| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 22001 |
\begin{align*}
y^{\prime }&=\frac {\left (2 x +2+y\right ) y}{\left (\ln \left (y\right )+2 x -1\right ) \left (x +1\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.007 |
|
| 22002 |
\begin{align*}
y^{\prime } x -y-x \sin \left (\frac {y}{x}\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.012 |
|
| 22003 |
\begin{align*}
\frac {x}{y^{2}}+x +\left (\frac {x^{2}}{y^{3}}+y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.012 |
|
| 22004 |
\begin{align*}
\left (x +2 y^{3}\right ) y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.015 |
|
| 22005 |
\begin{align*}
\sqrt {-x^{2}+1}+\sqrt {1-y^{2}}\, y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.023 |
|
| 22006 |
\begin{align*}
\left (x \sqrt {1+x^{2}+y^{2}}-y \left (x^{2}+y^{2}\right )\right ) y^{\prime }&=\left (x^{2}+y^{2}\right ) x +y \sqrt {1+x^{2}+y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.023 |
|
| 22007 |
\begin{align*}
t^{2} y^{\prime \prime }-2 y^{\prime } t +2 y&=4 t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.032 |
|
| 22008 |
\begin{align*}
y^{\prime }&=-\frac {1296 y}{216-570 y^{8}+216 x^{2}+216 x^{3}-1296 y+594 x y^{6}-846 y^{7}-612 y^{5}-1728 y^{3}+1080 x y^{3}+1080 x y^{5}-2376 y^{2}-432 y x +72 y^{8} x +216 y^{7} x -882 y^{6}-1944 y^{4}-216 x^{2} y^{4}-648 y^{2} x^{2}+1152 y^{4} x +216 x y^{2}-648 x^{2} y-324 x^{2} y^{3}-315 y^{9}-126 y^{10}-8 y^{12}-36 y^{11}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.034 |
|
| 22009 |
\begin{align*}
\left (x +2 y\right ) y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.036 |
|
| 22010 |
\begin{align*}
y^{\prime }&=\frac {\left (1+2 \,{\mathrm e}^{y}\right ) {\mathrm e}^{-y}}{t \ln \left (t \right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.038 |
|
| 22011 |
\begin{align*}
y^{\prime }&=\frac {x^{2}}{y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.043 |
|
| 22012 |
\begin{align*}
x^{3} y^{\prime }-\sin \left (y\right )&=1 \\
y \left (\infty \right ) &= 5 \pi \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
9.048 |
|
| 22013 |
\begin{align*}
x^{2}+y^{2}+1-2 y y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.056 |
|
| 22014 |
\begin{align*}
y^{\prime }&=-\frac {x}{2}+1+x^{2} \sqrt {x^{2}-4 x +4 y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.057 |
|
| 22015 |
\begin{align*}
1+y^{2}-y y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.057 |
|
| 22016 |
\begin{align*}
2 \left (-x^{2}+1\right ) y^{\prime }&=\sqrt {-x^{2}+1}+\left (x +1\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.060 |
|
| 22017 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-9\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
9.063 |
|
| 22018 |
\begin{align*}
y^{\prime \prime } x +\left (a \,x^{n}+b \right ) y^{\prime }+c \left (a \,x^{n}-c x +b \right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
9.065 |
|
| 22019 |
\begin{align*}
t y+y^{\prime }&=t y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.073 |
|
| 22020 |
\begin{align*}
y^{\prime } x +y&=y^{2} \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.075 |
|
| 22021 |
\begin{align*}
\left (x -y\right )^{2} y^{\prime }&=a^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.083 |
|
| 22022 |
\begin{align*}
2 x y^{2}+y+\left (2 y^{3}-x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.089 |
|
| 22023 |
\begin{align*}
\frac {\tan \left (y\right )}{\cos \left (x \right )}&=\cos \left (x \right ) y^{\prime } \\
y \left (\frac {\pi }{4}\right ) &= \frac {\pi }{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.093 |
|
| 22024 |
\begin{align*}
y^{\prime }&=-\frac {x}{4}+\frac {1}{4}+x^{2} \sqrt {x^{2}-2 x +1+8 y} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.100 |
|
| 22025 |
\begin{align*}
y^{\prime }&=y^{2}-4 t \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.105 |
|
| 22026 |
\begin{align*}
y^{\prime }&=\frac {x -\cos \left (x \right ) y}{y+\sin \left (x \right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.107 |
|
| 22027 |
\begin{align*}
y^{\prime } x -y \left (2 y \ln \left (x \right )-1\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.114 |
|
| 22028 |
\begin{align*}
\frac {1}{\left (-y x +1\right )^{2}}+\left (y^{2}+\frac {x^{2}}{\left (-y x +1\right )^{2}}\right ) y^{\prime }&=0 \\
y \left (4\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
9.117 |
|
| 22029 |
\begin{align*}
y^{\prime }+2 y x&=y^{2} {\mathrm e}^{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.121 |
|
| 22030 |
\begin{align*}
\left (2 y^{2}-x \right ) y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.121 |
|
| 22031 |
\begin{align*}
x +y+1-\left (2 x +2 y+1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.123 |
|
| 22032 |
\begin{align*}
