| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 24801 |
\begin{align*}
\sin \left (x \right )^{2} y^{\prime \prime }-\left (a^{2} \cos \left (x \right )^{2}+\cos \left (x \right ) b +\frac {b^{2}}{\left (2 a -3\right )^{2}}+3 a +2\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
15.809 |
|
| 24802 |
\begin{align*}
\left (3 x^{2}-y^{2}\right ) y^{\prime }-2 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
15.815 |
|
| 24803 |
\begin{align*}
y^{\prime \prime }+\left (1+\frac {2 \cot \left (x \right )}{x}-\frac {2}{x^{2}}\right ) y&=x \cos \left (x \right ) \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
15.822 |
|
| 24804 |
\begin{align*}
x^{2} y^{\prime }+y^{2}&=x y y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
15.824 |
|
| 24805 |
\begin{align*}
\left (2 x +y\right ) y^{\prime }+x -2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
15.826 |
|
| 24806 |
\begin{align*}
y^{\prime }&=\sqrt {y^{2}-1} \\
y \left (2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
15.845 |
|
| 24807 |
\begin{align*}
x y y^{\prime }&=2 x^{2}+2 y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
15.858 |
|
| 24808 |
\begin{align*}
y y^{\prime \prime }&=\ln \left (y\right ) y^{2}+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
15.859 |
|
| 24809 |
\begin{align*}
\left (t^{2}-x^{2}\right ) x^{\prime }&=x t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
15.867 |
|
| 24810 |
\begin{align*}
x \left (2 a x y+b \right ) y^{\prime }&=-a \left (m +3\right ) x y^{2}-b \left (m +2\right ) y+c \,x^{m} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
15.868 |
|
| 24811 |
\begin{align*}
x^{2}+y&={y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
15.877 |
|
| 24812 |
\begin{align*}
x -y+\left (3 x +y\right ) y^{\prime }&=0 \\
y \left (2\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
15.902 |
|
| 24813 |
\begin{align*}
{\mathrm e}^{\frac {t}{y}} \left (y-t \right ) y^{\prime }+y \left (1+{\mathrm e}^{\frac {t}{y}}\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
15.905 |
|
| 24814 |
\begin{align*}
2 y^{2}+4 x^{2}-x y y^{\prime }&=0 \\
y \left (1\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
15.933 |
|
| 24815 |
\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*} |
✓ |
✓ |
✓ |
✓ |
15.933 |
|
| 24816 |
\begin{align*}
\left (x^{2} \left (-a^{2}+1\right )+y^{2}\right ) {y^{\prime }}^{2}+2 a^{2} x y y^{\prime }+x^{2}+\left (-a^{2}+1\right ) y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
15.934 |
|
| 24817 |
\begin{align*}
2 x^{2} y+2 \sqrt {1+y^{2} x^{4}}+x^{3} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
15.959 |
|
| 24818 |
\begin{align*}
x y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime }+c \left (a \,x^{n}-c x +b \right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
15.963 |
|
| 24819 |
\begin{align*}
y^{\prime }-\sqrt {\left (b_{4} y^{4}+b_{3} y^{3}+b_{2} y^{2}+b_{1} y+b_{0} \right ) \left (a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0} \right )}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
15.978 |
|
| 24820 |
\begin{align*}
x +y y^{\prime }+y-x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
15.993 |
|
| 24821 |
\begin{align*}
x +y+1+\left (2 x +2 y-1\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
16.020 |
|
| 24822 |
\begin{align*}
t \left (s^{2}+t^{2}\right ) s^{\prime }-s \left (s^{2}-t^{2}\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
16.031 |
|
| 24823 |
\begin{align*}
a \left (\ln \left (y^{\prime }\right )-y^{\prime }\right )-x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
16.049 |
|
| 24824 |
\begin{align*}
2 x \tan \left (y\right )+3 y^{2}+x^{2}+\left (x^{2} \sec \left (y\right )^{2}+6 y x -y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
16.056 |
|
| 24825 |
\begin{align*}
y^{\prime }&=\frac {\sqrt {y}}{x} \\
y \left (-1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
16.067 |
|
| 24826 |
\begin{align*}
x^{\prime }&=\left (1+x\right ) \left (2-x\right ) \sin \left (x\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
16.070 |
|
| 24827 |
\begin{align*}
x +2 y+x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
16.080 |
|
| 24828 |
\begin{align*}
\left (12 y-5 x -8\right ) y^{\prime }-5 y+2 x +3&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
16.082 |
|
| 24829 |
\begin{align*}
y&=\left (2 x +1\right ) \left (1-y^{\prime }\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
16.082 |
|
| 24830 |
\begin{align*}
y^{\prime }&=\frac {2 y x}{x^{2}+y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
16.089 |
|
| 24831 |
\begin{align*}
y^{\prime }&=\sigma y^{2}+a y+b \,{\mathrm e}^{x}+c \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
16.092 |
|
| 24832 |
\begin{align*}
\left (a \,x^{n}+b \right ) y^{\prime \prime }+\left (c \,x^{n}+d \right ) y^{\prime }+\lambda \left (\left (-\lambda a +c \right ) x^{n}+d -b \lambda \right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
