| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 25401 |
\begin{align*}
y^{\prime }-\frac {3 y}{x}&=x^{4} y^{{1}/{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
48.338 |
|
| 25402 |
\begin{align*}
4 y x +2 x^{2}+y+\left (2 x^{2}+3 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
48.353 |
|
| 25403 |
\begin{align*}
y^{\prime }&=\frac {y}{x +y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
48.415 |
|
| 25404 |
\begin{align*}
\left (3 x +y\right )^{2} y^{\prime }&=4 \left (3 x +2 y\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
48.434 |
|
| 25405 |
\begin{align*}
y&=2 y^{\prime }+\sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
48.454 |
|
| 25406 |
\begin{align*}
y^{2}+\left (y x +3 y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
48.458 |
|
| 25407 |
\begin{align*}
x^{2}-y^{2}-2 y y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
48.459 |
|
| 25408 |
\begin{align*}
y^{\prime } x&=\lambda \arcsin \left (x \right )^{n} y^{2}+k y+\lambda \,b^{2} x^{2 k} \arcsin \left (x \right )^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
48.493 |
|
| 25409 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+3 y&=8 \,{\mathrm e}^{x}+9 \\
y \left (-\infty \right ) &= 3 \\
\end{align*} |
✗ |
✓ |
✗ |
✓ |
48.502 |
|
| 25410 |
\begin{align*}
{\mathrm e}^{2 x} y-\left (4+{\mathrm e}^{2 x}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
48.522 |
|
| 25411 |
\begin{align*}
y^{\prime } x +y&=y y^{\prime } x -y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
48.705 |
|
| 25412 |
\begin{align*}
y^{\prime } x&=a y^{2}+b \ln \left (x \right )+c \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
48.716 |
|
| 25413 |
\begin{align*}
2 x -y+\left (-x +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
48.741 |
|
| 25414 |
\begin{align*}
y^{\prime \prime } x +\left (1-3 n \right ) y^{\prime }-a^{2} n^{2} x^{2 n -1} y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
48.763 |
|
| 25415 |
\begin{align*}
y \left (2 y x +1\right )-y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
48.764 |
|
| 25416 |
\begin{align*}
\left (1-3 x^{2} y+6 y^{2}\right ) y^{\prime }-3 x y^{2}+x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
48.783 |
|
| 25417 |
\begin{align*}
x \left (2-9 x y^{2}\right )+y \left (4 y^{2}-6 x^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
48.784 |
|
| 25418 |
\begin{align*}
y^{\prime \prime }+\left (a \,{\mathrm e}^{x}+b \right ) y^{\prime }+\left (c \left (a -c \right ) {\mathrm e}^{2 x}+\left (a k +b c -2 c k +c \right ) {\mathrm e}^{x}+k \left (b -k \right )\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
48.794 |
|
| 25419 |
\begin{align*}
y^{\prime } \sqrt {b^{2}-x^{2}}&=\sqrt {a^{2}-y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
48.798 |
|
| 25420 |
\begin{align*}
3 y^{\prime } t +9 y&=2 t y^{{5}/{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
48.817 |
|
| 25421 |
\begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +4 y&=24 x +24 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
48.842 |
|
| 25422 |
\begin{align*}
y^{\prime }&=-\frac {\left (-\ln \left (-1+y\right )+\ln \left (1+y\right )+2 \ln \left (x \right )\right ) x \left (1+y\right )^{2}}{8} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
48.864 |
|
| 25423 |
\begin{align*}
y^{\prime }&=-\left (1+k \right ) x^{k} y^{2}+\lambda \arctan \left (x \right )^{n} \left (x^{1+k} y-1\right ) \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
48.875 |
|
| 25424 |
\begin{align*}
2+3 x^{2}-2 y x +\left (3-x^{2}+6 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
48.908 |
|
| 25425 |
\begin{align*}
{y^{\prime }}^{2}&=\frac {1}{x^{3} y^{4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