y^{\prime }&=-\frac {x}{4}+\frac {1}{4}+x \sqrt {x^{2}-2 x +1+8 y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.129 |
|
| 22033 |
\begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.130 |
|
| 22034 |
\begin{align*}
y^{\prime }&=\frac {y}{x}+\frac {y^{2}}{x^{2}} \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.130 |
|
| 22035 |
\begin{align*}
c y+\left (b x +a \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.135 |
|
| 22036 |
\begin{align*}
x^{\prime }&=-x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.137 |
|
| 22037 |
\begin{align*}
y^{\prime } x&=2 x^{2} y+y \ln \left (y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.137 |
|
| 22038 |
\begin{align*}
x^{5} y^{\prime }+y^{5}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.142 |
|
| 22039 |
\begin{align*}
\left (x -1\right ) y^{\prime }-3 y&=\left (x -1\right )^{5} \\
y \left (-1\right ) &= 16 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.143 |
|
| 22040 |
\begin{align*}
\left (p \left (1+p \right )-k^{2} \csc \left (x \right )^{2}\right ) y+\cot \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.144 |
|
| 22041 |
\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*} |
✓ |
✗ |
✓ |
✗ |
9.145 |
|
| 22042 |
\begin{align*}
\left (\sqrt {y x}-1\right ) x y^{\prime }-\left (\sqrt {y x}+1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.149 |
|
| 22043 |
\begin{align*}
\sqrt {t^{2}+1}\, y \,{\mathrm e}^{-t}+y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.151 |
|
| 22044 |
\begin{align*}
y {y^{\prime }}^{3}-3 y^{\prime } x +3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.151 |
|
| 22045 |
\begin{align*}
y^{\prime }&=\frac {1+2 F \left (\frac {4 x^{2} y+1}{4 x^{2}}\right ) x}{2 x^{3}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.155 |
|
| 22046 |
\begin{align*}
y^{\prime }&=a y^{2}+b \tan \left (x \right ) y+c \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.155 |
|
| 22047 |
\begin{align*}
y^{\prime }+\frac {y}{x}&=y^{6} x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.155 |
|
| 22048 |
\begin{align*}
x^{\prime }-2 x&={\mathrm e}^{2 t} t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.161 |
|
| 22049 |
\begin{align*}
y^{\prime }&=\sqrt {y x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.167 |
|
| 22050 |
\begin{align*}
\sin \left (y\right )+\cos \left (x \right ) y+\left (x \cos \left (y\right )+\sin \left (x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.177 |
|
| 22051 |
\begin{align*}
y^{\prime }&=\frac {1+F \left (\frac {a x y+1}{a x}\right ) a \,x^{2}}{a \,x^{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.177 |
|
| 22052 |
\begin{align*}
x^{2} y^{\prime }+\cos \left (2 y\right )&=1 \\
y \left (\infty \right ) &= \frac {5 \pi }{4} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
9.183 |
|
| 22053 |
\begin{align*}
y^{\prime }&=-\frac {x}{2}-\frac {a}{2}+x^{2} \sqrt {x^{2}+2 a x +a^{2}+4 y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.184 |
|
| 22054 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=3 x^{2}+2 \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.184 |
|
| 22055 |
\begin{align*}
6+12 y^{2} x^{2}+\left (7 x^{3} y+\frac {x}{y}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.189 |
|
| 22056 |
\begin{align*}
x^{2} \left (1-x \right ) y^{\prime }&=x \left (-x +2\right ) y-y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.194 |
|
| 22057 |
\begin{align*}
{y^{\prime \prime }}^{2}-2 y^{\prime \prime }+{y^{\prime }}^{2}-2 y^{\prime } x +x^{2}&=0 \\
y \left (0\right ) &= {\frac {1}{2}} \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
9.194 |
|
| 22058 |
\begin{align*}
y^{\prime }+\frac {3 y}{2}&=x^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.200 |
|
| 22059 |
\begin{align*}
x^{\prime }&=-x \left (1-x\right ) \left (2-x\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.210 |
|
| 22060 |
\begin{align*}
r^{\prime }&=\frac {r \left (1+\ln \left (t \right )\right )}{t \left (1+\ln \left (r\right )\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.210 |
|
| 22061 |
\begin{align*}
y^{\prime }&=-\frac {a x}{2}-\frac {b}{2}+x^{2} \sqrt {a^{2} x^{2}+2 a b x +b^{2}+4 a y-4 c} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.220 |
|
| 22062 |
\begin{align*}
y^{3} \sec \left (x \right )^{2}-\left (1-2 y^{2} \tan \left (x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.220 |
|
| 22063 |
\begin{align*}
y&=y^{\prime } x -\sqrt {x^{2}+y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.221 |
|
| 22064 |
\begin{align*}
y^{\prime } x +y&=y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.224 |
|
| 22065 |
\begin{align*}
x^{\prime }&=\left (4 t -x\right )^{2} \\
x \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.226 |
|
| 22066 |
\begin{align*}
