| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 22701 |
\begin{align*}
x^{\prime \prime }+x&=\left \{\begin {array}{cc} \cos \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
6.937 |
|
| 22702 |
\begin{align*}
y^{\prime }&=\sqrt {\frac {1-y^{2}}{-x^{2}+1}} \\
y \left (2\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.940 |
|
| 22703 |
\begin{align*}
y^{\prime }&=\frac {2 x +3 y}{x -4 y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.944 |
|
| 22704 |
\begin{align*}
t^{2} y^{\prime }+2 t y-y^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.944 |
|
| 22705 |
\begin{align*}
x y^{\prime } y&=x^{2}-y x +y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.949 |
|
| 22706 |
\begin{align*}
x^{2}+2 y^{2}+\left (4 y x -y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.952 |
|
| 22707 |
\begin{align*}
y^{\prime }&=25+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.954 |
|
| 22708 |
\begin{align*}
y^{\prime } y+1&=\left (x -1\right ) {\mathrm e}^{-\frac {y^{2}}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.957 |
|
| 22709 |
\begin{align*}
3 \sin \left (x \right ) \sin \left (y\right ) y^{\prime }+5 \cos \left (x \right )^{4} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.960 |
|
| 22710 |
\begin{align*}
y-x +\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.965 |
|
| 22711 |
\begin{align*}
f \left (x \right ) y^{m} y^{\prime }+g \left (x \right ) y^{m +1}+h \left (x \right ) y^{n}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
6.971 |
|
| 22712 |
\begin{align*}
y^{\prime }&=-F \left (x \right ) \left (-7 x y^{2}-x^{3}\right )+\frac {y}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.974 |
|
| 22713 |
\begin{align*}
y^{\prime }&=\left (1+y^{2} {\mathrm e}^{-2 b x}+y^{3} {\mathrm e}^{-3 b x}\right ) {\mathrm e}^{b x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.986 |
|
| 22714 |
\begin{align*}
x^{2}+2 y^{\prime } y&=0 \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.987 |
|
| 22715 |
\begin{align*}
x^{2}+2 y x -y^{2}+\left (y^{2}+2 y x -x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.991 |
|
| 22716 |
\begin{align*}
y-y^{\prime } x&=b \left (1+x^{2} y^{\prime }\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.992 |
|
| 22717 |
\begin{align*}
y \left (y^{2}+2 x \right )+x \left (y^{2}-x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.993 |
|
| 22718 | \begin{align*}
y^{\prime }&=\frac {x +y}{x} \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 6.994 |
|
| 22719 |
\begin{align*}
2 x +3 y-5+\left (3 x -y-2\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.994 |
|
| 22720 |
\begin{align*}
6 x -3 y+6+\left (2 x -y+5\right ) y^{\prime }&=0 \\
y \left (-1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.996 |
|
| 22721 |
\begin{align*}
x \left (x +a \right ) y^{\prime }&=\left (b +c y\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.996 |
|
| 22722 |
\begin{align*}
2 x y^{\prime } y&=y^{2}+x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
6.998 |
|
| 22723 |
\begin{align*}
\left (x \cos \left (\frac {y}{x}\right )+\sin \left (\frac {y}{x}\right ) y\right ) y&=\left (\sin \left (\frac {y}{x}\right ) y-x \cos \left (\frac {y}{x}\right )\right ) x y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
6.999 |
|
| 22724 |
\begin{align*}
-\frac {\sin \left (\frac {x}{y}\right )}{y}+\frac {x \sin \left (\frac {x}{y}\right ) y^{\prime }}{y^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.001 |
|
| 22725 |
\begin{align*}
y^{\prime }&=\frac {\left (x^{4}+x^{3}+x +3 y^{2}\right ) y}{\left (x +6 y^{2}\right ) x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.002 |
|
| 22726 |
\begin{align*}
x^{\prime \prime }&=x-x^{3} \\
x \left (0\right ) &= \frac {\sqrt {2}}{2} \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
7.002 |
|
| 22727 |
\begin{align*}
3 y^{\prime }&=x +\sqrt {x^{2}-3 y} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.009 |
|
| 22728 |
\begin{align*}
x^{2} y^{\prime }+x y^{3}+a y^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
7.010 |
|
| 22729 |
\begin{align*}
y^{\prime }&=-\frac {y^{2} \left (2 x -F \left (-\frac {y x -2}{2 y}\right )\right )}{4 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.010 |
|
| 22730 |
\begin{align*}
y^{\prime } x&=y-\sqrt {y^{2}+x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.012 |
|
| 22731 |
\begin{align*}
\left (2 y x +4 x^{3}\right ) y^{\prime }+y^{2}+112 x^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.014 |
|
| 22732 |
\begin{align*}
2 y x +y^{2}+\left (x^{2}+2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.015 |
|
| 22733 |
\begin{align*}
\theta ^{\prime \prime }-p^{2} \theta &=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.025 |
|
| 22734 |
