| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 22001 |
\begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=\frac {1}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
17.729 |
|
| 22002 |
\begin{align*}
S^{\prime }&=S^{3}-2 S^{2}+S \\
S \left (0\right ) &= {\frac {3}{2}} \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
17.738 |
|
| 22003 |
\begin{align*}
y^{3}+x^{3} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
17.776 |
|
| 22004 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=3 \,{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
17.782 |
|
| 22005 |
\begin{align*}
4 y^{\prime \prime }-4 y^{\prime }+y&=\ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
17.810 |
|
| 22006 |
\begin{align*}
y^{\prime \prime }+\left (3 a +y\right ) y^{\prime }-y^{3}+a y^{2}+2 a^{2} y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
17.812 |
|
| 22007 |
\begin{align*}
x^{\prime \prime }+b x^{\prime }+c x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
17.819 |
|
| 22008 |
\begin{align*}
\left (-2 x^{2}+1\right ) y+4 x^{3} \left (2 x^{2}+1\right ) y^{\prime }+4 x^{6} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
17.835 |
|
| 22009 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=2 \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
17.847 |
|
| 22010 |
\begin{align*}
y^{\prime }&=-\frac {\left (-1-y^{4}+2 y^{2} x^{2}-x^{4}-y^{6}+3 x^{2} y^{4}-3 y^{2} x^{4}+x^{6}\right ) x}{y} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
17.862 |
|
| 22011 |
\begin{align*}
x^{\prime \prime }-\left (1-\frac {{x^{\prime }}^{2}}{3}\right ) x^{\prime }+x&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
17.866 |
|
| 22012 |
\begin{align*}
y^{\prime \prime }+y^{\prime } t +{\mathrm e}^{-t^{2}} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
17.871 |
|
| 22013 |
\begin{align*}
x^{2} y^{\prime \prime }+2 x f \left (x \right ) y^{\prime }+\left (f^{\prime }\left (x \right ) x +f \left (x \right )^{2}-f \left (x \right )+a \,x^{2}+b x +c \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
17.876 |
|
| 22014 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
17.882 |
|
| 22015 |
\begin{align*}
2 t \sin \left (\frac {y}{t}\right )-y \cos \left (\frac {y}{t}\right )+t \cos \left (\frac {y}{t}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
17.887 |
|
| 22016 |
\begin{align*}
{y^{\prime }}^{2}+a x y^{\prime }-b \,x^{2}-c&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
17.900 |
|
| 22017 |
\begin{align*}
y^{\prime }&=\frac {y^{2}}{y x -x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
17.905 |
|
| 22018 |
\begin{align*}
x \cos \left (y\right ) y^{\prime }+\sin \left (y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
17.915 |
|
| 22019 |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}-f \left (x \right ) g \left (x \right ) y+g^{\prime }\left (x \right ) \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
17.924 |
|
| 22020 |
\begin{align*}
y^{\prime }&=\frac {x +1+2 \sqrt {4 x^{2} y+1}\, x^{3}}{2 x^{3} \left (x +1\right )} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
17.932 |
|
| 22021 |
\begin{align*}
x^{\prime \prime }-2 a x^{\prime }+b x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
17.945 |
|
| 22022 |
\begin{align*}
y^{\prime } x -2 y&=\frac {x^{6}}{y+x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
17.968 |
|
| 22023 |
\begin{align*}
\left (1-x \right ) x y^{\prime \prime }-3 y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
17.973 |
|
| 22024 |
\begin{align*}
y^{\prime \prime }&=\frac {y^{\prime }}{x +1}-\frac {\left (1+3 x \right ) y}{4 x^{2} \left (x +1\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.006 |
|
| 22025 |
\begin{align*}
2 x -y-y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.047 |
|
| 22026 |
\begin{align*}
y^{\prime }&=\frac {x \left (x +2 \sqrt {x^{3}-6 y}\right )}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
18.048 |
|
| 22027 |
\begin{align*}
\left (x -a \right )^{2} y^{\prime }+k \left (x +y-a \right )^{2}+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.049 |
|
| 22028 |
\begin{align*}
\ln \left (t y\right )+\frac {t y^{\prime }}{y}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.052 |
|
| 22029 |
\begin{align*}
y^{\prime }&=\frac {1+y^{4}-8 a x y^{2}+16 a^{2} x^{2}+y^{6}-12 y^{4} a x +48 y^{2} a^{2} x^{2}-64 a^{3} x^{3}}{y} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
18.059 |
|
| 22030 |
\begin{align*}
\left (-x +y\right ) y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.077 |
|
| 22031 |
\begin{align*}
x^{\prime \prime }-2 {x^{\prime }}^{2}+x^{\prime }-2 x&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
18.078 |
|
| 22032 |
\begin{align*}