2 x^{2} y^{\prime \prime }-3 y^{\prime } x +2 y&=\ln \left (x^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.234 |
|
| 22067 |
\begin{align*}
y^{\prime }&=\frac {x^{2}+y^{2}}{y x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.234 |
|
| 22068 |
\begin{align*}
y^{\prime } \sqrt {b \,x^{4}+a \,x^{2}+1}+\sqrt {1+a y^{2}+b y^{4}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.237 |
|
| 22069 |
\begin{align*}
y^{\prime \prime }+a^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.238 |
|
| 22070 |
\begin{align*}
x {y^{\prime }}^{2}+y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.239 |
|
| 22071 |
\begin{align*}
\left (x +\sqrt {x^{2}+y^{2}}\right ) y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.239 |
|
| 22072 |
\begin{align*}
y^{\prime }&=\sqrt {1-y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.242 |
|
| 22073 |
\begin{align*}
\left (x +1\right ) y^{\prime }+y x&={\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.244 |
|
| 22074 |
\begin{align*}
2 n y-2 y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.250 |
|
| 22075 |
\begin{align*}
y^{\prime }&=\frac {y^{2} x^{2}+2 y}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.254 |
|
| 22076 |
\begin{align*}
\left (2 x +y\right ) y^{\prime }+x -2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.256 |
|
| 22077 |
\begin{align*}
n y-y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.259 |
|
| 22078 |
\begin{align*}
12 y x +6 y^{3}+\left (9 x^{2}+10 x y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.260 |
|
| 22079 |
\begin{align*}
x^{2} y^{\prime }+a y^{3}-a \,x^{2} y^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.260 |
|
| 22080 |
\begin{align*}
y^{\prime }&=-\frac {x}{2}-\frac {a}{2}+x \sqrt {x^{2}+2 a x +a^{2}+4 y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.263 |
|
| 22081 |
\begin{align*}
x \left (\ln \left (x \right )-\ln \left (y\right )\right ) y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.264 |
|
| 22082 |
\begin{align*}
\left (x +1\right ) y^{\prime }&=1+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.264 |
|
| 22083 |
\begin{align*}
\left (x -a \right ) \left (-b +x \right ) y^{\prime }+k \left (x +y-a \right ) \left (x +y-b \right )+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.267 |
|
| 22084 |
\begin{align*}
y^{\prime }&=25+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.267 |
|
| 22085 |
\begin{align*}
y^{\prime }&=\alpha y^{2}+\beta +\gamma \cosh \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.268 |
|
| 22086 |
\begin{align*}
t^{2} y^{\prime \prime }-y^{\prime } t +y&=t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.274 |
|
| 22087 |
\begin{align*}
y \ln \left (y\right )+y^{\prime } x&=1 \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
9.277 |
|
| 22088 |
\begin{align*}
x^{3} y^{\prime }&=y \left (y+x^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.287 |
|
| 22089 |
\begin{align*}
x^{2} y^{\prime }+y \left (x +y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.287 |
|
| 22090 |
\begin{align*}
y^{\prime } x +x \tan \left (\frac {y}{x}\right )-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.290 |
|
| 22091 |
\begin{align*}
x^{\prime }+p \left (t \right ) x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.312 |
|
| 22092 |
\begin{align*}
x^{\prime }&={\mathrm e}^{t +x} \\
x \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.313 |
|
| 22093 |
\begin{align*}
y^{\prime }&=\frac {\sqrt {1-y^{2}}}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.313 |
|
| 22094 |
\begin{align*}
y^{\prime }&=\frac {y+{\mathrm e}^{\frac {x +1}{x -1}} x^{3}+{\mathrm e}^{\frac {x +1}{x -1}} x y^{2}}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.314 |
|
| 22095 |
\begin{align*}
y^{\prime }&=\frac {2 x^{2} \cos \left (x \right )+2 x^{3} \sin \left (x \right )-2 x \sin \left (x \right )+2 x +2 y^{2} x^{2}-4 x \sin \left (x \right ) y+4 y \cos \left (x \right ) x^{2}+4 y x +3-\cos \left (2 x \right )-2 \sin \left (2 x \right ) x -4 \sin \left (x \right )+x^{2} \cos \left (2 x \right )+x^{2}+4 \cos \left (x \right ) x}{2 x^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.316 |
|
| 22096 |
\begin{align*}
x^{2} \left ({y^{\prime }}^{2}-y^{2}\right )+y^{2}&=x^{4}+2 y y^{\prime } x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.316 |
|
| 22097 |
\begin{align*}
\left (b x +a \right ) y+8 y^{\prime }+16 y^{\prime \prime } x&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.319 |
|
| 22098 |
\begin{align*}
2 y y^{\prime } x -y^{2}+a \,x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.320 |
|
| 22099 |
\begin{align*}
\ln \left (y^{\prime }\right )+y^{\prime } x +a y+b&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.326 |
|
| 22100 |
\begin{align*}
s^{\prime }&=\frac {1}{s+t +1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.326 |
|