime } x +a x y^{2}+2 y+b x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.677 |
|
| 19287 |
\begin{align*}
y^{\prime \prime }&=y^{\prime }+{y^{\prime }}^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.678 |
|
| 19288 |
\begin{align*}
\left (x^{3}+1\right ) y^{\prime }&=x^{2} y \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.680 |
|
| 19289 |
\begin{align*}
\left (1-x \right ) x y^{\prime \prime }+2 \left (1-x \right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.680 |
|
| 19290 |
\begin{align*}
y x +x^{2} y^{\prime }&=\sqrt {x}\, \sin \left (x \right ) \\
y \left (2\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.681 |
|
| 19291 |
\begin{align*}
\cos \left (y\right ) \sin \left (t \right ) y^{\prime }&=\cos \left (t \right ) \sin \left (y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.682 |
|
| 19292 |
\begin{align*}
\left ({\mathrm e}^{v}+1\right ) \cos \left (u \right )+{\mathrm e}^{v} \left (1+\sin \left (u \right )\right ) v^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.682 |
|
| 19293 |
\begin{align*}
x^{4}+2 y-y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.682 |
|
| 19294 | \begin{align*}
\left (t +1\right ) y+t y^{\prime }&=2 t \,{\mathrm e}^{-t} \\
y \left (1\right ) &= a \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 2.683 |
|
| 19295 |
\begin{align*}
\left (2 x -y+3\right ) y^{\prime }+2&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.683 |
|
| 19296 |
\begin{align*}
y^{\prime }&=y^{3} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.685 |
|
| 19297 |
\begin{align*}
y^{\prime }-\frac {4 t y}{4 t^{2}+1}&=4 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.685 |
|
| 19298 |
\begin{align*}
x^{2} y^{\prime }+2 y x&=5 y^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.686 |
|
| 19299 |
\begin{align*}
{y^{\prime \prime }}^{2} x^{2} \left (x^{2}-1\right )-1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.686 |
|
| 19300 |
\begin{align*}
\left (t +1\right ) y+t y^{\prime }&=2 t \,{\mathrm e}^{-t} \\
y \left (1\right ) &= a \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.687 |
|