48.952 |
|
| 25426 |
\begin{align*}
y^{2}-x^{2}+y y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
48.954 |
|
| 25427 |
\begin{align*}
y \left (\operatorname {a2} +\operatorname {b2} \,x^{k}+\operatorname {c2} \,x^{2 k}+\left (-1+\operatorname {a1} +\operatorname {b1} \,x^{k}\right ) f \left (x \right )+f \left (x \right )^{2}+f^{\prime }\left (x \right )\right )+x \left (\operatorname {a1} +\operatorname {b1} \,x^{k}+2 f \left (x \right )\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
49.019 |
|
| 25428 |
\begin{align*}
\left (a \,{\mathrm e}^{\lambda x}+b \right ) y^{\prime \prime }+\left (c \,{\mathrm e}^{\lambda x}+d \right ) y^{\prime }+k \left (\left (-a k +c \right ) {\mathrm e}^{\lambda x}+d -b k \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
49.046 |
|
| 25429 |
\begin{align*}
y^{\prime } t +2 y \ln \left (t \right )&=4 \ln \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
49.056 |
|
| 25430 |
\begin{align*}
x^{2}+2 y x -2 y^{2}+\left (y^{2}+2 y x -2 x^{2}\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
49.088 |
|
| 25431 |
\begin{align*}
L x^{\prime \prime }+g \sin \left (x\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
49.102 |
|
| 25432 |
\begin{align*}
-y+y^{\prime } x&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
49.104 |
|
| 25433 |
\begin{align*}
y&=y^{\prime } x -\sqrt {x^{2}+y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
49.115 |
|
| 25434 |
\begin{align*}
y+3 x +y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
49.141 |
|
| 25435 |
\begin{align*}
{y^{\prime }}^{3}-2 y y^{\prime }+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
49.143 |
|
| 25436 |
\begin{align*}
y^{\prime }&=1+y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
49.148 |
|
| 25437 |
\begin{align*}
-\left (4 p^{2}+1\right ) y-8 y^{\prime } x +4 \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
49.149 |
|
| 25438 |
\begin{align*}
y^{\prime \prime }+\sin \left (y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
49.177 |
|
| 25439 |
\begin{align*}
y^{\prime } \sqrt {b^{2}+x^{2}}&=\sqrt {y^{2}+a^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
49.214 |
|
| 25440 |
\begin{align*}
x \sin \left (\frac {y}{x}\right ) y^{\prime }&=y \sin \left (\frac {y}{x}\right )+x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
49.283 |
|
| 25441 |
\begin{align*}
2 u^{2}+2 u v+\left (u^{2}+v^{2}\right ) v^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
49.319 |
|
| 25442 |
\begin{align*}
3 x^{2}+2 y x -2 y^{2}+\left (2 x^{2}+6 y x +y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
49.321 |
|
| 25443 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+a x y^{\prime }+\left (b \,x^{2}+c x +d \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
49.334 |
|
| 25444 |
\begin{align*}
y-\left ({\mathrm e}^{3 x}+1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
49.347 |
|
| 25445 |
\begin{align*}
2 y y^{\prime } x&=x^{2}-y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
49.353 |
|
| 25446 |
\begin{align*}
y^{\prime }&=x^{3}+y^{3} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
49.424 |
|
| 25447 |
\begin{align*}
3 \sin \left (y\right )-5 x +2 x^{2} \cot \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
49.456 |
|
| 25448 |
\begin{align*}
y^{\prime }+\frac {y}{x}&=2 x^{{3}/{2}} \sqrt {y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
49.493 |
|
| 25449 |
\begin{align*}
y^{\prime }&=y^{2} \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
49.542 |
|
| 25450 |
\begin{align*}
\left (a y+b x +c \right ) y^{\prime }+\alpha y+\beta x +\gamma &=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
49.546 |
|
| 25451 |
\begin{align*}