16.100 |
|
| 24833 |
\begin{align*}
x -y+1+\left (x -y-1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
16.102 |
|
| 24834 |
\begin{align*}
y^{\prime }&=-\frac {-y x -y+\sqrt {x^{2}+y^{2}}\, x^{2}-x \sqrt {x^{2}+y^{2}}\, y}{x \left (x +1\right )} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
16.106 |
|
| 24835 |
\begin{align*}
y y^{\prime }+f \left (x \right )&=g \left (x \right ) y \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
16.115 |
|
| 24836 |
\begin{align*}
y^{\prime }-\frac {y}{\left (\pi -1\right ) x}&=\frac {3 x y^{\pi }}{1-\pi } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
16.118 |
|
| 24837 |
\begin{align*}
2 x +y-\left (4 x +2 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
16.125 |
|
| 24838 |
\begin{align*}
\left (2+3 x -y x \right ) y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
16.127 |
|
| 24839 |
\begin{align*}
x^{\prime }&={\mathrm e}^{\frac {x}{t}}+\frac {x}{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
16.130 |
|
| 24840 |
\begin{align*}
y^{\prime }&=-\sin \left (y\right )^{5} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
16.146 |
|
| 24841 |
\begin{align*}
y^{\prime }&=\left (1+y^{2}\right ) \sqrt {1+\cos \left (x^{3}\right )} \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
16.156 |
|
| 24842 |
\begin{align*}
x y^{\prime }&=k +a \,x^{n}+b y+c y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
16.161 |
|
| 24843 |
\begin{align*}
2 x -2 y+\left (-1+y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
16.161 |
|
| 24844 |
\begin{align*}
2 y t +2 t^{3}+\left (t^{2}-y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
16.161 |
|
| 24845 |
\begin{align*}
y^{\prime }&=y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
16.164 |
|
| 24846 |
\begin{align*}
a^{2} \left (b^{2}-\left (c x -a y\right )^{2}\right ) {y^{\prime }}^{2}+2 a \,b^{2} c y^{\prime }+c^{2} \left (b^{2}-\left (c x -a y\right )^{2}\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
16.180 |
|
| 24847 |
\begin{align*}
x y^{\prime }&=\left (y \ln \left (x \right )-2\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
16.195 |
|
| 24848 |
\begin{align*}
2 x +2 y+2 x^{3} y+4 x^{2} y^{2}+\left (2 x +x^{4}+2 x^{3} y\right ) y^{\prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
16.207 |
|
| 24849 |
\begin{align*}
y^{\prime }&=\sin \left (y\right ) x +{\mathrm e}^{x} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
16.209 |
|
| 24850 |
\begin{align*}
x \left (4+y\right ) y^{\prime }-y^{2}-2 y-2 x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
16.214 |
|
| 24851 |
\begin{align*}
2 x -y+1+\left (2 y-x -1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
16.220 |
|
| 24852 |
\begin{align*}
x y^{\prime \prime }-3 y^{\prime }+\frac {3 y}{x}&=x +2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
16.222 |
|
| 24853 |
\begin{align*}
\left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y&=4 \cos \left (\ln \left (x +1\right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
16.227 |
|
| 24854 |
\begin{align*}
x^{2} y^{\prime }&=3 \left (x^{2}+y^{2}\right ) \arctan \left (\frac {y}{x}\right )+y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
16.238 |
|
| 24855 |
\begin{align*}
y^{\prime }&=\frac {y}{x}+\tanh \left (\frac {y}{x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
16.249 |
|
| 24856 |
\begin{align*}
y^{\prime }&=-y^{3}+a \,{\mathrm e}^{\lambda x} y^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
16.252 |
|
| 24857 |
\begin{align*}
y^{\prime }&=1+x y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
16.259 |
|
| 24858 |
\begin{align*}
y^{\prime }&=\frac {\left (3 x y^{2}+x +3 y^{2}\right ) y}{\left (x +6 y^{2}\right ) x \left (x +1\right )} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
16.263 |
|
| 24859 |
\begin{align*}
x +y+\left (2 x +2 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
16.269 |
|
| 24860 |
\begin{align*}
{\mathrm e}^{y} \left (x y^{\prime }+1\right )&=5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
16.274 |
|
| 24861 |
\begin{align*}
\left (a \,x^{n}+b \right )^{2} y^{\prime \prime }+\left (a \,x^{n}+b \right ) \left (c \,x^{n}+d \right ) y^{\prime }+n \left (-a d +b c \right ) x^{n -1} y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
16.275 |
|
| 24862 |
\begin{align*}
y \left (x -y-2\right )+x \left (-x +y+4\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
16.276 |
|
| 24863 |
\begin{align*}
y^{\prime }&=-\frac {x}{2}-\frac {a}{2}+\sqrt {x^{2}+2 a x +a^{2}+4 y}+x^{2} \sqrt {x^{2}+2 a x +a^{2}+4 y}+x^{3} \sqrt {x^{2}+2 a x +a^{2}+4 y} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
16.278 |
|
| 24864 |
\begin{align*}
y^{2}+\left (x^{2}+3 y x +4 y^{2}\right ) y^{\prime }&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
16.284 |
|
| 24865 |
\begin{align*}
y^{\prime }+x \sin \left (2 y\right )&=x \,{\mathrm e}^{-x^{2}} \cos \left (y\right )^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