y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }+5 y&={\mathrm e}^{x} \sec \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
18.078 |
|
| 22033 |
\begin{align*}
y^{\prime \prime }+9 y&=\sin \left (2 x \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.091 |
|
| 22034 |
\begin{align*}
-y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.105 |
|
| 22035 |
\begin{align*}
4 y {y^{\prime }}^{2} y^{\prime \prime }&=3+{y^{\prime }}^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
18.117 |
|
| 22036 |
\begin{align*}
\left (x -2 \sqrt {y x}\right ) y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.121 |
|
| 22037 |
\begin{align*}
\cos \left (\frac {t}{y+t}\right )+{\mathrm e}^{\frac {2 y}{t}} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
18.129 |
|
| 22038 |
\begin{align*}
-\left (-x^{2}+1\right ) y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.136 |
|
| 22039 |
\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*} |
✓ |
✓ |
✓ |
✗ |
18.140 |
|
| 22040 |
\begin{align*}
4 x^{2} y y^{\prime }&=3 x \left (3 y^{2}+2\right )+2 \left (3 y^{2}+2\right )^{3} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
18.145 |
|
| 22041 |
\begin{align*}
y^{\prime } \sin \left (2 x \right )+\sin \left (2 y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.160 |
|
| 22042 |
\begin{align*}
y^{\prime }+x \sin \left (2 y\right )&=2 x \,{\mathrm e}^{-x^{2}} \cos \left (y\right )^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
18.198 |
|
| 22043 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime } x +\left (\operatorname {a1} \,x^{2 n}+\operatorname {b1} \,x^{n}+\operatorname {c1} \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
18.207 |
|
| 22044 |
\begin{align*}
4+\left (x -y+2\right )^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.217 |
|
| 22045 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x -9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
18.224 |
|
| 22046 |
\begin{align*}
y y^{\prime }-y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
18.227 |
|
| 22047 |
\begin{align*}
\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y&=\left (2+x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
18.251 |
|
| 22048 |
\begin{align*}
8 y+\left (1-2 x \right ) y^{\prime }+2 \left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
18.256 |
|
| 22049 |
\begin{align*}
\frac {1}{y}+\sec \left (\frac {y}{x}\right )-\frac {x y^{\prime }}{y^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
18.270 |
|
| 22050 |
\begin{align*}
y^{\prime }&=y^{{1}/{5}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
18.277 |
|
| 22051 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=6 x \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.286 |
|
| 22052 |
\begin{align*}
x^{\prime \prime }-x&=t^{2} \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.292 |
|
| 22053 |
\begin{align*}
x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }+\ln \left (x \right )+2 y^{\prime } x -y-2 x^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.293 |
|
| 22054 |
\begin{align*}
a y^{\prime \prime }+\left (b -a \right ) y^{\prime }+c y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.293 |
|
| 22055 |
\begin{align*}
2 y^{\prime \prime }+2 y^{\prime }+3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.295 |
|
| 22056 |
\begin{align*}
2 y+3 y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
18.308 |
|
| 22057 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=12 x \,{\mathrm e}^{3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.313 |
|
| 22058 |
\begin{align*}
y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \\
y \left (\sqrt {\pi }\right ) &= 3 \\
y^{\prime }\left (\sqrt {\pi }\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.316 |
|
| 22059 |
\begin{align*}
x^{4} y^{\prime \prime }+2 x^{3} \left (x +1\right ) y^{\prime }+n^{2} y&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
18.319 |
|
| 22060 |
\begin{align*}
y^{\prime }&=\frac {x^{2} \left (1+2 \sqrt {x^{3}-6 y}\right )}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.325 |
|
| 22061 |
\begin{align*}
2 x \tan \left (y\right )+3 y^{2}+x^{2}+\left (x^{2} \sec \left (y\right )^{2}+6 y x -y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
18.341 |
|
| 22062 |
\begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}+a y y^{\prime }-2 a y^{2}+y^{3} b&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
18.354 |
|
| 22063 |
\begin{align*}
\left (a +x \left (x +y\right )\right ) y^{\prime }-y \left (x +y\right )-b&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.367 |
|
| 22064 |
\begin{align*}
{y^{\prime }}^{2}-2 x^{3} y^{2} y^{\prime }-4 x^{2} y^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
18.371 |
|
| 22065 |
\begin{align*}
y^{\prime }&=\frac {x^{2}+y x +y^{2}}{y x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
