| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 21801 |
\begin{align*}
y&=\arcsin \left (y^{\prime }\right )+\ln \left (1+{y^{\prime }}^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.201 |
|
| 21802 |
\begin{align*}
{\mathrm e}^{y}+\cos \left (x \right ) y+\left (x \,{\mathrm e}^{y}+\sin \left (x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.204 |
|
| 21803 |
\begin{align*}
-a y^{3}-\frac {b}{x^{{3}/{2}}}+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.204 |
|
| 21804 |
\begin{align*}
\left (x \sqrt {1+y^{2}}+1\right ) \left (1+y^{2}\right )&=x y y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.204 |
|
| 21805 |
\begin{align*}
x y^{\prime }+y \left (1+y^{2}\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.205 |
|
| 21806 |
\begin{align*}
x^{\prime }&=t^{3} \left (1-x\right ) \\
x \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.209 |
|
| 21807 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }-n \left (n +1\right ) y+\frac {\left (n +1\right ) \operatorname {LegendreP}\left (n +1, x\right )-\left (n +1\right ) x \operatorname {LegendreP}\left (n , x\right )}{x^{2}-1}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
6.210 |
|
| 21808 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}-2 x \right ) y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
6.214 |
|
| 21809 |
\begin{align*}
y^{\prime \prime }&={\mathrm e}^{y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.216 |
|
| 21810 |
\begin{align*}
c y^{\prime }&=\frac {a x +b y^{2}}{r x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.220 |
|
| 21811 |
\begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }+\left (a x +b \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
6.220 |
|
| 21812 |
\begin{align*}
y^{\prime }+\frac {3 y}{t}&=y^{2} t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.220 |
|
| 21813 |
\begin{align*}
y^{\prime }&=\cot \left (x \right ) \left (\sqrt {y}-y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.222 |
|
| 21814 |
\begin{align*}
x y^{\prime \prime }+\left (-x +b \right ) y^{\prime }-a y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
6.222 |
|
| 21815 |
\begin{align*}
y^{\prime }&=a y-b y^{2} \\
y \left (0\right ) &= \operatorname {y0} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.223 |
|
| 21816 |
\begin{align*}
y^{\prime }&=x^{2}+y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
6.224 |
|
| 21817 |
\begin{align*}
\cos \left (y\right ) y^{\prime }+\sin \left (y\right )&=x +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.226 |
|
| 21818 |
\begin{align*}
\left (x^{2}-4\right ) y^{\prime \prime }+y&=0 \\
\end{align*}
Series expansion around \(x=2\). |
✓ |
✓ |
✓ |
✓ |
6.227 |
|
| 21819 |
\begin{align*}
y^{\left (8\right )}+y&=x^{15} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.229 |
|
| 21820 |
\begin{align*}
2 x^{3} y y^{\prime }+3 x^{2} y^{2}+7&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.234 |
|
| 21821 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-\left (x^{2}+4\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
6.235 |
|
| 21822 |
\begin{align*}
y^{\prime }+\left (4 y-\frac {8}{y^{3}}\right ) x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.237 |
|
| 21823 |
\begin{align*}
y^{\prime }&=x \,{\mathrm e}^{y} \\
y \left (1\right ) &= {\frac {5}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.238 |
|
| 21824 |
\begin{align*}
\sin \left (y\right )^{2}+\cos \left (x \right )^{2} y^{\prime }&=0 \\
y \left (\frac {\pi }{4}\right ) &= \frac {\pi }{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.239 |
|
| 21825 |
\begin{align*}
y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\
y \left (-6\right ) &= 0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
6.242 |
|
| 21826 |
\begin{align*}
y^{\prime }&=\frac {y}{x} \\
y \left (-1\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.243 |
|
| 21827 |
\begin{align*}
x y^{\prime }+2 y&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.245 |
|
| 21828 |
\begin{align*}
x^{3} y^{\prime }&=2 y^{2}+2 x^{2} y-2 x^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.246 |
|
| 21829 |
\begin{align*}
x y^{\prime }+x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.246 |
|
| 21830 |
\begin{align*}
y^{\prime }&=x^{2}+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.247 |
|
| 21831 |
\begin{align*}
y^{\prime }&=\frac {-3 x^{2} y-2 x^{3}-2 x -x y^{2}-y+x^{3} y^{3}+3 y^{2} x^{4}+3 x^{5} y+x^{6}}{x \left (x^{2}+y x +1\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.247 |
|
| 21832 |
\begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
y \left (\frac {1}{2}\right ) &= -4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.251 |
|
| 21833 |
\begin{align*}
2 y y^{\prime \prime }&=1+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.252 |
|
| 21834 |