16.284 |
|
| 24866 |
\begin{align*}
a \,x^{2} y^{\prime \prime }+b x y^{\prime }+\left (c \,x^{2}+d x +f \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
16.287 |
|
| 24867 |
\begin{align*}
x^{2} \ln \left (a x \right ) \left (y^{\prime }-y^{2}\right )&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
16.290 |
|
| 24868 |
\begin{align*}
x \cos \left (y\right ) y^{\prime }+\sin \left (y\right )&=5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
16.299 |
|
| 24869 |
\begin{align*}
y^{\prime }&=-\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
16.325 |
|
| 24870 |
\begin{align*}
y^{\prime }&=\frac {\left (3 x +y^{3}-1\right )^{2}}{y^{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
16.329 |
|
| 24871 |
\begin{align*}
y^{\prime }&=f \left (x \right ) y^{2}+2 a \lambda x \,{\mathrm e}^{\lambda \,x^{2}}-a^{2} f \left (x \right ) {\mathrm e}^{2 \lambda \,x^{2}} \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
16.354 |
|
| 24872 |
\begin{align*}
x y^{\prime }-y&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
16.356 |
|
| 24873 |
\begin{align*}
\left (x +y\right ) y^{\prime }+x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
16.359 |
|
| 24874 |
\begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+4 y^{\prime }-4 y&=\left \{\begin {array}{cc} 1 & 0\le t <5 \\ 2 & 5\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
16.367 |
|
| 24875 |
\begin{align*}
{y^{\prime }}^{2}&=\frac {1}{y x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
16.381 |
|
| 24876 |
\begin{align*}
y^{\prime }&=a y^{3}+\frac {b}{x^{{3}/{2}}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
16.392 |
|
| 24877 |
\begin{align*}
\left (x +2 y^{3}\right ) y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
16.408 |
|
| 24878 |
\begin{align*}
3 x^{2} \tan \left (y\right )-\frac {2 y^{3}}{x^{3}}+\left (x^{3} \sec \left (y\right )^{2}+4 y^{3}+\frac {3 y^{2}}{x^{2}}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
16.411 |
|
| 24879 |
\begin{align*}
y^{\prime } \left (y^{2}+2 x \right )&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
16.425 |
|
| 24880 |
\begin{align*}
2 t^{2}-y+\left (t +y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
16.439 |
|
| 24881 |
\begin{align*}
\left (3 x^{2}-y^{2}\right ) y^{\prime }-2 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
16.442 |
|
| 24882 |
\begin{align*}
b y+a y {y^{\prime }}^{2}+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
16.451 |
|
| 24883 |
\begin{align*}
y^{\prime }&=\frac {2 x +y}{y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
16.455 |
|
| 24884 |
\begin{align*}
2 \ln \left (x \right ) y^{\prime }+\frac {y}{x}&=\frac {\cos \left (x \right )}{y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
16.462 |
|
| 24885 |
\begin{align*}
x \tan \left (\frac {y}{x}\right )+y-x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
16.479 |
|
| 24886 |
\begin{align*}
x^{2}+6 y^{2}-4 x y y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
16.492 |
|
| 24887 |
\begin{align*}
y^{\prime }&=\frac {2 y}{x}+\frac {x^{3}}{y}+x \tan \left (\frac {y}{x^{2}}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
16.494 |
|
| 24888 |
\begin{align*}
y^{2}+x y y^{\prime }&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
16.502 |
|
| 24889 |
\begin{align*}
\left (b +k^{2} \cos \left (x \right )^{2}\right ) y+a \cot \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
16.513 |
|
| 24890 |
\begin{align*}
\left (y^{2}-x^{2}\right ) y^{\prime }+2 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
16.541 |
|
| 24891 |
\begin{align*}
x^{2}+y^{2}-x y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
16.543 |
|
| 24892 |
\begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime }&=2 y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
16.550 |
|
| 24893 |
\begin{align*}
2 y x +3 y^{2}-\left (x^{2}+2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
16.555 |
|
| 24894 |
\begin{align*}
\left (a +b x +y\right ) y^{\prime }+a -b x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
16.557 |
|
| 24895 |
\begin{align*}
\left (a b x +a n +b m \right ) y+\left (m +n +x \left (a +b \right )\right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
16.563 |
|
| 24896 |
\begin{align*}
4 x -3 y+\left (-3 x +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
16.563 |
|
| 24897 |
\begin{align*}
x +y+\left (2 x +3 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
16.566 |
|
| 24898 |
\begin{align*}
{y^{\prime }}^{2} x^{2}-\left (a +2 y x \right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
16.568 |
|
| 24899 |
\begin{align*}
y^{\prime }&=-\frac {3 x^{2}}{2 y} \\
y \left (-1\right ) &= {\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
16.570 |
|
| 24900 |
\begin{align*}
y^{\prime }&=\frac {x -y}{x +y} \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
16.576 |
|