| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 20801 |
\begin{align*}
y^{\prime }&=\sqrt {\frac {y-4}{x}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.559 |
|
| 20802 |
\begin{align*}
y^{\prime }&=\frac {x +y+4}{x +y-6} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.563 |
|
| 20803 |
\begin{align*}
x^{\prime \prime }+\left (x^{2}+1\right ) x^{\prime }+x^{3}&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
10.566 |
|
| 20804 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.568 |
|
| 20805 |
\begin{align*}
x^{2} y^{\prime \prime }-2 n x y^{\prime }+\left (a^{2} x^{2}+n^{2}+n \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.572 |
|
| 20806 |
\begin{align*}
x^{3} y^{\prime }-y^{2} x^{4}+x^{2} y+20&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.573 |
|
| 20807 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }-5 y&=0 \\
y \left (-1\right ) &= 3 \\
y^{\prime }\left (-1\right ) &= 9 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.583 |
|
| 20808 |
\begin{align*}
3 x +2 y+7+\left (2 x -y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.587 |
|
| 20809 |
\begin{align*}
{y^{\prime }}^{6}+f \left (x \right ) \left (y-a \right )^{5} \left (y-b \right )^{4}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.589 |
|
| 20810 |
\begin{align*}
y^{\prime }-\frac {\tan \left (y\right )}{x +1}&=\left (x +1\right ) {\mathrm e}^{x} \sec \left (y\right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
10.594 |
|
| 20811 |
\begin{align*}
x^{2} y^{\prime }+y x +\sqrt {y}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.603 |
|
| 20812 |
\begin{align*}
y y^{\prime \prime }&=c y^{2}+b y y^{\prime }+a {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.609 |
|
| 20813 |
\begin{align*}
x^{\prime \prime }-4 x&=t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.611 |
|
| 20814 |
\begin{align*}
y^{\prime } x&=y+\sqrt {x^{2}+y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.612 |
|
| 20815 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+2 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.623 |
|
| 20816 |
\begin{align*}
u^{\prime \prime }+\frac {u^{\prime }}{4}+u&=\frac {\left (\left \{\begin {array}{cc} 1 & \frac {3}{2}\le t <\frac {5}{2} \\ 0 & \operatorname {otherwise} \end {array}\right .\right )}{2} \\
u \left (0\right ) &= 0 \\
u^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
10.627 |
|
| 20817 |
\begin{align*}
y^{\prime }&=y^{2}+a \lambda +b \lambda +2 a b +a \left (\lambda -a \right ) \tan \left (\lambda x \right )^{2}+b \left (\lambda -b \right ) \cot \left (\lambda x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
10.634 |
|
| 20818 |
\begin{align*}
y^{\prime \prime }-4 y&=2 \sin \left (\frac {x}{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.642 |
|
| 20819 |
\begin{align*}
y^{\prime }&=1+y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.656 |
|
| 20820 |
\begin{align*}
2 x^{2} y^{\prime \prime }+5 y^{\prime } x +y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.663 |
|
| 20821 |
\begin{align*}
y^{2}+7 y x +16 x^{2}+x^{2} y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.666 |
|
| 20822 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+6 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.675 |
|
| 20823 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.681 |
|
| 20824 |
\begin{align*}
-y+y^{\prime } x&=x^{2} y y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.689 |
|
| 20825 |
\begin{align*}
-y+y^{\prime } x&=\left (x +y\right ) \ln \left (\frac {x +y}{x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.690 |
|
| 20826 |
\begin{align*}
t^{2} y^{\prime }+2 t y-y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.690 |
|
| 20827 |
\begin{align*}
y^{\prime }&=\frac {y \left (x +y\right )}{x \left (x -y\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.691 |
|
| 20828 |
\begin{align*}
2 x \sqrt {1-y^{2}}&=\left (x^{2}+1\right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.696 |
|
| 20829 |
\begin{align*}
\left (2 s^{2}+2 t s+t^{2}\right ) s^{\prime }+s^{2}+2 t s-t^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.700 |
|
| 20830 |
\begin{align*}
x^{2}+y^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.700 |
|
| 20831 |
\begin{align*}
x^{4} y^{\prime \prime }+x^{3} y^{\prime }-4 x^{2} y&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.707 |
|
| 20832 |
\begin{align*}
x +y+\left (x -2 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.713 |
|
| 20833 |
\begin{align*}
1+y^{2}&=\left (\arctan \left (y\right )-x \right ) y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.713 |
|
| 20834 |
\begin{align*}
2 y^{\prime } x -y&=1-\frac {2}{\sqrt {x}} \\