\begin{align*}
y^{\prime }&=\left (x -y+3\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.252 |
|
| 21835 |
\begin{align*}
y^{\prime }&=\lambda \sinh \left (\lambda x \right ) y^{2}-\lambda \sinh \left (\lambda x \right )^{3} \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
6.254 |
|
| 21836 |
\begin{align*}
x^{3} y^{\prime }&=b \,x^{2} y+a \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.256 |
|
| 21837 |
\begin{align*}
y^{\prime }-x y^{2}&=2 y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.256 |
|
| 21838 |
\begin{align*}
y^{\prime \prime \prime \prime }-16 y&=g \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
6.256 |
|
| 21839 |
\begin{align*}
3 x^{4} {y^{\prime }}^{2}-y x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.257 |
|
| 21840 |
\begin{align*}
y^{\prime }-\frac {2 y}{x}&=\frac {1}{y x} \\
y \left (1\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.260 |
|
| 21841 |
\begin{align*}
4 y {y^{\prime }}^{2} y^{\prime \prime }&=3+{y^{\prime }}^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.261 |
|
| 21842 |
\begin{align*}
y^{\prime }&=\frac {y}{x} \\
y \left (-1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.261 |
|
| 21843 |
\begin{align*}
y^{\prime }&=\frac {\left (x +y+1\right ) y}{\left (x +y+2 y^{3}\right ) \left (x +1\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.262 |
|
| 21844 |
\begin{align*}
y^{\prime }&=\frac {y^{2}}{y^{2}+y^{{3}/{2}}+x^{2} \sqrt {y}-2 x y^{{3}/{2}}+y^{{5}/{2}}+x^{3}-3 x^{2} y+3 x y^{2}-y^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.263 |
|
| 21845 |
\begin{align*}
9 y {y^{\prime }}^{2}+4 x^{3} y^{\prime }-4 x^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.264 |
|
| 21846 |
\begin{align*}
m^{\prime }&=-\frac {k}{m^{2}} \\
m \left (0\right ) &= m_{0} \\
\end{align*} |
✓ |
✗ |
✓ |
✓ |
6.267 |
|
| 21847 |
\begin{align*}
\cos \left (x \right ) \sin \left (x \right ) y^{\prime }-y-\sin \left (x \right )^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.269 |
|
| 21848 |
\begin{align*}
y^{\prime }&=-\frac {y}{t}+2 \\
y \left (1\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.272 |
|
| 21849 |
\begin{align*}
2 x y^{\prime \prime }-\left (x -1\right ) y^{\prime }+a y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
6.275 |
|
| 21850 |
\begin{align*}
\left (x^{4}+y^{2}\right ) y^{\prime }-4 x^{3} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.278 |
|
| 21851 |
\begin{align*}
y^{\prime }+y x&=x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.279 |
|
| 21852 |
\begin{align*}
y^{\prime } \left (x^{3}+1\right )^{{2}/{3}}+\left (y^{3}+1\right )^{{2}/{3}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.280 |
|
| 21853 |
\begin{align*}
x^{4} y^{3}+y+\left (x^{5} y^{2}-x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.282 |
|
| 21854 |
\begin{align*}
y&=\left (x y^{\prime }+2 y\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.282 |
|
| 21855 |
\begin{align*}
3 y+y^{\prime }&=\sqrt {y}\, \sin \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.285 |
|
| 21856 |
\begin{align*}
1+v^{2}+\left (u^{2}+1\right ) v v^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.285 |
|
| 21857 |
\begin{align*}
y^{\prime }&=\frac {x^{2}+2 x +1+2 \sqrt {x^{2}+2 x +1-4 y}}{2 x +2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.286 |
|
| 21858 |
\begin{align*}
y^{\prime }&=\frac {2 y}{t}+\frac {y^{2}}{t^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.289 |
|
| 21859 |
\begin{align*}
2 x y y^{\prime }-2 y^{2}-x^{2} {\mathrm e}^{-\frac {y^{2}}{x^{2}}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.289 |
|
| 21860 |
\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*} |
✓ |
✓ |
✗ |
✗ |
6.289 |
|
| 21861 |
\begin{align*}
y^{\prime }&=y \left (x +y\right ) \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
6.290 |
|
| 21862 |
\begin{align*}
2 y^{2}+3 y x -2 y+6 x +x \left (x +2 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.291 |
|
| 21863 |
\begin{align*}
{y^{\prime }}^{2}&=a +b y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.293 |
|
| 21864 |
\begin{align*}
-{y^{\prime }}^{2}+{y^{\prime }}^{3}+y y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.293 |
|
| 21865 |
\begin{align*}
y^{\prime }&=-\frac {x}{4}+1+y^{2}+\frac {7 x^{2} y}{16}-\frac {y x}{2}+\frac {5 x^{4}}{128}-\frac {5 x^{3}}{64}+\frac {x^{2}}{16}+y^{3}+\frac {3 x^{2} y^{2}}{8}-\frac {3 x y^{2}}{4}+\frac {3 x^{4} y}{64}-\frac {3 x^{3} y}{16}+\frac {x^{6}}{512}-\frac {3 x^{5}}{256} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.293 |
|
| 21866 |
\begin{align*}
y^{\prime }&=\frac {a^{3} x^{3} y^{3}+3 y^{2} a^{2} x^{2}+3 a x y+1+a^{2} x}{x^{3} a^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.295 |
|
| 21867 |
\begin{align*}
3 \left (2-y\right ) y^{\prime }+y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.296 |