\begin{align*}
y^{\prime }&=\frac {y+x^{3} a \,{\mathrm e}^{x}+a \,x^{4}+a \,x^{3}-x y^{2} {\mathrm e}^{x}-y^{2} x^{2}-x y^{2}}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.027 |
|
| 22735 |
\begin{align*}
\left (2 s^{2}+2 s t +t^{2}\right ) s^{\prime }+s^{2}+2 s t -t^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.029 |
|
| 22736 |
\begin{align*}
\left (a^{2}+x^{2}\right ) y^{\prime }+y x +b x y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.030 |
|
| 22737 | \begin{align*}
y^{\prime }&=\frac {y^{2}+2 y x +x^{2}+{\mathrm e}^{2 F \left (-\left (x -y\right ) \left (x +y\right )\right )}}{y^{2}+2 y x +x^{2}-{\mathrm e}^{2 F \left (-\left (x -y\right ) \left (x +y\right )\right )}} \\
\end{align*} | ✓ | ✓ | ✓ | ✗ | 7.030 |
|
| 22738 |
\begin{align*}
y^{\prime }&=a \,x^{n} y^{2}+\lambda x y+a \,b^{2} x^{n} {\mathrm e}^{\lambda \,x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.033 |
|
| 22739 |
\begin{align*}
y-y^{\prime } x&=x^{2} y y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.037 |
|
| 22740 |
\begin{align*}
x +y^{2}+B \left (x \right ) y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.038 |
|
| 22741 |
\begin{align*}
y^{\prime }&=\frac {2 y}{x}+\frac {x^{3}}{y}+x \tan \left (\frac {y}{x^{2}}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.041 |
|
| 22742 |
\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*} |
✓ |
✓ |
✓ |
✗ |
7.042 |
|
| 22743 |
\begin{align*}
y^{\prime } x&=y-x \cot \left (\frac {y}{x}\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.047 |
|
| 22744 |
\begin{align*}
y \left (x +y^{2}\right )+x \left (x -y^{2}\right ) y^{\prime }&=0 \\
y \left (2\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
7.056 |
|
| 22745 |
\begin{align*}
y^{\prime } x -y+\sqrt {y^{2}-x^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.059 |
|
| 22746 |
\begin{align*}
y^{\prime }-\frac {9 x y}{9 x^{2}+49}&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.060 |
|
| 22747 |
\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*} |
✓ |
✓ |
✓ |
✗ |
7.061 |
|
| 22748 |
\begin{align*}
\left (2+3 x -y x \right ) y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.061 |
|
| 22749 |
\begin{align*}
x^{\prime }&=\sqrt {1-x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.062 |
|
| 22750 |
\begin{align*}
y^{\prime } x&=y-2 x \tanh \left (\frac {y}{x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.065 |
|
| 22751 |
\begin{align*}
\cos \left (x \right ) \cot \left (y\right )+\sin \left (x \right ) \cos \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.068 |
|
| 22752 |
\begin{align*}
x^{2}-y x +y^{2}-x y^{\prime } y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.070 |
|
| 22753 |
\begin{align*}
2 y^{\prime } x +y \left (1+y^{2}\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.075 |
|
| 22754 |
\begin{align*}
3 x^{2} \left (1+\ln \left (y\right )\right )+\left (\frac {x^{3}}{y}-2 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.075 |
|
| 22755 |
\begin{align*}
y^{\prime }&=\left (a +b x +c y\right )^{6} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.083 |
|
| 22756 | \begin{align*}
-y+y^{\prime } x&=\left (x +y\right ) \ln \left (\frac {x +y}{x}\right ) \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 7.084 |
|
| 22757 |
\begin{align*}
y^{\prime }+\cot \left (x \right ) y&=y^{4} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
7.084 |
|
| 22758 |
\begin{align*}
2 y^{\prime }&=\frac {y}{x}+\frac {y^{2}}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.087 |
|
| 22759 |
\begin{align*}
x^{\prime }&=\mu -x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.087 |
|
| 22760 |
\begin{align*}
3 x +y-2+\left (3 x +y+4\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.087 |
|
| 22761 |
\begin{align*}
y^{\prime }&=\frac {\left (\ln \left (y\right )+x^{3}\right ) y}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.090 |
|
| 22762 |
\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*} |
✓ |
✓ |
✓ |
✗ |
7.093 |
|
| 22763 |
\begin{align*}
\sin \left (2 t \right ) y+\left (\sqrt {y}+\cos \left (2 t \right )\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.093 |
|
| 22764 |
\begin{align*}
2 y^{2}+4 x^{2}-x y^{\prime } y&=0 \\
y \left (1\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.095 |
|
| 22765 |
\begin{align*}
\left (x +2 y+y^{2}\right ) y^{\prime }+y \left (1+y\right )+\left (x +y\right )^{2} y^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
7.095 |
|
| 22766 |
\begin{align*}
x -2 y+3+\left (1-x +2 y\right ) y^{\prime }&=0 \\
y \left (-4\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.098 |
|
| 22767 |
\begin{align*}
\left (2 s-{\mathrm e}^{2 t}\right ) s^{\prime }&=2 s \,{\mathrm e}^{2 t}-2 \cos \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.099 |