y \left (\infty \right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.713 |
|
| 20835 |
\begin{align*}
x^{\prime }&=k \left (a -x\right ) \left (b -x\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.713 |
|
| 20836 |
\begin{align*}
y x +\left (x^{2}-3 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.715 |
|
| 20837 |
\begin{align*}
y^{\prime \prime }-4 y&=\cosh \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.716 |
|
| 20838 |
\begin{align*}
y y^{\prime }-y&=a^{2} f^{\prime }\left (x \right ) f^{\prime \prime }\left (x \right )-\frac {\left (f \left (x \right )+b \right )^{2} f^{\prime \prime }\left (x \right )}{{f^{\prime }\left (x \right )}^{3}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
10.718 |
|
| 20839 |
\begin{align*}
\frac {2 x^{{5}/{2}}-3 y^{{5}/{3}}}{2 x^{{5}/{2}} y^{{2}/{3}}}+\frac {\left (3 y^{{5}/{3}}-2 x^{{5}/{2}}\right ) y^{\prime }}{3 x^{{3}/{2}} y^{{5}/{3}}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.724 |
|
| 20840 |
\begin{align*}
y^{\prime }&=x y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.725 |
|
| 20841 |
\begin{align*}
{y^{\prime }}^{2}&=\frac {1}{x y^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.731 |
|
| 20842 |
\begin{align*}
x^{3}+3 x y^{2}+\left (y^{3}+3 x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.734 |
|
| 20843 |
\begin{align*}
y^{\prime \prime }-2 a y^{\prime }+\left (a^{2}+\omega ^{2}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.735 |
|
| 20844 |
\begin{align*}
y^{\prime } x&=y+x \cos \left (\frac {y}{x}\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.740 |
|
| 20845 |
\begin{align*}
y^{\prime }&=\frac {-4 \cos \left (x \right ) x +4 x^{2} \sin \left (x \right )+4 x +4+4 y^{2}+8 y \cos \left (x \right ) x -8 y x +2 x^{2} \cos \left (2 x \right )+6 x^{2}-8 \cos \left (x \right ) x^{2}+4 y^{3}+12 y^{2} \cos \left (x \right ) x -12 x y^{2}+6 y x^{2} \cos \left (2 x \right )+18 x^{2} y-24 y \cos \left (x \right ) x^{2}+x^{3} \cos \left (3 x \right )+15 \cos \left (x \right ) x^{3}-6 x^{3} \cos \left (2 x \right )-10 x^{3}}{4 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.744 |
|
| 20846 |
\begin{align*}
y^{\prime \prime }-\frac {y^{\prime }}{x}-y x -x^{2}-\frac {1}{x}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
10.748 |
|
| 20847 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=1-y x -3 x^{2}+2 x^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.751 |
|
| 20848 |
\begin{align*}
y^{\prime } x&=y+\sqrt {y^{2}-x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.756 |
|
| 20849 |
\begin{align*}
y^{\prime \prime }&=y+x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.763 |
|
| 20850 |
\begin{align*}
x^{5} y^{\prime }+y^{5}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.765 |
|
| 20851 |
\begin{align*}
x^{\prime }&=a x+b x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.766 |
|
| 20852 |
\begin{align*}
x^{3}+y^{3}-y^{\prime } y^{2} x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.766 |
|
| 20853 |
\begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.769 |
|
| 20854 |
\begin{align*}
y&=y^{\prime } x -x^{2} {y^{\prime }}^{3} \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
10.771 |
|
| 20855 |
\begin{align*}
9 y^{\prime \prime }+18 y^{\prime }+10 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.778 |
|
| 20856 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.779 |
|
| 20857 |
\begin{align*}
y^{\prime \prime }-y&=4-x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.799 |
|
| 20858 |
\begin{align*}
\left (1+y^{\prime }\right ) \ln \left (\frac {x +y}{x +3}\right )&=\frac {x +y}{x +3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.806 |
|
| 20859 |
\begin{align*}
y^{\prime }+2 y x&=-\frac {{\mathrm e}^{-x^{2}} \left (3 x +2 y \,{\mathrm e}^{x^{2}}\right )}{2 x +3 y \,{\mathrm e}^{x^{2}}} \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.808 |
|
| 20860 |
\begin{align*}
4 y^{\prime \prime }-y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.808 |
|
| 20861 |
\begin{align*}
x +y+\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.810 |
|
| 20862 |
\begin{align*}
{\mathrm e}^{\frac {x}{y}}-\frac {y y^{\prime }}{x}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.816 |
|
| 20863 |
\begin{align*}
\sin \left (y\right )+\sin \left (x \right ) y+\frac {1}{x}+\left (x \cos \left (y\right )-\cos \left (x \right )+\frac {1}{y}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.816 |
|
| 20864 |
\begin{align*}
s^{\prime \prime }+2 s^{\prime }+s&=0 \\
s \left (0\right ) &= 4 \\
s^{\prime }\left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.820 |
|
| 20865 |
\begin{align*}
\left (\frac {x}{y}+\frac {y}{x}\right ) y^{\prime }+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.822 |