|
| 21868 |
\begin{align*}
x^{2}+2 x +y+\left (3 x^{2} y-x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.300 |
|
| 21869 |
\begin{align*}
2 x \left (a \,x^{2}+b x +c \right ) y^{\prime \prime }+\left (a \left (2-k \right ) x^{2}+b \left (1-k \right ) x -c k \right ) y^{\prime }+\lambda \,x^{1+k} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.300 |
|
| 21870 |
\begin{align*}
y^{\prime }&=\sin \left (x -y\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.302 |
|
| 21871 |
\begin{align*}
x \sqrt {1+y^{2}}&=y y^{\prime } \sqrt {x^{2}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.302 |
|
| 21872 |
\begin{align*}
x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y&=64 x^{2} \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.303 |
|
| 21873 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
6.305 |
|
| 21874 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-9 y&=\sqrt {x}+\frac {1}{\sqrt {x}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.306 |
|
| 21875 |
\begin{align*}
y^{\prime }&=\frac {y}{x} \\
y \left (-1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.307 |
|
| 21876 |
\begin{align*}
\left (x +2 y+1\right ) y^{\prime }&=3+2 x +4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.309 |
|
| 21877 |
\begin{align*}
x^{\prime \prime }+\lambda x-x^{3}&=0 \\
x \left (0\right ) &= 0 \\
x \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
6.309 |
|
| 21878 |
\begin{align*}
\left (x -x \sqrt {x^{2}-y^{2}}\right ) y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.313 |
|
| 21879 |
\begin{align*}
y^{\prime }&=\frac {x^{2}+y^{2}}{2 x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.316 |
|
| 21880 |
\begin{align*}
x y^{\prime }+y&=3 x^{2} \\
y \left (2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.318 |
|
| 21881 |
\begin{align*}
x \ln \left (x \right ) y^{\prime }&=a x \left (1+\ln \left (x \right )\right )-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.319 |
|
| 21882 |
\begin{align*}
y^{\prime }&=-\frac {x^{2}-x -2-2 \sqrt {x^{2}-4 x +4 y}}{2 \left (x +1\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.319 |
|
| 21883 |
\begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\frac {3 y}{4}&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
6.319 |
|
| 21884 |
\begin{align*}
y&=3 x +a \ln \left (y^{\prime }\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.319 |
|
| 21885 |
\begin{align*}
\left (2 x +1\right ) \left (y^{\prime }+y^{2}\right )-2 y-2 x -3&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.320 |
|
| 21886 |
\begin{align*}
\sqrt {1+y^{2}}\, y^{\prime }&=\frac {t y^{3}}{\sqrt {t^{2}+1}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
6.322 |
|
| 21887 |
\begin{align*}
y^{\prime }+\frac {4 y}{x -1}&=\frac {1}{\left (x -1\right )^{5}}+\frac {\sin \left (x \right )}{\left (x -1\right )^{4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.323 |
|
| 21888 |
\begin{align*}
1+y^{2} \sin \left (2 x \right )-2 y \cos \left (x \right )^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.323 |
|
| 21889 |
\begin{align*}
y^{\prime }&=-\frac {\left (-\frac {y \,{\mathrm e}^{\frac {1}{x}}}{x}-\textit {\_F1} \left (y \,{\mathrm e}^{\frac {1}{x}}\right )\right ) {\mathrm e}^{-\frac {1}{x}}}{x} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
6.327 |
|
| 21890 |
\begin{align*}
y^{\prime \prime }+\alpha ^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.328 |
|
| 21891 |
\begin{align*}
{y^{\prime \prime }}^{2} x^{2} \left (x^{2}-1\right )-1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.328 |
|
| 21892 |
\begin{align*}
y^{\prime }&=4 \left (y x \right )^{{1}/{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.332 |
|
| 21893 |
\begin{align*}
x^{\prime \prime }&=4 x^{3}-4 x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.332 |
|
| 21894 |
\begin{align*}
x y^{\prime }+y^{2}&=1 \\
y \left (-2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.333 |
|
| 21895 |
\begin{align*}
y^{\prime }&=x y^{3}-y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.336 |
|
| 21896 |
\begin{align*}
x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+a&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.336 |
|
| 21897 |
\begin{align*}
y^{\prime }&=x^{2}+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.339 |
|
| 21898 |
\begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
y \left (2\right ) &= {\frac {1}{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.339 |
|
| 21899 |
\begin{align*}
{\mathrm e}^{x} \sin \left (y\right )+{\mathrm e}^{x} \cos \left (y\right ) y^{\prime }&=y \sin \left (y x \right )+x \sin \left (y x \right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.339 |
|
| 21900 |
\begin{align*}
x -3 y&=\left (3 y-x +2\right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.342 |
|