| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 14401 |
\begin{align*}
y y^{\prime \prime }&={y^{\prime }}^{2} \left (1-y^{\prime } \cos \left (y\right )+y y^{\prime } \sin \left (y\right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.879 |
|
| 14402 |
\begin{align*}
x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.880 |
|
| 14403 |
\begin{align*}
y y^{\prime }&=\sin \left (x \right ) \\
y \left (0\right ) &= -4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.880 |
|
| 14404 |
\begin{align*}
y^{\prime \prime }+y&={\mathrm e}^{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.880 |
|
| 14405 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }-4 y&=12 \,{\mathrm e}^{2 x} \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.881 |
|
| 14406 |
\begin{align*}
\left (t -1\right ) y^{\prime \prime }-y^{\prime } t +y&=2 t \,{\mathrm e}^{-t} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.881 |
|
| 14407 |
\begin{align*}
y+x^{3}+x y^{2}-y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.882 |
|
| 14408 |
\begin{align*}
\sec \left (y\right )^{2} y^{\prime }+2 x \tan \left (y\right )&=x^{3} \\
\end{align*} |
✓ |
✗ |
✓ |
✗ |
2.884 |
|
| 14409 |
\begin{align*}
-y^{\prime } x +y&=3-2 x^{2} y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.885 |
|
| 14410 |
\begin{align*}
y^{\prime } x&=x^{3}-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.885 |
|
| 14411 |
\begin{align*}
\cos \left (y\right ) \sin \left (x \right )-\cos \left (x \right ) \sin \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.885 |
|
| 14412 |
\begin{align*}
z^{\prime }&=10^{x +z} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.885 |
|
| 14413 |
\begin{align*}
3 x^{2} y^{\prime \prime }+x^{6} y^{\prime }+2 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.885 |
|
| 14414 |
\begin{align*}
\left (1+a \cos \left (2 x \right )\right ) y^{\prime \prime }+\lambda y&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
2.885 |
|
| 14415 |
\begin{align*}
\sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y&=x \sin \left (x \right ) \\
y \left (\frac {\pi }{2}\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.886 |
|
| 14416 |
\begin{align*}
x^{2} y^{\prime \prime }&=2 y^{\prime } x +{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.887 |
|
| 14417 |
\begin{align*}
y^{\prime }&=-a n \,x^{n -1} y^{2}+c \,x^{m} \left (a \,x^{n}+b \right ) y-c \,x^{m} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.887 |
|
| 14418 |
\begin{align*}
y+\frac {y^{3}}{3}+\frac {x^{2}}{2}+\frac {\left (x y^{2}+x \right ) y^{\prime }}{4}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.887 |
|
| 14419 |
\begin{align*}
y^{\prime }-y&={\mathrm e}^{2 x} y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.888 |
|
| 14420 |
\begin{align*}
y^{\prime }&=x \\
y \left (0\right ) &= -3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.888 |
|
| 14421 |
\begin{align*}
y^{\prime \prime }&={\mathrm e}^{y} y^{\prime } \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
2.888 |
|
| 14422 |
\begin{align*}
y^{\prime }&=\frac {1}{y x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.889 |
|
| 14423 |
\begin{align*}
\tan \left (x \right ) \sin \left (y\right )+3 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.889 |
|
| 14424 |
\begin{align*}
y^{\prime }&=\frac {1}{y x +x^{3} y^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.890 |
|
| 14425 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+2 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.890 |
|
| 14426 |
\begin{align*}
\left (-x^{2}+4\right ) y^{\prime }+4 y&=\left (2+x \right ) y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.890 |
|
| 14427 |
\begin{align*}
3 x \left (1+y^{2}\right )+y \left (x^{2}+2\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.890 |
|
| 14428 |
\begin{align*}
4 y^{\prime \prime }+9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.890 |
|
| 14429 |
\begin{align*}
{y^{\prime }}^{3}+y y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.890 |
|
| 14430 |
\begin{align*}
y^{\prime \prime }+y&=3 \cos \left (2 x \right ) {\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.891 |
|
| 14431 |
\begin{align*}
y^{\prime }&=2 x y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.891 |
|
| 14432 |
\begin{align*}
3 y^{\prime } y^{2} x +y^{3}-2 x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.891 |
|
| 14433 |
\begin{align*}
x^{2} y^{\prime }&=1-x^{2}+y^{2}-y^{2} x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.892 |
|
| 14434 |
