| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 20701 |
\begin{align*}
\left (x -2\right ) y^{\prime }+y&=5 \left (x -2\right )^{2} \sqrt {y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.217 |
|
| 20702 |
\begin{align*}
x \left (1-y\right ) y^{\prime }+\left (x +1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.218 |
|
| 20703 |
\begin{align*}
y^{\prime }-\frac {y}{x}&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.219 |
|
| 20704 |
\begin{align*}
x^{3} y^{\prime }&=2 y^{2}+2 x^{2} y-2 x^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.220 |
|
| 20705 |
\begin{align*}
y^{\prime } x&=x^{3}+\left (2 x^{2}+1\right ) y+x y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.225 |
|
| 20706 |
\begin{align*}
y^{\prime }&=-\lambda \,{\mathrm e}^{\lambda x} y^{2}+a \,x^{n} {\mathrm e}^{\lambda x} y-a \,x^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.226 |
|
| 20707 |
\begin{align*}
\frac {y^{\prime }}{x}&=y \sin \left (x^{2}-1\right )-\frac {2 y}{\sqrt {x}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.226 |
|
| 20708 |
\begin{align*}
x^{2}+2 y^{2}-y y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.230 |
|
| 20709 |
\begin{align*}
\left (2 x^{2} y+4 x^{3}-12 x y^{2}+3 y^{2}-x \,{\mathrm e}^{y}+{\mathrm e}^{2 x}\right ) y^{\prime }+12 x^{2} y+2 x y^{2}+4 x^{3}-4 y^{3}+2 y \,{\mathrm e}^{2 x}-{\mathrm e}^{y}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.232 |
|
| 20710 |
\begin{align*}
\left (x^{2}-1\right ) y+x \left (x^{2}+1\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.233 |
|
| 20711 |
\begin{align*}
y^{\prime }&=\frac {x y^{2}+2 y^{3}}{x^{3}+x^{2} y+x y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.234 |
|
| 20712 |
\begin{align*}
y^{\prime }&=\frac {32 y x^{5}+8 x^{3}+32 x^{5}+64 x^{6} y^{3}+48 y^{2} x^{4}+12 x^{2} y+1}{16 x^{6} \left (4 x^{2} y+1+4 x^{2}\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.234 |
|
| 20713 |
\begin{align*}
y^{\prime }&=\frac {\left (1+\cos \left (4 t \right )\right ) y}{4}-\frac {\left (1-\cos \left (4 t \right )\right ) y^{2}}{800} \\
y \left (0\right ) &= 100 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.240 |
|
| 20714 |
\begin{align*}
\sqrt {-u^{2}+1}\, v^{\prime }&=2 u \sqrt {1-v^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.242 |
|
| 20715 |
\begin{align*}
y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\
y \left (-6\right ) &= 0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
6.242 |
|
| 20716 |
\begin{align*}
y^{\prime }+\cos \left (x \right ) y&=y^{3} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.243 |
|
| 20717 |
\begin{align*}
\frac {x +y y^{\prime }}{\sqrt {1+x^{2}+y^{2}}}+\frac {-y^{\prime } x +y}{x^{2}+y^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.243 |
|
| 20718 |
\begin{align*}
{y^{\prime }}^{2}-2 x^{2} y^{\prime }+2 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.247 |
|
| 20719 |
\begin{align*}
x^{2}+2 y x -4 y^{2}-\left (x^{2}-8 y x -4 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.247 |
|
| 20720 |
\begin{align*}
y^{\prime \prime }+x \left (1-x \right ) y^{\prime }+{\mathrm e}^{x} y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
6.248 |
|
| 20721 |
\begin{align*}
y^{3}-25 y+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.250 |
|
| 20722 |
\begin{align*}
y^{\prime }&=-F \left (x \right ) \left (y^{2}-2 y x -x^{2}\right )+\frac {y}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.253 |
|
| 20723 |
\begin{align*}
y^{\prime } x +y&=a \left (x^{2}+1\right ) y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.255 |
|
| 20724 |
\begin{align*}
\left (-x^{4}+x^{3}\right ) y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+827 y&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
6.255 |
|
| 20725 |
\begin{align*}
f \left (x -\frac {3 {y^{\prime }}^{2}}{2}\right )+{y^{\prime }}^{3}-y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
6.257 |
|
| 20726 |
\begin{align*}
{\mathrm e}^{3 x} y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+\frac {2 y}{x^{2}+4}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
6.257 |
|
| 20727 |
\begin{align*}
y \,{\mathrm e}^{y x}+2 y x +\left (x \,{\mathrm e}^{y x}+x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.258 |
|
| 20728 |
\begin{align*}
y^{\prime } x +x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.259 |
|
| 20729 |
\begin{align*}
y^{\prime }+3 y&=\frac {28 \,{\mathrm e}^{2 x}}{y^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.263 |
|
| 20730 |
\begin{align*}
\left (1+y\right ) y^{\prime }&=x \sqrt {y} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.263 |
|
| 20731 |
\begin{align*}
\csc \left (y\right )+\sec \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.266 |
|
| 20732 |
\begin{align*}
y x^{\prime }&=2 y \,{\mathrm e}^{3 y}+x \left (3 y +2\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.267 |
