| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 23301 |
\begin{align*}
y^{\prime }&=\frac {x \,{\mathrm e}^{2 x}}{y}+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.359 |
|
| 23302 |
\begin{align*}
x^{2} y^{\prime }+y^{2}&=x y y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.362 |
|
| 23303 |
\begin{align*}
x^{2}+y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.366 |
|
| 23304 |
\begin{align*}
x \left (3-2 x^{2} y\right ) y^{\prime }&=4 x -3 y+3 x^{2} y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.369 |
|
| 23305 |
\begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
9.377 |
|
| 23306 |
\begin{align*}
y \sqrt {1+y^{2}}+\left (x \sqrt {1+y^{2}}-y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.381 |
|
| 23307 |
\begin{align*}
y^{\prime }&=\sin \left (x \right ) \cos \left (y\right ) \\
y \left (3\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.382 |
|
| 23308 |
\begin{align*}
x y^{\prime }-y&=\sqrt {9 x^{2}+y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.388 |
|
| 23309 |
\begin{align*}
y y^{\prime \prime }&=1+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.389 |
|
| 23310 |
\begin{align*}
y y^{\prime }&=-x \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.392 |
|
| 23311 |
\begin{align*}
x +y^{3}+\left (3 y^{5}-3 x y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.395 |
|
| 23312 |
\begin{align*}
x y^{\prime }&=y-{\mathrm e}^{\frac {y}{x}} x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.398 |
|
| 23313 |
\begin{align*}
x \left ({\mathrm e}^{y}+4\right )&={\mathrm e}^{x +y} y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.404 |
|
| 23314 |
\begin{align*}
y^{\prime \prime }+a \,x^{n} y^{\prime }+\left (b \,x^{2 n}+c \,x^{n -1}\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.405 |
|
| 23315 |
\begin{align*}
y^{\prime }&=\sinh \left (\lambda x \right ) y^{2} a +b \sinh \left (\lambda x \right ) \cosh \left (\lambda x \right )^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.408 |
|
| 23316 |
\begin{align*}
\sin \left (x \right ) y^{2}+\cos \left (x \right )^{2} \ln \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.414 |
|
| 23317 |
\begin{align*}
x \cos \left (x \right ) y^{\prime }+y \left (x \sin \left (x \right )+\cos \left (x \right )\right )&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.414 |
|
| 23318 |
\begin{align*}
2 x \left (1+\sqrt {x^{2}-y}\right )&=\sqrt {x^{2}-y}\, y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.417 |
|
| 23319 |
\begin{align*}
y^{3} {y^{\prime }}^{3}&=27 x \left (y^{2}-2 x^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.418 |
|
| 23320 |
\begin{align*}
x&=\ln \left (y^{\prime }\right )+\sin \left (y^{\prime }\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.419 |
|
| 23321 |
\begin{align*}
y^{2}+12 x^{2} y+\left (2 y x +4 x^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.420 |
|
| 23322 |
\begin{align*}
y^{\prime }&=\frac {y \left (-1-x \,{\mathrm e}^{\frac {x +1}{x -1}}+x^{2} {\mathrm e}^{\frac {x +1}{x -1}} y-x^{2} {\mathrm e}^{\frac {x +1}{x -1}}+x^{3} {\mathrm e}^{\frac {x +1}{x -1}} y\right )}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.422 |
|
| 23323 |
\begin{align*}
x^{n} y^{\prime \prime }+\left (a \,x^{n +m}+1\right ) y^{\prime }+a \,x^{m} \left (1+m \,x^{n -1}\right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
9.422 |
|
| 23324 |
\begin{align*}
x^{3}+y^{3}-x y^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.430 |
|
| 23325 |
\begin{align*}
\frac {y}{1-x^{2} y^{2}}+\frac {x y^{\prime }}{1-x^{2} y^{2}}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.443 |
|
| 23326 |
\begin{align*}
x y^{\prime }-y&=x \tan \left (\frac {y}{x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.446 |
|
| 23327 |
\begin{align*}
y x -\left (x^{2}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.447 |
|
| 23328 |
\begin{align*}
{\mathrm e}^{x} \sin \left (y\right )+3 y-\left (3 x -{\mathrm e}^{x} \sin \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
9.454 |
|
| 23329 |
\begin{align*}
x +\left (2 x +3 y+2\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.457 |
|
| 23330 |
\begin{align*}
y^{\prime \prime }&=c \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.457 |
|
| 23331 |
\begin{align*}
\left (x -y\right ) y^{\prime }&=x +y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.465 |
|
| 23332 |
\begin{align*}
\left (\sin \left (y\right ) x -1\right ) y^{\prime }+\cos \left (y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.466 |
|
| 23333 |
\begin{align*}
y^{\prime }&=\frac {x}{y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.466 |
|
| 23334 |
\begin{align*}
2 x \left (1-x \right ) y^{\prime }+x +\left (1-x \right ) y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.474 |
|
| 23335 |
\begin{align*}