\left (a \,x^{3}+\left (a x +b y\right )^{3}\right ) y y^{\prime }+x \left (\left (a x +b y\right )^{3}+y^{3} b \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
49.552 |
|
| 25452 |
\begin{align*}
y^{\prime \prime }+{\mathrm e}^{\lambda x} \left (a \,{\mathrm e}^{2 \mu x}+b \right ) y^{\prime }+\mu \left ({\mathrm e}^{\lambda x} \left (b -a \,{\mathrm e}^{2 \mu x}\right )-\mu \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
49.552 |
|
| 25453 |
\begin{align*}
y^{\prime \prime }+6 y {y^{\prime }}^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
49.578 |
|
| 25454 |
\begin{align*}
\left (y+2\right ) x +y \left (2+x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
49.585 |
|
| 25455 |
\begin{align*}
2 t^{2}-y+\left (t +y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
49.593 |
|
| 25456 |
\begin{align*}
5 x +3 \,{\mathrm e}^{y}+2 x \,{\mathrm e}^{y} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
49.594 |
|
| 25457 |
\begin{align*}
3 x +\frac {6}{y}+\left (\frac {x^{2}}{y}+\frac {3 y}{x}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
49.617 |
|
| 25458 |
\begin{align*}
y^{\prime \prime }-2 \left (-1+x \right ) y^{\prime }+x^{2} y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
49.620 |
|
| 25459 |
\begin{align*}
y^{\prime } \left (\cos \left (y\right )-\sin \left (\alpha \right ) \sin \left (x \right )\right ) \cos \left (y\right )+\left (\cos \left (x \right )-\sin \left (\alpha \right ) \sin \left (y\right )\right ) \cos \left (x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
49.641 |
|
| 25460 |
\begin{align*}
y^{\prime }&=\frac {-3+x +y}{y-x +1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
49.730 |
|
| 25461 |
\begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime }+2 x \left (2 x +y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
49.738 |
|
| 25462 |
\begin{align*}
y^{\prime }&=y-x y^{3} {\mathrm e}^{-2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
49.741 |
|
| 25463 |
\begin{align*}
y^{\prime }&=\frac {y}{y^{3}+x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
49.753 |
|
| 25464 |
\begin{align*}
5 x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y&=\sqrt {x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
49.762 |
|
| 25465 |
\begin{align*}
y^{\prime }&=1+\left (t -y\right )^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
49.779 |
|
| 25466 |
\begin{align*}
x^{2} {y^{\prime }}^{3}+y \left (x^{2} y+1\right ) {y^{\prime }}^{2}+y^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
49.794 |
|
| 25467 |
\begin{align*}
2 \sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y&=y^{3} \left (\cos \left (x \right ) x -\sin \left (x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
49.824 |
|
| 25468 |
\begin{align*}
y y^{\prime \prime }&=-b y^{2}-a y y^{\prime }+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
49.838 |
|
| 25469 |
\begin{align*}
y^{\prime }&=\frac {2 y^{2}-y x +2 x^{2}}{y x +2 x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
49.843 |
|
| 25470 |
\begin{align*}
\frac {-4+6 y x +2 y^{2}}{3 x^{2}+4 y x +3 y^{2}}+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
49.845 |
|
| 25471 |
\begin{align*}
y^{\prime }&=-\frac {2}{t}+\frac {y}{t}+\frac {y^{2}}{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
49.848 |
|
| 25472 |
\begin{align*}
y^{\prime }&=y \left (1-y\right ) \left (2-y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
49.868 |
|
| 25473 |
\begin{align*}
\frac {y}{x}+\left (y^{3}+\ln \left (x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
49.877 |
|
| 25474 |
\begin{align*}
y&=y^{\prime } x +a x \sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
49.881 |
|
| 25475 |
\begin{align*}