|
| 20733 |
\begin{align*}
x^{2} y^{\prime }&=a +b y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.267 |
|
| 20734 |
\begin{align*}
y^{\prime }&=y^{2}-x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.268 |
|
| 20735 |
\begin{align*}
y^{\prime \prime }-\frac {2 y^{\prime }}{y^{3}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.269 |
|
| 20736 |
\begin{align*}
{\mathrm e}^{y x} \left (x^{4} y+4 x^{3}\right )+3 y+\left (x^{5} {\mathrm e}^{y x}+3 x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.273 |
|
| 20737 |
\begin{align*}
\left (x^{2} y \sin \left (y x \right )-4 x \right ) y^{\prime }+x y^{2} \sin \left (y x \right )-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.274 |
|
| 20738 |
\begin{align*}
2 y^{2}+4 x^{2}-y y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.274 |
|
| 20739 |
\begin{align*}
1+y^{2}-\left (y+\sqrt {1+y^{2}}\right ) \left (x^{2}+1\right )^{{3}/{2}} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.276 |
|
| 20740 |
\begin{align*}
y^{\prime }&=-\frac {x \left ({\mathrm e}^{-3 x^{2}} x^{6}-6 \,{\mathrm e}^{-2 x^{2}} x^{4} y-2 \,{\mathrm e}^{-2 x^{2}} x^{4}+12 x^{2} {\mathrm e}^{-x^{2}} y^{2}+8 x^{2} {\mathrm e}^{-x^{2}} y+8 x^{2} {\mathrm e}^{-x^{2}}-8 y^{3}-8 y^{2}-8 \,{\mathrm e}^{-x^{2}}-8\right )}{8} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.277 |
|
| 20741 |
\begin{align*}
y^{\prime }&=\frac {y}{x}+\sin \left (\frac {y}{x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.277 |
|
| 20742 |
\begin{align*}
y^{\prime } x +y&=x^{2} y^{\prime }+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.279 |
|
| 20743 |
\begin{align*}
y y^{\prime }-y^{2}&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.279 |
|
| 20744 |
\begin{align*}
x -y+y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.282 |
|
| 20745 |
\begin{align*}
y^{\prime } x +\tan \left (y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.283 |
|
| 20746 |
\begin{align*}
y^{\prime }&=\frac {y^{2}}{x -1}-\frac {x y}{x -1}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.283 |
|
| 20747 |
\begin{align*}
x^{2} y^{\prime }&=x^{2}+y x +y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.289 |
|
| 20748 |
\begin{align*}
-y^{\prime } x +y&=a \left (y^{\prime }+y^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.290 |
|
| 20749 |
\begin{align*}
\frac {2 x^{2}}{x^{2}+y^{2}}+\ln \left (x^{2}+y^{2}\right )+\frac {2 x y y^{\prime }}{x^{2}+y^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.292 |
|
| 20750 |
\begin{align*}
y^{\prime }-y x&=\frac {x}{y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.292 |
|
| 20751 |
\begin{align*}
x^{2} y+\left (x^{3}+1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.293 |
|
| 20752 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }&=0 \\
y \left (0\right ) &= 13 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.296 |
|
| 20753 |
\begin{align*}
3 x \left (1+y^{2}\right )+y \left (x^{2}+2\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.298 |
|
| 20754 |
\begin{align*}
y^{\prime } x +2 y&=6 \sqrt {y}\, x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.299 |
|
| 20755 |
\begin{align*}
\frac {x}{\left (x +y\right )^{2}}+\frac {\left (2 x +y\right ) y^{\prime }}{\left (x +y\right )^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.300 |
|
| 20756 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+\cos \left (x \right )&=2 y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.301 |
|
| 20757 |
\begin{align*}
\left (4 k x -4 p^{2}-x^{2}+1\right ) y+4 x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
6.304 |
|
| 20758 |
\begin{align*}
y y^{\prime }&=a x +b y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.306 |
|
| 20759 |
\begin{align*}
x \sqrt {1+y^{2}}&=y y^{\prime } \sqrt {x^{2}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.312 |
|
| 20760 |
\begin{align*}
-y+\left (1+a \right ) y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
6.313 |
|
| 20761 |
\begin{align*}
y^{\prime } x +y&=x y \left (y^{\prime }-1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.314 |
|
| 20762 |
\begin{align*}
y^{\prime \prime }+3 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -6 \sqrt {3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.315 |
|
| 20763 |
\begin{align*}
x^{\prime }&=\frac {3 x^{2}-2 t^{2}}{t x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.317 |
|
| 20764 |
\begin{align*}
y^{\prime }&=\frac {-{\mathrm e}^{x} y+y x -x^{3} \ln \left (x \right )-x^{3}-x y^{2} \ln \left (x \right )-x y^{2}}{\left (x -{\mathrm e}^{x}\right ) x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.318 |
|
| 20765 |
\begin{align*}
y^{\prime }-2 y&=\frac {x \,{\mathrm e}^{2 x}}{1-y \,{\mathrm e}^{-2 x}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.319 |
|
| 20766 |
\begin{align*}
