| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 22701 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.590 |
|
| 22702 |
\begin{align*}
x \left (x -3 y^{2}\right ) y^{\prime }+\left (2 x -y^{2}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.592 |
|
| 22703 |
\begin{align*}
x +y-\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.592 |
|
| 22704 |
\begin{align*}
y^{\prime }-\frac {2 y}{x}&=\frac {1}{y x} \\
y \left (1\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.600 |
|
| 22705 |
\begin{align*}
y^{\prime }&=\frac {6 x^{3}+5 \sqrt {x}+5 F \left (y-\frac {2 x^{3}}{5}-2 \sqrt {x}\right )}{5 x} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
11.600 |
|
| 22706 |
\begin{align*}
y y^{\prime \prime }&=-2 y^{2}+2 {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.601 |
|
| 22707 |
\begin{align*}
y^{\prime }&=-\frac {{\mathrm e}^{2 \lambda x} y^{3}}{3 \lambda }+\frac {2 \lambda ^{2} {\mathrm e}^{-\lambda x}}{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.602 |
|
| 22708 |
\begin{align*}
\left (a +x \right ) y+y^{\prime \prime } x&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
11.605 |
|
| 22709 |
\begin{align*}
y^{\prime } x -2 y&=2 x^{4} \\
y \left (2\right ) &= 8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.605 |
|
| 22710 |
\begin{align*}
4 \left (x -1\right )^{2} y^{\prime }-3 \left (3+y\right )^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.609 |
|
| 22711 |
\begin{align*}
\left (x +y\right ) y^{\prime }&=-x +y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.612 |
|
| 22712 |
\begin{align*}
y^{\prime }&=\frac {\left (3+2 y\right )^{2}}{\left (5+4 x \right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.614 |
|
| 22713 |
\begin{align*}
y y^{\prime }&=\sqrt {x^{2}+y^{2}}-x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.625 |
|
| 22714 |
\begin{align*}
y^{\prime }&=\frac {y^{3} {\mathrm e}^{-\frac {4 x}{3}}}{y \,{\mathrm e}^{-\frac {2 x}{3}}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.628 |
|
| 22715 |
\begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.631 |
|
| 22716 |
\begin{align*}
\frac {y^{\prime }}{y}-\frac {2 \ln \left (y\right )}{x}&=\frac {1-2 \ln \left (x \right )}{x} \\
y \left (1\right ) &= {\mathrm e} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.632 |
|
| 22717 |
\begin{align*}
y^{\prime }&=a \,x^{\frac {n}{1-n}}+b y^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.633 |
|
| 22718 |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}-f \left (x \right ) \left (a \,{\mathrm e}^{\lambda x}+b \right ) y+a \lambda \,{\mathrm e}^{\lambda x} \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
11.636 |
|
| 22719 |
\begin{align*}
y^{\prime }+\cot \left (x \right ) y&=y^{4} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.638 |
|
| 22720 |
\begin{align*}
y^{\prime }&=\frac {y}{x}+\tan \left (\frac {y}{x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.639 |
|
| 22721 |
\begin{align*}
y^{\prime }&=\frac {x +y-2}{y-x -4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.643 |
|
| 22722 |
\begin{align*}
3 x^{2} y \ln \left (y\right )+\left (2 x^{3}+2 y^{3}+3 y^{3} \ln \left (y\right )^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.644 |
|
| 22723 |
\begin{align*}
y^{\prime }&=\frac {y \left (-\tanh \left (\frac {1}{x}\right )-\ln \left (\frac {x^{2}+1}{x}\right ) x +\ln \left (\frac {x^{2}+1}{x}\right ) x^{2} y\right )}{x \tanh \left (\frac {1}{x}\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.645 |
|
| 22724 |
\begin{align*}
y^{\prime } x&=2 y \left (-1+y\right ) \\
y \left (\frac {1}{2}\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.663 |
|
| 22725 |
\begin{align*}
y^{\prime }&=2-\frac {y}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.676 |
|
| 22726 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=x y \left (1+a y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.681 |
|
| 22727 |
\begin{align*}
y^{\prime } x&=a y+b \left (x^{2}+1\right ) y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.684 |
|
| 22728 |
\begin{align*}
x +y+\left (3 x +3 y-4\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
11.689 |
|
| 22729 |
\begin{align*}
t^{2} y^{\prime \prime }+3 y^{\prime } t +y&=\ln \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.690 |
|
| 22730 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a \,x^{2}+b \right ) x y^{\prime }+f \left (x \right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
11.692 |
|
| 22731 |
\begin{align*}
x -y-2-\left (2 x -2 y-3\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.701 |
|
| 22732 |
\begin{align*}
\left (x -1\right )^{2} y^{\prime \prime }-\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