|
| 22768 |
\begin{align*}
3 x -3 y-2-\left (x -y+1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.099 |
|
| 22769 |
\begin{align*}
2 x +4 y-1-\left (x +2 y-3\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.102 |
|
| 22770 |
\begin{align*}
y^{\prime }+\frac {y}{x}&=\frac {y^{2}}{x} \\
y \left (-1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.103 |
|
| 22771 |
\begin{align*}
3 y^{\prime }&=x -\sqrt {x^{2}-3 y} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.111 |
|
| 22772 |
\begin{align*}
x {y^{\prime }}^{2}+y^{\prime } y-x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.119 |
|
| 22773 |
\begin{align*}
{y^{\prime }}^{3}&=\frac {y^{2}}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.121 |
|
| 22774 |
\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*} |
✓ |
✓ |
✓ |
✓ |
7.121 |
|
| 22775 | \begin{align*}
2 x +4 y+\left (2 x -2 y\right ) y^{\prime }&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✗ | 7.122 |
|
| 22776 |
\begin{align*}
2 x -3 y+\left (-3 x +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.124 |
|
| 22777 |
\begin{align*}
x \left (y^{2}+x^{2} y+x^{2}\right ) y^{\prime }-2 y^{3}-2 y^{2} x^{2}+x^{4}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.127 |
|
| 22778 |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (-\left (a^{2} b^{2}-\left (a +1\right )^{2}\right ) \sin \left (x \right )^{2}-a \left (a +1\right ) b \sin \left (2 x \right )-a \left (a -1\right )\right ) y}{\sin \left (x \right )^{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
7.138 |
|
| 22779 |
\begin{align*}
y \left (y^{2} x^{2}-m \right )+x \left (y^{2} x^{2}+n \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.139 |
|
| 22780 |
\begin{align*}
-y+y^{\prime } x&=\sqrt {y^{2}+x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.146 |
|
| 22781 |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}+\lambda y+a^{2} {\mathrm e}^{2 \lambda x} f \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.147 |
|
| 22782 |
\begin{align*}
\left (x^{2}-y\right ) y^{\prime }&=4 y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.148 |
|
| 22783 |
\begin{align*}
\left (\operatorname {c2} \,x^{2}+\operatorname {b2} x +\operatorname {a2} \right ) y+\operatorname {a1} x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
7.149 |
|
| 22784 |
\begin{align*}
x^{\prime }&=k x-x^{2} \\
x \left (0\right ) &= x_{0} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.151 |
|
| 22785 |
\begin{align*}
y \ln \left (\frac {t}{y}\right )+\frac {t^{2} y^{\prime }}{t +y}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.155 |
|
| 22786 |
\begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
y \left (-2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.159 |
|
| 22787 |
\begin{align*}
y^{\prime }&=a \ln \left (x \right )^{n} y^{2}+b \ln \left (x \right )^{m} y+b c \ln \left (x \right )^{m}-a \,c^{2} \ln \left (x \right )^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.161 |
|
| 22788 |
\begin{align*}
2 y^{2}-6 y x +\left (3 y x -4 x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.168 |
|
| 22789 |
\begin{align*}
x^{\prime }&=-\left (1+p \right ) t^{p} x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.174 |
|
| 22790 |
\begin{align*}
y^{\prime \prime }&=a y \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.179 |
|
| 22791 |
\begin{align*}
\left (x +4 y\right ) y^{\prime }&=2 x +3 y-5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.180 |
|
| 22792 |
\begin{align*}
y^{\prime }&=\frac {-6 x +y-3}{2 x -y-1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.190 |
|
| 22793 |
\begin{align*}
x y^{\prime } y-y^{2}&=1 \\
y \left (2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.194 |
|
| 22794 | \begin{align*}
x y^{\prime } y&=2 x^{2}-y^{2} \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 7.196 |
|
| 22795 |
\begin{align*}
\left (c \,x^{2}+b x +a \right ) y+\left (1-x \right )^{2} x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
7.200 |
|
| 22796 |
\begin{align*}
y^{\prime }&=\frac {y^{2}}{x^{2}+y x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.201 |
|
| 22797 |
\begin{align*}
y^{\prime }&=\frac {\left (-256 a \,x^{2}+512+512 y^{2}+128 y a \,x^{4}+8 a^{2} x^{8}+512 y^{3}+192 x^{4} a y^{2}+24 y a^{2} x^{8}+a^{3} x^{12}\right ) x}{512} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.204 |
|
| 22798 |
\begin{align*}
\left (x -y\right ) y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.210 |
|
| 22799 |
\begin{align*}
2 \left (x -y^{4}\right ) y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
7.211 |
|
| 22800 |
\begin{align*}
y^{\prime } x&=k +a \,x^{n}+b y+c y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
7.213 |
|