| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 21801 |
\begin{align*}
-y+y^{\prime } x&=\left (x +y\right ) \ln \left (\frac {x +y}{x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.519 |
|
| 21802 |
\begin{align*}
4 y+y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.521 |
|
| 21803 |
\begin{align*}
1+y^{2}+\left (y+x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.531 |
|
| 21804 |
\begin{align*}
x^{n} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime }+c \left (\left (a -c \right ) x^{n}+b \right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
8.535 |
|
| 21805 |
\begin{align*}
y^{\prime }&=\frac {1}{\left (1+y\right ) \left (-2+t \right )} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.536 |
|
| 21806 |
\begin{align*}
y^{\prime } x&=a x +b y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.539 |
|
| 21807 |
\begin{align*}
\left (c \,x^{2}+2 b x +a \right )^{{3}/{2}} y^{\prime \prime }&=f \left (\frac {x}{\sqrt {c \,x^{2}+2 b x +a}}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.540 |
|
| 21808 |
\begin{align*}
x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y x&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.541 |
|
| 21809 |
\begin{align*}
y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.544 |
|
| 21810 |
\begin{align*}
\frac {\sin \left (\frac {x}{y}\right )}{y}-\frac {y \cos \left (\frac {y}{x}\right )}{x^{2}}+1+\left (\frac {\cos \left (\frac {y}{x}\right )}{x}-\frac {x \sin \left (\frac {x}{y}\right )}{y^{2}}+\frac {1}{y^{2}}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.551 |
|
| 21811 |
\begin{align*}
y^{\prime }-\frac {y}{t}&=\frac {y^{2}}{t^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.555 |
|
| 21812 |
\begin{align*}
y \sin \left (2 x \right )-\cos \left (x \right )+\left (1+\sin \left (x \right )^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.556 |
|
| 21813 |
\begin{align*}
a y-2 x^{2} \tan \left (x \right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
8.558 |
|
| 21814 |
\begin{align*}
y^{\prime }&=y^{2}+\lambda \arctan \left (x \right )^{n} y-a^{2}+a \lambda \arctan \left (x \right )^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.569 |
|
| 21815 |
\begin{align*}
y^{\prime }&=-\frac {x +y}{3 x +3 y-4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.574 |
|
| 21816 |
\begin{align*}
y x +y^{2}-x^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.576 |
|
| 21817 |
\begin{align*}
y^{\prime }&=\sin \left (x \right ) \cos \left (y\right ) \\
y \left (3\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.576 |
|
| 21818 |
\begin{align*}
y^{\prime }&=\frac {x \left (x +2 \sqrt {x^{3}-6 y}\right )}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.583 |
|
| 21819 |
\begin{align*}
\left (2 x +2 y+1\right ) y^{\prime }&=x +y+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.585 |
|
| 21820 |
\begin{align*}
y^{\prime } x&=y^{2}-y \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.586 |
|
| 21821 |
\begin{align*}
x^{4}-3 y+3 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.587 |
|
| 21822 |
\begin{align*}
8 \left (-x^{3}+1\right ) y y^{\prime \prime }-4 \left (-x^{3}+1\right ) {y^{\prime }}^{2}-12 x^{2} y y^{\prime }+3 x y^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
8.595 |
|
| 21823 |
\begin{align*}
y^{\prime }&=y-y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.599 |
|
| 21824 |
\begin{align*}
y^{\prime }&=\frac {2 t^{5}}{5 y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.602 |
|
| 21825 |
\begin{align*}
\left (1-\sin \left (x \right )\right ) y^{\prime }+\cos \left (x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.605 |
|
| 21826 |
\begin{align*}
y^{\prime }&=\frac {x^{2} \left (1+2 \sqrt {x^{3}-6 y}\right )}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.608 |
|
| 21827 |
\begin{align*}
x^{2} y^{\prime }+y^{2}-y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.611 |
|
| 21828 |
\begin{align*}
8 \cos \left (y\right )^{2}+\csc \left (x \right )^{2} y^{\prime }&=0 \\
y \left (\frac {\pi }{12}\right ) &= \frac {\pi }{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.619 |
|
| 21829 |
\begin{align*}
-y+y^{\prime } x&=1 \\
y \left (2\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.619 |
|
| 21830 |
\begin{align*}
y^{\prime \prime }&=1+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.621 |
|
| 21831 |
\begin{align*}
y^{\prime }-\frac {2 y}{x}&=-x^{2} y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.628 |
|
| 21832 |
\begin{align*}
x +y {y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.633 |
|
| 21833 |
\begin{align*}
y^{\prime }&=\left (1+\cos \left (x \right ) \sin \left (y\right )\right ) \tan \left (y\right ) \\