11.706 |
|
| 22733 |
\begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
y \left (-2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.706 |
|
| 22734 |
\begin{align*}
y \left (y \,{\mathrm e}^{y x}+1\right )+\left (x y \,{\mathrm e}^{y x}+{\mathrm e}^{y x}+x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.713 |
|
| 22735 |
\begin{align*}
\left (x +1\right )^{2} y^{\prime \prime }-\left (x +3\right ) y&=0 \\
\end{align*} Series expansion around \(x=-1\). |
✓ |
✓ |
✓ |
✓ |
11.723 |
|
| 22736 |
\begin{align*}
x \cos \left (y\right )^{2}+{\mathrm e}^{x} \tan \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.725 |
|
| 22737 |
\begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}+1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.725 |
|
| 22738 |
\begin{align*}
x +y+\left (x +y-1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.726 |
|
| 22739 |
\begin{align*}
y^{\prime }&=\left (1+y^{2}\right ) \sqrt {1+\cos \left (x^{3}\right )} \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
11.729 |
|
| 22740 |
\begin{align*}
y^{\prime } x&=2 y^{2}-6 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.729 |
|
| 22741 |
\begin{align*}
2 y y^{\prime } x&=x^{2}+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.732 |
|
| 22742 |
\begin{align*}
y^{\prime }&=-F \left (x \right ) \left (-y^{2}+2 x^{2} y+1-x^{4}\right )+2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.733 |
|
| 22743 |
\begin{align*}
\ln \left (y^{\prime }\right )+a \left (-y+y^{\prime } x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.736 |
|
| 22744 |
\begin{align*}
x y^{2} {y^{\prime }}^{2}-y^{3} y^{\prime }+x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.736 |
|
| 22745 |
\begin{align*}
x +2 y+y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.753 |
|
| 22746 |
\begin{align*}
y^{\prime }&=\frac {y \left (\cos \left (x \right ) x +\sin \left (x \right )-1\right )}{3 x -3 x \sin \left (x \right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.753 |
|
| 22747 |
\begin{align*}
x -y^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.762 |
|
| 22748 |
\begin{align*}
2 y&=\left (x^{2} y^{4}+x \right ) y^{\prime } \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.765 |
|
| 22749 |
\begin{align*}
y^{\prime }&=\frac {-\ln \left (x \right )+2 \ln \left (2 x \right ) x y+\ln \left (2 x \right )+\ln \left (2 x \right ) y^{2}+\ln \left (2 x \right ) x^{2}}{\ln \left (x \right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.770 |
|
| 22750 |
\begin{align*}
x^{2} y^{\prime } \cos \left (\frac {1}{x}\right )-y \sin \left (\frac {1}{x}\right )&=-1 \\
y \left (\infty \right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.770 |
|
| 22751 |
\begin{align*}
x^{3} \left (1+y^{2}\right ) y^{\prime }+3 x^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.771 |
|
| 22752 |
\begin{align*}
x^{3}+y^{3}-y^{2} y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.772 |
|
| 22753 |
\begin{align*}
y^{\prime \prime }+3 a y^{\prime }-2 y^{3}+2 a^{2} y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
11.780 |
|
| 22754 |
\begin{align*}
y^{\prime \prime }+x^{2} y^{\prime }-4 y&=x^{3} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
11.780 |
|
| 22755 |
\begin{align*}
x +y y^{\prime }&=2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.785 |
|
| 22756 |
\begin{align*}
y&=x {y^{\prime }}^{2}+\ln \left ({y^{\prime }}^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.799 |
|
| 22757 |
\begin{align*}
y^{\prime }&=\frac {x -2 y+1}{2 x -4 y} \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.808 |
|
| 22758 |
\begin{align*}
y^{\prime }&=t y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.815 |
|
| 22759 |
\begin{align*}
\left (x^{2}-y^{2}\right ) y^{\prime }&=2 y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.816 |
|
| 22760 |
\begin{align*}
y^{\prime }&=\frac {2 t y^{2}}{t^{2}+1} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.817 |
|
| 22761 |
\begin{align*}
\frac {\sin \left (y\right )}{y}-2 \,{\mathrm e}^{-x} \sin \left (x \right )+\frac {\left (\cos \left (y\right )+2 \cos \left (x \right ) {\mathrm e}^{-x}\right ) y^{\prime }}{y}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.817 |
|
| 22762 |
\begin{align*}
y y^{\prime }+y^{2} \tan \left (x \right )&=\cos \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.817 |
|
| 22763 |
\begin{align*}
y^{\prime }&=\frac {x -1}{y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.818 |
|
| 22764 |
\begin{align*}
y-x +\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.826 |
|
| 22765 |
\begin{align*}
x^{2} y^{\prime }+y^{2}&=0 \\
y \left (3\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.829 |