y+\left (x^{3}+x^{3} y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.478 |
|
| 23336 |
\begin{align*}
y^{\prime }&=\frac {x^{3}+y^{3}}{x y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.479 |
|
| 23337 |
\begin{align*}
y^{\prime }-\cos \left (x \right ) y&=y^{2} \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.482 |
|
| 23338 |
\begin{align*}
\left (x +1\right ) y^{\prime }&=y+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.490 |
|
| 23339 |
\begin{align*}
\left (x +y\right )^{2} y^{\prime }-a^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.491 |
|
| 23340 |
\begin{align*}
\sin \left (2 t \right ) y+\left (\sqrt {y}+\cos \left (2 t \right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.491 |
|
| 23341 |
\begin{align*}
y^{\prime }&=\frac {x -y}{x +y} \\
y \left (1\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.497 |
|
| 23342 |
\begin{align*}
y^{\prime \prime } \cos \left (y\right )+\left (\cos \left (y\right )-y^{\prime } \sin \left (y\right )\right ) y^{\prime }-2 y x&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
9.501 |
|
| 23343 |
\begin{align*}
x \left (-x^{2}+1\right ) y^{\prime }+\left (2 x^{2}-1\right ) y&=a \,x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.502 |
|
| 23344 |
\begin{align*}
k&=\frac {y^{\prime \prime }}{\left (y^{\prime }+1\right )^{{3}/{2}}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.502 |
|
| 23345 |
\begin{align*}
t y y^{\prime }-{\mathrm e}^{-\frac {y}{t}} t^{2}-y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.504 |
|
| 23346 |
\begin{align*}
y^{\prime }&=y^{2}+\lambda \arctan \left (x \right )^{n} y-a^{2}+a \lambda \arctan \left (x \right )^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.517 |
|
| 23347 |
\begin{align*}
y^{\prime }&=x^{3} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.527 |
|
| 23348 |
\begin{align*}
x y^{\prime }-x \left (-x +y\right ) \sqrt {x^{2}+y^{2}}-y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.529 |
|
| 23349 |
\begin{align*}
y^{\prime }&=y+{\mathrm e}^{2 t} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.529 |
|
| 23350 |
\begin{align*}
3 {y^{\prime }}^{2}+4 x y^{\prime }+x^{2}-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.530 |
|
| 23351 |
\begin{align*}
4 y y^{\prime \prime }&=a y+b y^{2}+c y^{3}+3 {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.533 |
|
| 23352 |
\begin{align*}
y^{2}-1+x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.536 |
|
| 23353 |
\begin{align*}
y^{\prime }&=y^{2}+a x \tanh \left (b x \right )^{m} y+a \tanh \left (b x \right )^{m} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.541 |
|
| 23354 |
\begin{align*}
y^{\prime }&=\frac {y \left (-1+\ln \left (x \left (x +1\right )\right ) y x^{4}-\ln \left (x \left (x +1\right )\right ) x^{3}\right )}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.542 |
|
| 23355 |
\begin{align*}
\left (-\left (1-y\right ) \left (a -y\right )+y \left (1-y\right )+\left (a -y\right ) y\right ) {y^{\prime }}^{2}+2 \left (1-y\right ) \left (a -y\right ) y y^{\prime \prime }&=\operatorname {a3} \left (1-y\right )^{2} \left (a -y\right )^{2}+\operatorname {a1} \left (1-y\right )^{2} y^{2}+\operatorname {a2} \left (a -y\right )^{2} y^{2}+\operatorname {a0} \left (a -y\right )^{2} y^{2} \left (1-y^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.548 |
|
| 23356 |
\begin{align*}
x y y^{\prime }&=-1+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.548 |
|
| 23357 |
\begin{align*}
x \sqrt {1-y^{2}}+y \sqrt {-x^{2}+1}\, y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.548 |
|
| 23358 |
\begin{align*}
y^{\prime }&=-\frac {3 x^{2}+2 y^{2}}{4 y x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.550 |
|
| 23359 |
\begin{align*}
\left (x +y+2\right ) y^{\prime }&=-x -y+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.558 |
|
| 23360 |
\begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.558 |
|
| 23361 |
\begin{align*}
2 x \left (x^{2}+y^{2}\right ) y^{\prime }&=\left (2 x^{2}+y^{2}\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.559 |
|
| 23362 |
\begin{align*}
x^{2}+y^{2}-2 x y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.560 |
|
| 23363 |
\begin{align*}
\left (x +2 y\right ) y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.563 |
|
| 23364 |
\begin{align*}
x^{3} x^{\prime \prime }+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.564 |
|
| 23365 |
\begin{align*}
x y^{\prime }&=-x \cos \left (\frac {y}{x}\right )^{2}+y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.565 |
|
| 23366 |
\begin{align*}
3 x \left (-x^{2}+1\right ) y^{2} y^{\prime }+\left (2 x^{2}-1\right ) y^{3}&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.567 |
|
| 23367 |
\begin{align*}
2 t +3 x+\left (x+2\right ) x^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.570 |
|
| 23368 |
\begin{align*}