\cos \left (x \right )^{2} y^{\prime \prime }-\cos \left (x \right ) \sin \left (x \right ) y^{\prime }-y&=\sin \left (x \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
49.950 |
|
| 25476 |
\begin{align*}
y^{\prime }&=\sqrt {1-y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
49.990 |
|
| 25477 |
\begin{align*}
y^{\prime } x&=\left (x^{2}+\tan \left (y\right )\right ) \cos \left (y\right )^{2} \\
\end{align*} |
✗ |
✗ |
✓ |
✗ |
50.030 |
|
| 25478 |
\begin{align*}
y^{\prime } x +y&=y^{\prime } \sqrt {1-y^{2} x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
50.046 |
|
| 25479 |
\begin{align*}
y^{\prime \prime }-\lambda ^{2} y&=0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime }\left (1\right ) &= \frac {1}{\lambda } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
50.104 |
|
| 25480 |
\begin{align*}
2 y x +\left (x^{2}-y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
50.122 |
|
| 25481 |
\begin{align*}
y^{\prime }&=\frac {x^{2}+2 y^{2}}{x^{2}-2 y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
50.139 |
|
| 25482 |
\begin{align*}
y y^{\prime } \sqrt {x^{2}+1}+x \sqrt {1+y^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
50.221 |
|
| 25483 |
\begin{align*}
4 x -y+2+\left (x +y+3\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
50.263 |
|
| 25484 |
\begin{align*}
\left (x^{2}-x^{3}+3 x y^{2}+2 y^{3}\right ) y^{\prime }+2 x^{3}+3 x^{2} y+y^{2}-y^{3}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
50.277 |
|
| 25485 |
\begin{align*}
y^{\prime }&=\lambda \arcsin \left (x \right )^{n} \left (y-a \,x^{m}-b \right )^{2}+a m \,x^{m -1} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
50.322 |
|
| 25486 |
\begin{align*}
y^{\prime }&=\frac {x +y}{x -y} \\
y \left (5\right ) &= 8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
50.324 |
|
| 25487 |
\begin{align*}
\left (3 x^{2}+2 y x +4 y^{2}\right ) y^{\prime }+2 x^{2}+6 y x +y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
50.329 |
|
| 25488 |
\begin{align*}
x +2 y-1+\left (2 x +4 y-3\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
50.330 |
|
| 25489 |
\begin{align*}
3+2 x +\left (-2+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
50.335 |
|
| 25490 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=x \,{\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
50.351 |
|
| 25491 |
\begin{align*}
\left (1-x \right ) y^{\prime \prime }-4 y^{\prime } x +5 y&=\cos \left (x \right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
50.376 |
|
| 25492 |
\begin{align*}
y \left (a^{2}+x^{2}+y^{2}\right ) y^{\prime }+x \left (-a^{2}+x^{2}+y^{2}\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
50.411 |
|
| 25493 |
\begin{align*}
\left (2 x^{2} y-x \right ) y^{\prime }-2 x y^{2}-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
50.421 |
|
| 25494 |
\begin{align*}
x \left (2 y x +1\right ) y^{\prime }+\left (1+2 y x -y^{2} x^{2}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
50.463 |
|
| 25495 |
\begin{align*}
x -y y^{\prime }&=a {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
50.471 |
|
| 25496 |
\begin{align*}
2+3 x y^{2}-4 x^{2} y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
50.488 |
|
| 25497 |
\begin{align*}
x^{\prime \prime }&=2 {x^{\prime }}^{3} x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
50.490 |
|
| 25498 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=3 x -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
50.507 |
|
| 25499 |
\begin{align*}
2 x \left (a \,x^{2}+b x +c \right ) y^{\prime \prime }+\left (a \,x^{2}-c \right ) y^{\prime }+\lambda \,x^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
50.541 |
|
| 25500 |
\begin{align*}
\left (x +y\right )^{2} y^{\prime }&=\left (x +y+2\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
50.549 |
|