|
| 22766 |
\begin{align*}
\left (x -y\right )^{2} y^{\prime }&=a^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.847 |
|
| 22767 |
\begin{align*}
x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&=4 \ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.849 |
|
| 22768 |
\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*} |
✗ |
✗ |
✗ |
✗ |
11.850 |
|
| 22769 |
\begin{align*}
y^{\prime } x -y^{2}+\left (2 x +1\right ) y&=x^{2}+2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.851 |
|
| 22770 |
\begin{align*}
y^{\prime }&=\frac {x +y+1}{2+x}-{\mathrm e}^{\frac {x +y+1}{2+x}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.853 |
|
| 22771 |
\begin{align*}
y^{\prime }&=\frac {t -y}{2 t +5 y} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.856 |
|
| 22772 |
\begin{align*}
y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.864 |
|
| 22773 |
\begin{align*}
-y-3 y^{\prime } x +\left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
11.865 |
|
| 22774 |
\begin{align*}
x \left (1-x^{2}+y^{2}\right ) y^{\prime }+\left (-y^{2}+x^{2}+1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.871 |
|
| 22775 |
\begin{align*}
y^{\prime }&=\frac {x +3 y}{-3 x +y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.872 |
|
| 22776 |
\begin{align*}
y-\left (x +\sqrt {y^{2}-x^{2}}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.873 |
|
| 22777 |
\begin{align*}
y^{\prime } x&=y-x \tan \left (\frac {y}{x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.875 |
|
| 22778 |
\begin{align*}
{y^{\prime }}^{3}&=a \,x^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.875 |
|
| 22779 |
\begin{align*}
y \left (y+x^{2}\right )+x \left (x^{2}-2 y\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.882 |
|
| 22780 |
\begin{align*}
\sin \left (y\right ) {y^{\prime }}^{2}+2 x y^{\prime } \cos \left (y\right )^{3}-\sin \left (y\right ) \cos \left (y\right )^{4}&=0 \\
\end{align*} |
✓ |
✗ |
✓ |
✗ |
11.892 |
|
| 22781 |
\begin{align*}
n y+\left (1+k -x \right ) y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
11.898 |
|
| 22782 |
\begin{align*}
x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=\frac {1}{x^{5}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.908 |
|
| 22783 |
\begin{align*}
a y^{3} x +b y^{2}+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.918 |
|
| 22784 |
\begin{align*}
y^{\prime }+\frac {x}{y}+2&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.920 |
|
| 22785 |
\begin{align*}
\sqrt {y}+\left (x^{2}+4\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.925 |
|
| 22786 |
\begin{align*}
x {y^{\prime }}^{2}-y y^{\prime }+a y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.931 |
|
| 22787 |
\begin{align*}
x -y \arctan \left (\frac {y}{x}\right )+x \arctan \left (\frac {y}{x}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.931 |
|
| 22788 |
\begin{align*}
2 x +3 y+1+\left (4 x +6 y+1\right ) y^{\prime }&=0 \\
y \left (-2\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.933 |
|
| 22789 |
\begin{align*}
\ln \left (y^{\prime }\right )+y^{\prime } x +a&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.937 |
|
| 22790 |
\begin{align*}
y y^{\prime } x +x^{2} {\mathrm e}^{-\frac {2 y}{x}}-y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.948 |
|
| 22791 |
\begin{align*}
y y^{\prime }&=\sqrt {x^{2}+y^{2}}-x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.951 |
|
| 22792 |
\begin{align*}
x^{2} y^{\prime \prime }-2 x \left (x^{2}-a \right ) y^{\prime }+\left (2 n \,x^{2}+\left (\left (-1\right )^{n}-1\right ) a \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
11.955 |
|
| 22793 |
\begin{align*}
y^{2}-x^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.960 |
|
| 22794 |
\begin{align*}
y^{\prime }-x^{-1+a} y^{1-b} f \left (\frac {x^{a}}{a}+\frac {y^{b}}{b}\right )&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
11.960 |
|
| 22795 |
\begin{align*}
y^{\prime } \sqrt {x \left (1-x \right ) \left (-a x +1\right )}&=\sqrt {y \left (1-y\right ) \left (1-a y\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.963 |
|
| 22796 |
\begin{align*}
y y^{\prime } x&=a +b y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.967 |
|
| 22797 |
\begin{align*}
3 x +y-2+\left (3 x +y+4\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
11.969 |
|
| 22798 |
\begin{align*}
x^{2} y^{\prime \prime }+\lambda x y^{\prime }+\left (a \,x^{2}+b x +c \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
11.979 |
|
| 22799 |
\begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
11.999 |
|
| 22800 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=x \,{\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
12.009 |
|