18.378 |
|
| 22066 |
\begin{align*}
y^{\prime }&=\frac {2 y^{6} \left (1+4 x y^{2}+y^{2}\right )}{y^{3}+4 x y^{5}+y^{5}+2+24 x y^{2}+96 x^{2} y^{4}+128 x^{3} y^{6}} \\
\end{align*} |
✓ |
✗ |
✓ |
✗ |
18.384 |
|
| 22067 |
\begin{align*}
y y^{\prime }+\frac {a \left (1-\frac {b}{x^{2}}\right ) y}{x}&=\frac {a^{2} b}{x} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
18.384 |
|
| 22068 |
\begin{align*}
\left (x \sin \left (y\right )-1\right ) y^{\prime }+\cos \left (y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.393 |
|
| 22069 |
\begin{align*}
y^{\prime }+\frac {x y}{a^{2}+x^{2}}&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.398 |
|
| 22070 |
\begin{align*}
x \left (x^{2}+a x y+2 y^{2}\right ) y^{\prime }&=\left (a x +2 y\right ) y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.406 |
|
| 22071 |
\begin{align*}
x +y+2-\left (x -y-4\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.414 |
|
| 22072 |
\begin{align*}
y^{\prime }&=\sqrt {x -y} \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
18.441 |
|
| 22073 |
\begin{align*}
\left (x +y\right )^{2} y^{\prime }-a^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.448 |
|
| 22074 |
\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*} |
✓ |
✓ |
✓ |
✗ |
18.464 |
|
| 22075 |
\begin{align*}
y^{\prime \prime } x +2 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.469 |
|
| 22076 |
\begin{align*}
x^{2} y^{\prime }-y x&=x^{2}-y^{2} \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.475 |
|
| 22077 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.482 |
|
| 22078 |
\begin{align*}
y^{\prime }-\frac {y}{\left (\pi -1\right ) x}&=\frac {3 x y^{\pi }}{1-\pi } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.487 |
|
| 22079 |
\begin{align*}
2 y y^{\prime } x -y^{2}+a \,x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.490 |
|
| 22080 |
\begin{align*}
y y^{\prime }-y&=\frac {A}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
18.494 |
|
| 22081 |
\begin{align*}
m x^{\prime \prime }+k x&=F_{0} \cos \left (\omega t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.516 |
|
| 22082 |
\begin{align*}
y^{\prime \prime } x +\left (a \,x^{3} b +b \,x^{2}+a x -1\right ) y^{\prime }+a^{2} b \,x^{3} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
18.516 |
|
| 22083 |
\begin{align*}
x^{2} y^{\prime }&=y^{2}-y y^{\prime } x \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.521 |
|
| 22084 |
\begin{align*}
y^{\prime }&=\frac {\sqrt {x^{2}+y^{2}}}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
18.531 |
|
| 22085 |
\begin{align*}
y^{\prime }+f \left (x \right ) \left (y^{2}+2 a y+b \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.536 |
|
| 22086 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.539 |
|
| 22087 |
\begin{align*}
4 y^{\prime \prime }+4 y^{\prime }+y&=3 x \,{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.587 |
|
| 22088 |
\begin{align*}
y x&=y^{\prime } \ln \left (\frac {y^{\prime }}{x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.588 |
|
| 22089 |
\begin{align*}
\left (\operatorname {b2} x +\operatorname {a2} \right ) y+\operatorname {a1} x y^{\prime }+x^{3} y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
18.591 |
|
| 22090 |
\begin{align*}
y^{\prime }&=\frac {-6 x +y-3}{2 x -y-1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.609 |
|
| 22091 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.614 |
|
| 22092 |
\begin{align*}
y^{\prime }&=\left (\pi +x +7 y\right )^{{7}/{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
18.621 |
|
| 22093 |
\begin{align*}
y-y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
18.631 |
|
| 22094 |
\begin{align*}
\frac {2 t}{t^{2}+1}+y+\left ({\mathrm e}^{y}+t \right ) y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
18.660 |
|
| 22095 |
\begin{align*}
S^{\prime }&=S^{3}-2 S^{2}+S \\
S \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
18.673 |
|
| 22096 |
\begin{align*}
y^{\prime }&=y^{2}+a \lambda +b \lambda -2 a b -a \left (a +\lambda \right ) \tanh \left (\lambda x \right )^{2}-b \left (b +\lambda \right ) \coth \left (\lambda x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
18.677 |
|
| 22097 |
\begin{align*}
\left (x^{2} y^{\prime }+y^{2}\right ) \left (y^{\prime } x +y\right )&=\left (1+y^{\prime }\right )^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
18.679 |
|
| 22098 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
18.703 |
|
| 22099 |
\begin{align*}
y y^{\prime } x&=x^{2}-y x +y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
18.708 |
|
| 22100 |
\begin{align*}
x^{2} y^{\prime }&=\sec \left (y\right )+3 x \tan \left (y\right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
18.727 |
|