\left (a +x \left (x +y\right )\right ) y^{\prime }-y \left (x +y\right )-b&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.573 |
|
| 23369 |
\begin{align*}
x y^{\prime }&=\left (-y x +1\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.580 |
|
| 23370 |
\begin{align*}
y^{\prime }&=y^{2}+a x \coth \left (b x \right )^{m} y+a \coth \left (b x \right )^{m} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.583 |
|
| 23371 |
\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*} |
✗ |
✓ |
✓ |
✗ |
9.586 |
|
| 23372 |
\begin{align*}
x^{2}+y+\left (x -2 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.594 |
|
| 23373 |
\begin{align*}
y^{\prime }&=\frac {y}{x}+\sec \left (\frac {y}{x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.595 |
|
| 23374 |
\begin{align*}
2 y y^{\prime \prime }&=y^{2} \left (a +b y\right )+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.595 |
|
| 23375 |
\begin{align*}
y^{\prime }&=\frac {\left ({\mathrm e}^{-\frac {y}{x}} y x +{\mathrm e}^{-\frac {y}{x}} y+{\mathrm e}^{-\frac {y}{x}} x^{2}+x \,{\mathrm e}^{-\frac {y}{x}}+x \right ) {\mathrm e}^{\frac {y}{x}}}{x \left (x +1\right )} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.599 |
|
| 23376 |
\begin{align*}
x \left (y+a \right )^{2} y^{\prime }&=b y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.602 |
|
| 23377 |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (b \,x^{2}+c x +d \right ) y}{a \,x^{2} \left (x -1\right )^{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.603 |
|
| 23378 |
\begin{align*}
x^{2}+y^{2}-2 x y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.603 |
|
| 23379 |
\begin{align*}
2 x y^{2}-y+x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.605 |
|
| 23380 |
\begin{align*}
{y^{\prime }}^{2} x&=a \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.607 |
|
| 23381 |
\begin{align*}
2 \left (1-x \right ) x \left (1-y\right ) \left (x -y\right ) y y^{\prime \prime }&=-y^{2} \left (1-y^{2}\right )+2 \left (1-y\right ) y \left (x^{2}+y-2 y x \right ) y^{\prime }+\left (1-x \right ) x \left (x -2 y-2 y x +3 y^{2}\right ) {y^{\prime }}^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
9.611 |
|
| 23382 |
\begin{align*}
4 y^{\prime \prime }-25 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.612 |
|
| 23383 |
\begin{align*}
y^{\prime }&=\left (2 \csc \left (2 x \right )+\cot \left (x \right )\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.616 |
|
| 23384 |
\begin{align*}
y^{\prime }+\frac {y}{x}&=y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.618 |
|
| 23385 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }+y&=\arctan \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.619 |
|
| 23386 |
\begin{align*}
y {y^{\prime }}^{2}-{\mathrm e}^{2 x}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.630 |
|
| 23387 |
\begin{align*}
\left (a x +c \right ) y^{\prime }&=\alpha \left (b x +a y\right )^{2}+\beta \left (b x +a y\right )-b x +\gamma \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.631 |
|
| 23388 |
\begin{align*}
2 {y^{\prime }}^{3}+x y^{\prime }-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
9.645 |
|
| 23389 |
\begin{align*}
y^{\prime }-2 y x&=\cos \left (x \right )-2 x \sin \left (x \right ) \\
y \left (\infty \right ) &= y_{0} \\
\end{align*} |
✗ |
✓ |
✗ |
✓ |
9.645 |
|
| 23390 |
\begin{align*}
x^{2} y^{\prime \prime }-4 x^{2} y^{\prime }+\left (x^{2}+1\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.649 |
|
| 23391 |
\begin{align*}
\left (x +y\right ) {y^{\prime }}^{2}+2 x y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.652 |
|
| 23392 |
\begin{align*}
\left (-2+y\right ) y^{\prime }&=x -3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.656 |
|
| 23393 |
\begin{align*}
y \left (x +y\right )+\left (x +2 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.658 |
|
| 23394 |
\begin{align*}
x \cos \left (y\right ) y^{\prime }-\left (x^{2}+1\right ) \sin \left (y\right )&=0 \\
y \left (1\right ) &= \frac {\pi }{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.661 |
|
| 23395 |
\begin{align*}
x^{2} y^{\prime }-3 y x -2 y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.664 |
|
| 23396 |
\begin{align*}
y^{\prime }&=\sin \left (x \right ) \cos \left (y\right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.664 |
|
| 23397 |
\begin{align*}
y^{\prime }&=\left (\tan \left (x \right )+y^{3} \sec \left (x \right )\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.677 |
|
| 23398 |
\begin{align*}
y^{\prime }&=t^{2} y^{3} \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.678 |
|
| 23399 |
\begin{align*}
y^{\prime }&=\left (a +b y+c y^{2}\right ) f \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.682 |
|
| 23400 |
\begin{align*}
y^{\prime }&=\sqrt {\frac {9 y^{2}-6 y+2}{x^{2}-2 x +5}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.690 |
|