\begin{align*}
\cosh \left (y\right ) y^{\prime }+\sinh \left (y\right )-{\mathrm e}^{-x}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.892 |
|
| 14435 |
\begin{align*}
y^{\prime \prime }+y&=\cos \left (2 x \right ) {\mathrm e}^{x} x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.892 |
|
| 14436 |
\begin{align*}
y^{\prime } x +y&=\cos \left (x \right ) x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.892 |
|
| 14437 |
\begin{align*}
1-y^{\prime } x&=\ln \left (y\right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.893 |
|
| 14438 |
\begin{align*}
y^{\prime \prime }+y&=\csc \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.894 |
|
| 14439 |
\begin{align*}
x \ln \left (x \right ) y^{\prime }-x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.895 |
|
| 14440 |
\begin{align*}
y^{\prime }&=6 x y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.895 |
|
| 14441 |
\begin{align*}
y^{\prime \prime } x +\left (x +3\right ) y^{\prime }+7 x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
2.895 |
|
| 14442 |
\begin{align*}
x^{\prime }&=-3 x+3 y+z+5 \sin \left (2 t \right ) \\
y^{\prime }&=x-5 y-3 z+5 \cos \left (2 t \right ) \\
z^{\prime }&=-3 x+7 y+3 z+23 \,{\mathrm e}^{t} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 2 \\
z \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.895 |
|
| 14443 |
\begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y \left (2 \pi \right ) &= 1 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
2.896 |
|
| 14444 |
\begin{align*}
-y+2 \tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.897 |
|
| 14445 |
\begin{align*}
\tan \left (x \right ) y^{\prime }&=y \\
y \left (\frac {\pi }{2}\right ) &= \frac {\pi }{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.898 |
|
| 14446 |
\begin{align*}
t^{2} y^{\prime \prime }+y^{\prime } t -\left (1+t \right ) y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
2.898 |
|
| 14447 |
\begin{align*}
y^{\prime }&=\frac {2 x \left (-1+y\right )}{x^{2}+3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.898 |
|
| 14448 |
\begin{align*}
x^{2} y^{\prime \prime }-\left (a^{2} x^{2 n}+a \left (2 b +n -1\right ) x^{n}+b \left (b -1\right )\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
2.898 |
|
| 14449 |
\begin{align*}
\cos \left (y\right ) \sin \left (x \right )+\cos \left (x \right ) \sin \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.898 |
|
| 14450 |
\begin{align*}
y^{\prime }&=\frac {y \ln \left (x \right )}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.898 |
|
| 14451 |
\begin{align*}
x^{2} y^{\prime }+2 x \left (1-x \right ) y&={\mathrm e}^{x} \left (2 \,{\mathrm e}^{x}-1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.899 |
|
| 14452 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }&=4 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.899 |
|
| 14453 |
\begin{align*}
\left (x +1\right ) y^{\prime }+y \left (-x +y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.900 |
|
| 14454 |
\begin{align*}
t^{2} x^{\prime \prime }+t x^{\prime }+t^{2} x&=\lambda x \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✗ |
✗ |
✓ |
✓ |
2.900 |
|
| 14455 |
\begin{align*}
2 x^{2} y^{\prime }&=2 y^{2}+3 y x -2 a^{2} x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.902 |
|
| 14456 |
\begin{align*}
y^{3}+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.903 |
|
| 14457 |
\begin{align*}
-8 y+2 y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.903 |
|
| 14458 |
\begin{align*}
-y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.903 |
|
| 14459 |
\begin{align*}
y^{\prime }-y&=\sin \left (x \right )+\cos \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.903 |
|
| 14460 |
\begin{align*}
y^{\prime }&=\frac {x y}{1-y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.904 |
|
| 14461 |
\begin{align*}
s^{\prime }+x^{2}&=x^{2} {\mathrm e}^{3 s} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.904 |
|
| 14462 |
\begin{align*}
\cos \left (\theta \right ) v^{\prime }+v&=3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.905 |
|
| 14463 |
\begin{align*}
y^{\prime }&=\frac {2 y}{t}+\frac {y^{2}}{t^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.906 |
|
| 14464 |
\begin{align*}
y^{\prime }&=y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.906 |
|
| 14465 |
\begin{align*}
y^{\prime \prime }+16 y&=4 \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.906 |
|
| 14466 |
\begin{align*}
3 y^{\prime \prime }-2 y^{\prime }-8 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.906 |