x^{\prime \prime }-\omega ^{2} x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.319 |
|
| 20767 |
\begin{align*}
4 x^{2} y^{\prime \prime }+5 y^{\prime } x -y-\ln \left (x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.319 |
|
| 20768 |
\begin{align*}
3 x^{2} y^{\prime \prime }-4 y^{\prime } x +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.320 |
|
| 20769 |
\begin{align*}
1&=\frac {y}{1-y^{2} x^{2}}+\frac {x y^{\prime }}{1-y^{2} x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.320 |
|
| 20770 |
\begin{align*}
y^{\prime }&=\left (x -y+3\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.321 |
|
| 20771 |
\begin{align*}
x x^{\prime \prime }-2 {x^{\prime }}^{2}-x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.325 |
|
| 20772 |
\begin{align*}
y^{\prime }&=y^{2}+a \sin \left (\beta x \right ) y+a b \sin \left (\beta x \right )-b^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.327 |
|
| 20773 |
\begin{align*}
y^{\prime }&=a +b \cos \left (y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.328 |
|
| 20774 |
\begin{align*}
y^{2}-2 y x +6 x -\left (x^{2}-2 y x +2\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.328 |
|
| 20775 |
\begin{align*}
x^{2}+y^{2}+1-2 y y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.329 |
|
| 20776 |
\begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime }&=y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.330 |
|
| 20777 |
\begin{align*}
y^{\prime \prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
6.331 |
|
| 20778 |
\begin{align*}
y-\left (x +x y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.335 |
|
| 20779 |
\begin{align*}
y^{\prime }&=3 y-3 x +3+\left (x -y\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.335 |
|
| 20780 |
\begin{align*}
x \left (6 y x +5\right )+\left (2 x^{3}+3 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.336 |
|
| 20781 |
\begin{align*}
y^{\prime }&=\frac {-2 y x +2 x^{3}-2 x -y^{3}+3 y^{2} x^{2}-3 x^{4} y+x^{6}}{-y+x^{2}-1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.336 |
|
| 20782 |
\begin{align*}
4 x {y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.336 |
|
| 20783 |
\begin{align*}
y^{\prime }&=8 x^{3} {\mathrm e}^{-2 y} \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.343 |
|
| 20784 |
\begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{x}}{2 y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.343 |
|
| 20785 |
\begin{align*}
3 x^{2}+y+\left (x^{2} y-x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.350 |
|
| 20786 |
\begin{align*}
x^{2} \left (-y+y^{\prime } x \right )&=y \left (x +y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.351 |
|
| 20787 |
\begin{align*}
x^{\prime }&=\frac {x}{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.353 |
|
| 20788 |
\begin{align*}
y^{\prime \prime }+2 a x y^{\prime }+\left (b \,x^{4}+a^{2} x^{2}+c x +a \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
6.356 |
|
| 20789 |
\begin{align*}
y^{\prime }&=\frac {-x^{2}+x +1+y^{2}+5 x^{2} y-2 y x +4 x^{4}-3 x^{3}+y^{3}+3 y^{2} x^{2}-3 x y^{2}+3 x^{4} y-6 x^{3} y+x^{6}-3 x^{5}}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.357 |
|
| 20790 |
\begin{align*}
y^{\prime }&=-\left (-\frac {\ln \left (y\right )}{x}+\frac {\ln \left (y\right )}{x \ln \left (x \right )}-\textit {\_F1} \left (x \right )\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.358 |
|
| 20791 |
\begin{align*}
w^{\prime }&=\left (w^{2}-2\right ) \arctan \left (w\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.359 |
|
| 20792 |
\begin{align*}
y^{\prime }&=\frac {y^{{3}/{2}}}{y^{{3}/{2}}+x^{2}-2 y x +y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.362 |
|
| 20793 |
\begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +5 y&=0 \\
y \left (1\right ) &= -2 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.363 |
|
| 20794 |
\begin{align*}
\sin \left (x \right ) y^{\prime }+2 \cos \left (x \right ) y&=4 \cos \left (x \right )^{3} \\
y \left (\frac {\pi }{4}\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.364 |
|
| 20795 |
\begin{align*}
y^{\prime }+\frac {y}{x}&=x y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.365 |
|
| 20796 |
\begin{align*}
\tan \left (y\right ) \sec \left (y\right )^{2} y^{\prime }+\cos \left (2 x \right )^{3} \sin \left (2 x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.368 |
|
| 20797 |
\begin{align*}
y^{\prime }+\frac {2 y}{x}-y^{2}&=-\frac {2}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.369 |
|
| 20798 |
\begin{align*}
3 t&={\mathrm e}^{t} y^{\prime }+y \ln \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.370 |
|
| 20799 |
\begin{align*}
y^{\prime }&=\frac {1+\sqrt {x -y}}{1-\sqrt {x -y}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.370 |
|
| 20800 |
\begin{align*}
y^{\prime \prime }-a x y^{\prime }-b x y-c x&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
6.374 |
|