\end{align*} |
✗ |
✗ |
✓ |
✓ |
8.635 |
|
| 21834 |
\begin{align*}
{\mathrm e}^{t y}+\frac {t \,{\mathrm e}^{t y} y^{\prime }}{y}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.635 |
|
| 21835 |
\begin{align*}
-y+y^{\prime } x&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.635 |
|
| 21836 |
\begin{align*}
\left (x -y\right )^{2} y^{\prime }&=4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.638 |
|
| 21837 |
\begin{align*}
w^{\prime }&=t w+t^{3} w^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.638 |
|
| 21838 |
\begin{align*}
R^{\prime }&=\left (1+t \right ) \left (1+R^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.640 |
|
| 21839 |
\begin{align*}
x^{n -1} {y^{\prime }}^{n}-n x y^{\prime }+y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
8.643 |
|
| 21840 |
\begin{align*}
\left (1+y^{2}\right ) y^{\prime \prime }+{y^{\prime }}^{3}+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.647 |
|
| 21841 |
\begin{align*}
y^{\prime }&=\cos \left (x \right )+\frac {y^{2}}{x} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
8.647 |
|
| 21842 |
\begin{align*}
\left (y+\sqrt {1+y^{2}}\right ) \left (x^{2}+1\right )^{{3}/{2}} y^{\prime }&=1+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.655 |
|
| 21843 |
\begin{align*}
y^{4}+\left (x^{2}-3 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
8.655 |
|
| 21844 |
\begin{align*}
y^{\prime \prime }-4 y&=0 \\
y \left (0\right ) &= 10 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.660 |
|
| 21845 |
\begin{align*}
x^{2}+2 y x -y^{2}+\left (y^{2}+2 y x -x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.662 |
|
| 21846 |
\begin{align*}
y^{\prime }&=\frac {y \left (y^{2} x^{7}+x^{4} y+x -3\right )}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.662 |
|
| 21847 |
\begin{align*}
y^{\prime \prime }+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.662 |
|
| 21848 |
\begin{align*}
y x -y^{2}-x^{2} y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.665 |
|
| 21849 |
\begin{align*}
y^{\prime }&=\frac {y+x \,{\mathrm e}^{-\frac {2 y}{x}}}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.668 |
|
| 21850 |
\begin{align*}
r^{\prime }&=t -\frac {r}{3 t} \\
r \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.671 |
|
| 21851 |
\begin{align*}
\sin \left (x \right ) y^{\prime \prime }+\left (3 \sin \left (x \right )^{2}-\cos \left (x \right )\right ) y^{\prime }+2 \sin \left (x \right )^{3} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.671 |
|
| 21852 |
\begin{align*}
\left (1+y^{2}\right ) y^{\prime \prime }+{y^{\prime }}^{3}+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.680 |
|
| 21853 |
\begin{align*}
\left (2 x -3\right )^{2} y^{\prime \prime }-6 \left (2 x -3\right ) y^{\prime }+12 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.680 |
|
| 21854 |
\begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=6 x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.681 |
|
| 21855 |
\begin{align*}
\left (1+{y^{\prime }}^{2}\right ) y^{\prime \prime \prime }-\left (a +3 y^{\prime }\right ) {y^{\prime \prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.686 |
|
| 21856 |
\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*} |
✗ |
✓ |
✓ |
✗ |
8.687 |
|
| 21857 |
\begin{align*}
y^{\prime }&=\frac {x \left (-2+3 \sqrt {x^{2}+3 y}\right )}{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.690 |
|
| 21858 |
\begin{align*}
2 x +y+1-\left (4 x +2 y-3\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.691 |
|
| 21859 |
\begin{align*}
x +y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.693 |
|
| 21860 |
\begin{align*}
y^{\prime } x +y&=y^{2} \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.696 |
|
| 21861 |
\begin{align*}
y^{\prime } \sqrt {x^{4}+x^{2}+1}&=\sqrt {1+y^{2}+y^{4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.700 |
|
| 21862 |
\begin{align*}
y^{\prime }&=a y+b y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.700 |
|
| 21863 |
\begin{align*}
\left (a^{2}+x^{2}\right ) y^{\prime }&=a^{2}+3 y x -2 y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.701 |
|
| 21864 |
\begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime \prime }-2 \left (1+{y^{\prime }}^{2}\right ) \left (-y+y^{\prime } x \right )&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
8.701 |
|
| 21865 |
\begin{align*}
y^{\prime }+\frac {y}{x}&=-\frac {4 x}{y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.709 |
|
| 21866 |
\begin{align*}
y^{\prime }&=x -y x -y+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.714 |
|
| 21867 |
\begin{align*}