|
| 14467 |
\begin{align*}
y^{\prime }&=y^{2}+a \lambda \,{\mathrm e}^{\lambda x}-a^{2} {\mathrm e}^{2 \lambda x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.908 |
|
| 14468 |
\begin{align*}
y^{\prime }&=\frac {t \left (4-y\right ) y}{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.909 |
|
| 14469 |
\begin{align*}
\left ({\mathrm e}^{x}-3 y^{2} x^{2}\right ) y^{\prime }+{\mathrm e}^{x} y&=2 x y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.909 |
|
| 14470 |
\begin{align*}
\sin \left (x \right ) y+\cos \left (x \right )^{2}-\cos \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.909 |
|
| 14471 |
\begin{align*}
2 n y-2 y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.909 |
|
| 14472 |
\begin{align*}
y^{\prime \prime }-5 y^{\prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.909 |
|
| 14473 |
\begin{align*}
y^{\prime }&=y \,{\mathrm e}^{-x^{2}} \\
y \left (4\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.910 |
|
| 14474 |
\begin{align*}
2 y x -3+\left (x^{2}+4 y\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.910 |
|
| 14475 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }&=2 \cos \left (4 x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.910 |
|
| 14476 |
\begin{align*}
\left (x^{2}+y^{2}+x \right ) y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.911 |
|
| 14477 |
\begin{align*}
y^{\prime }&=10+{\mathrm e}^{x +y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.911 |
|
| 14478 |
\begin{align*}
\left (3 y-2\right ) {y^{\prime }}^{2}-4+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.911 |
|
| 14479 |
\begin{align*}
-2 y+y^{\prime }&={\mathrm e}^{2 t} t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.911 |
|
| 14480 |
\begin{align*}
x^{3}-3 x^{2} y+5 x y^{2}-7 y^{3}+\left (y^{4}+2 y^{2}-x^{3}+5 x^{2} y-21 x y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.912 |
|
| 14481 |
\begin{align*}
y^{\prime }+\frac {y}{x \ln \left (x \right )}&=9 x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.913 |
|
| 14482 |
\begin{align*}
y^{\prime \prime }+y&=\sin \left (x \right )+{\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.913 |
|
| 14483 |
\begin{align*}
y^{\prime }+3 y&=3 x^{2} {\mathrm e}^{-3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.913 |
|
| 14484 |
\begin{align*}
y^{\prime \prime }&=\left (x^{2}+a \right ) y \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
2.914 |
|
| 14485 |
\begin{align*}
y^{\prime \prime }&=2 y^{\prime }-6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.914 |
|
| 14486 |
\begin{align*}
y^{\prime } x +y&=y^{2} \ln \left (x \right ) \\
y \left (1\right ) &= {\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.915 |
|
| 14487 |
\begin{align*}
y^{\prime \prime }+9 y&=18 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.915 |
|
| 14488 |
\begin{align*}
-y+y^{\prime }&=4 \operatorname {Heaviside}\left (t -\frac {\pi }{4}\right ) \sin \left (t +\frac {\pi }{4}\right ) \\
y \left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
2.916 |
|
| 14489 |
\begin{align*}
y^{\prime }&=\frac {-2 x -y+F \left (x \left (x +y\right )\right )}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.916 |
|
| 14490 |
\begin{align*}
y^{\prime }-y&=\sin \left (x \right )+\cos \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.917 |
|
| 14491 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +4 y&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.918 |
|
| 14492 |
\begin{align*}
4 y+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.918 |
|
| 14493 |
\begin{align*}
y^{\prime }&=\sqrt {y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.919 |
|
| 14494 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+2 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.919 |
|
| 14495 |
\begin{align*}
1+y+\left (1-x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.920 |
|
| 14496 |
\begin{align*}
x^{\prime \prime }-4 x&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.920 |
|
| 14497 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.920 |
|
| 14498 |
\begin{align*}
t^{2} y^{\prime \prime }+\left (t^{2}-3 t \right ) y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
2.921 |
|
| 14499 |
\begin{align*}
y^{\prime }&=-\cot \left (t \right ) y+6 \cos \left (t \right )^{2} \\
y \left (\frac {\pi }{4}\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
2.921 |
|
| 14500 |
\begin{align*}
2 x {y^{\prime }}^{2}+\left (2 x -y\right ) y^{\prime }+1-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
2.921 |
|