|
| 20866 |
\begin{align*}
\left (1+x +9 y\right ) y^{\prime }+1+x +5 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.827 |
|
| 20867 |
\begin{align*}
v^{3}+\left (u^{3}-u v^{2}\right ) v^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.827 |
|
| 20868 |
\begin{align*}
x^{\prime \prime }+2 h x^{\prime }+k^{2} x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.828 |
|
| 20869 |
\begin{align*}
x y^{3} y^{\prime }&=y^{4}+x^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.837 |
|
| 20870 |
\begin{align*}
3 y^{2}+4 y x +\left (x^{2}+2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.838 |
|
| 20871 |
\begin{align*}
y^{\prime \prime }-y&=2+5 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.843 |
|
| 20872 |
\begin{align*}
\frac {\left (3 x^{3}-x y^{2}\right ) y^{\prime }}{y^{3}+3 x^{2} y}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.847 |
|
| 20873 |
\begin{align*}
a \left (y^{\prime } x +2 y\right )&=y y^{\prime } x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.866 |
|
| 20874 |
\begin{align*}
y^{\prime }&=\frac {\left (a y^{2}+b \,x^{2}\right )^{2} x}{a^{{5}/{2}} y} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
10.868 |
|
| 20875 |
\begin{align*}
\left (3 x -1\right ) \left (y^{\prime }+y^{2}\right )-\left (3 x +2\right ) y-6 x +8&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.869 |
|
| 20876 |
\begin{align*}
t^{2} x^{\prime \prime }+a t x^{\prime }+x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.869 |
|
| 20877 |
\begin{align*}
x +\sin \left (x \right )+\sin \left (y\right )+y^{\prime } \cos \left (y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.870 |
|
| 20878 |
\begin{align*}
2 y^{\prime } x +y \left (1+y^{2}\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.882 |
|
| 20879 |
\begin{align*}
2 y y^{\prime } x&=x^{2}-y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.883 |
|
| 20880 |
\begin{align*}
x -2 y-3+\left (2 x +y-1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.887 |
|
| 20881 |
\begin{align*}
y^{\prime \prime }+y&={\mathrm e}^{-x}+\cos \left (x \right )+x^{3}+{\mathrm e}^{x} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.895 |
|
| 20882 |
\begin{align*}
6 x +4 y+3+\left (3 x +2 y+2\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.898 |
|
| 20883 |
\begin{align*}
x^{2}+y^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.900 |
|
| 20884 |
\begin{align*}
\sin \left (y\right ) y+x \left (\sin \left (y\right )-y \cos \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.902 |
|
| 20885 |
\begin{align*}
t y^{\prime \prime }-y^{\prime }+4 t^{3} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.902 |
|
| 20886 |
\begin{align*}
3 x +2 y+1-\left (3 x +2 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.906 |
|
| 20887 |
\begin{align*}
y^{\prime \prime }+{y^{\prime }}^{2}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.911 |
|
| 20888 |
\begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.914 |
|
| 20889 |
\begin{align*}
y^{\prime }&=\frac {2 x}{y} \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.917 |
|
| 20890 |
\begin{align*}
\left (a \cos \left (x \right )^{2}-\sec \left (x \right )^{2}\right ) y-\tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.918 |
|
| 20891 |
\begin{align*}
y^{\prime }&=\frac {x^{3}+x^{2} y-y^{3}}{x^{3}-x y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.925 |
|
| 20892 |
\begin{align*}
y^{\prime }&=\frac {y \ln \left (x -1\right )+x^{4}+x^{3}+y^{2} x^{2}+x y^{2}}{\ln \left (x -1\right ) x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.927 |
|
| 20893 |
\begin{align*}
y^{\prime \prime }+\frac {2 y^{\prime }}{x}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.927 |
|
| 20894 |
\begin{align*}
9 {y^{\prime }}^{4}+8 y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.932 |
|
| 20895 |
\begin{align*}
3 y+\left (7 x -y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.933 |
|
| 20896 |
\begin{align*}
4 y+2 x \left (x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime }&=\arctan \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.950 |
|
| 20897 |
\begin{align*}
x \left (2 x^{2}+y^{2}\right ) y^{\prime }&=\left (2 x^{2}+3 y^{2}\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.954 |
|
| 20898 |
\begin{align*}
\cos \left (x \right ) y^{\prime \prime }&=y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.956 |
|
| 20899 |
\begin{align*}
\frac {2 x}{y}-\frac {3 y^{2}}{x^{4}}+\left (\frac {2 y}{x^{3}}-\frac {x^{2}}{y^{2}}+\frac {1}{\sqrt {y}}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
10.961 |
|
| 20900 |
\begin{align*}
y^{\prime }&=a_{0} +a_{1} y+a_{2} y^{2}+a_{3} y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.961 |
|