3 x^{2} {\mathrm e}^{x^{3}}+{\mathrm e}^{2 y}+\left (2 x \,{\mathrm e}^{2 y}-3\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.715 |
|
| 21868 |
\begin{align*}
y^{\prime }&=\frac {3 x^{5}+3 y^{2} x^{2}}{2 x^{3} y-2 y^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.722 |
|
| 21869 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +2 y&=\ln \left (x \right ) x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.727 |
|
| 21870 |
\begin{align*}
y^{\prime }&=\frac {\left (1+x y^{2}\right )^{2}}{y x^{4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.728 |
|
| 21871 |
\begin{align*}
\frac {y}{x}+\cos \left (y\right )+\left (\ln \left (x \right )-x \sin \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.728 |
|
| 21872 |
\begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.734 |
|
| 21873 |
\begin{align*}
\left (x^{2}+1\right ) y y^{\prime }+4&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.735 |
|
| 21874 |
\begin{align*}
\frac {3 t^{2}}{y}-\frac {t^{3} y^{\prime }}{y^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.736 |
|
| 21875 |
\begin{align*}
\sqrt {x^{2}-1}\, y^{\prime }-\sqrt {-1+y^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.737 |
|
| 21876 |
\begin{align*}
y \left (2 x +y^{2}\right )+x \left (y^{2}-x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.737 |
|
| 21877 |
\begin{align*}
\left (2 x -y^{2}\right ) y^{\prime }&=2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.743 |
|
| 21878 |
\begin{align*}
4 x +3 y-7+\left (4 x +3 y+1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.746 |
|
| 21879 |
\begin{align*}
y^{\prime } \sqrt {-x^{2}+1}&=1+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.749 |
|
| 21880 |
\begin{align*}
y^{\prime } x&=y-{\mathrm e}^{\frac {y}{x}} x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.750 |
|
| 21881 |
\begin{align*}
y^{\prime } x&=y \left (1-2 y\right ) \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.750 |
|
| 21882 |
\begin{align*}
\left (\sin \left (y\right )^{2}+x \cot \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.756 |
|
| 21883 |
\begin{align*}
y&=2 y^{\prime } x +\ln \left (y^{\prime }\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.756 |
|
| 21884 |
\begin{align*}
y+\left (2 x +y x -3\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.757 |
|
| 21885 |
\begin{align*}
{x^{\prime }}^{2}&=k^{2} \left (1-{\mathrm e}^{-\frac {2 g x}{k^{2}}}\right ) \\
x \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
8.758 |
|
| 21886 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 2 & 0<t <4 \\ 0 & 4<t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
8.759 |
|
| 21887 |
\begin{align*}
x +y y^{\prime }&=m \left (-y+y^{\prime } x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.763 |
|
| 21888 |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}+g \left (x \right ) y+a \lambda \,{\mathrm e}^{\lambda x}-a \,{\mathrm e}^{\lambda x} g \left (x \right )-a^{2} {\mathrm e}^{2 \lambda x} f \left (x \right ) \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
8.764 |
|
| 21889 |
\begin{align*}
\left (x +y\right ) y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.764 |
|
| 21890 |
\begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{t}}{1+y} \\
y \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.766 |
|
| 21891 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=4 x +\sin \left (\ln \left (x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.767 |
|
| 21892 |
\begin{align*}
y+x \left (x^{2}+y^{2}\right )^{2}+\left (y \left (x^{2}+y^{2}\right )^{2}-x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.770 |
|
| 21893 |
\begin{align*}
y^{\prime } x&=y^{2} x^{2}+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.778 |
|
| 21894 |
\begin{align*}
\frac {r^{\prime }}{r}&=\tan \left (\theta \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.781 |
|
| 21895 |
\begin{align*}
\left (x -y\right ) y^{\prime }&=x +y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.785 |
|
| 21896 |
\begin{align*}
x^{2} y^{\prime }+y^{2}&=y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.787 |
|
| 21897 |
\begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime \prime }-\left (1+{y^{\prime }}^{2}\right ) \left (-y+y^{\prime } x \right )&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
8.790 |
|
| 21898 |
\begin{align*}
y {y^{\prime }}^{2}-\left (-2 b x +a \right ) y^{\prime }-b y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.792 |
|
| 21899 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }-y^{2}-2 y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
8.794 |
|
| 21900 |
\begin{align*}
y^{\prime } x&=2 x +3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.795 |
|