| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 26901 |
\begin{align*}
y^{\prime }&=\frac {y^{3} x \,{\mathrm e}^{3 x^{2}} {\mathrm e}^{-\frac {9 x^{2}}{2}}}{9 \,{\mathrm e}^{\frac {3 x^{2}}{2}}+3 \,{\mathrm e}^{\frac {3 x^{2}}{2}} y+9 y} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
61.912 |
|
| 26902 |
\begin{align*}
y y^{\prime }+a x +b y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
61.969 |
|
| 26903 |
\begin{align*}
2 y^{\prime \prime }&=1+12 y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
62.012 |
|
| 26904 |
\begin{align*}
x \left (-x^{2}+1\right ) {y^{\prime }}^{2}-2 \left (-x^{2}+1\right ) y y^{\prime }+x \left (1-y^{2}\right )&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
62.017 |
|
| 26905 |
\begin{align*}
y^{\prime }&=\lambda \sin \left (\lambda x \right ) y^{2}+f \left (x \right ) \cos \left (\lambda x \right ) y-f \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
62.062 |
|
| 26906 |
\begin{align*}
{y^{\prime }}^{2}+a y y^{\prime }-b x -c&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
62.069 |
|
| 26907 |
\begin{align*}
48 x \left (x -1\right ) y^{\prime \prime }+\left (152 x -40\right ) y^{\prime }+53 y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
62.123 |
|
| 26908 |
\begin{align*}
y^{\prime \prime }+\frac {a^{2}}{y^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
62.467 |
|
| 26909 |
\begin{align*}
y^{2} y^{\prime \prime }-a&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
62.474 |
|
| 26910 |
\begin{align*}
x^{2}-2 y^{2}+x y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
62.487 |
|
| 26911 |
\begin{align*}
\left (x^{2}-y^{2}\right ) y^{\prime }&=2 y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
62.535 |
|
| 26912 |
\begin{align*}
x \left (x -y \tan \left (\frac {y}{x}\right )\right ) y^{\prime }+\left (x +y \tan \left (\frac {y}{x}\right )\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
62.564 |
|
| 26913 |
\begin{align*}
4 y y^{\prime \prime }&=12 y^{2}+3 {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
62.671 |
|
| 26914 |
\begin{align*}
2 t y y^{\prime }&=3 y^{2}-t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
62.696 |
|
| 26915 |
\begin{align*}
-x^{\prime \prime }&=\frac {1}{\sqrt {x^{2}+1}}-x \\
x \left (a \right ) &= 0 \\
x \left (b \right ) &= 0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
62.753 |
|
| 26916 |
\begin{align*}
\left (-a^{2}+1\right ) x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }-a^{2} x^{2}+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
62.861 |
|
| 26917 |
\begin{align*}
\left (\left (-4 a^{2}+1\right ) x^{2}+y^{2}\right ) {y^{\prime }}^{2}-8 a^{2} x y y^{\prime }+x^{2}+\left (-4 a^{2}+1\right ) y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
62.863 |
|
| 26918 |
\begin{align*}
\sin \left (x +y\right )-y y^{\prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
62.884 |
|
| 26919 |
\begin{align*}
y^{\prime }&=-\frac {4 x +3 y+15}{2 x +y+7} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
62.911 |
|
| 26920 |
\begin{align*}
x y y^{\prime }&=2 y^{2}-3 x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
62.950 |
|
| 26921 |
\begin{align*}
y^{\prime }&=\frac {t -y}{t +y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
62.964 |
|
| 26922 |
\begin{align*}
x^{2} y^{\prime }+y^{2}&=x y y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
63.029 |
|
| 26923 |
\begin{align*}
x \left (1+2 y x \right ) y^{\prime }+\left (1+2 y x -x^{2} y^{2}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
63.033 |
|
| 26924 |
\begin{align*}
2 x y^{\prime \prime }+x^{2} y^{\prime }-y \sin \left (x \right )&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
63.063 |
|
| 26925 |
\begin{align*}
y \left (x^{2}-y x +y^{2}\right )+x y^{\prime } \left (x^{2}+y x +y^{2}\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
63.104 |
|
| 26926 |
\begin{align*}
x^{3}-3 x y^{2}+\left (y^{3}-3 x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
63.154 |
|
| 26927 |
\begin{align*}
\left (2 y x +4 x^{3}\right ) y^{\prime }+y^{2}+112 x^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
63.178 |
|
| 26928 |
\begin{align*}
144 x \left (x -1\right ) y^{\prime \prime }+\left (120 x -48\right ) y^{\prime }+y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
63.268 |
|
| 26929 |
\begin{align*}
\left (1-x \right ) y^{\prime \prime }-4 x y^{\prime }+5 y&=\cos \left (x \right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
63.310 |
|
| 26930 |
\begin{align*}
x y^{\prime }&=\lambda \arccos \left (x \right )^{n} y^{2}+k y+\lambda \,b^{2} x^{2 k} \arccos \left (x \right )^{n} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
63.324 |
|
| 26931 |
\begin{align*}
\left (2 t +1\right ) x^{\prime \prime }+t^{3} x^{\prime }+x&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
63.505 |
|
| 26932 |
\begin{align*}
x^{2}+2 y x +2 y^{2}+\left (x^{2}+4 y x +5 y^{2}\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
63.518 |
|
| 26933 |
\begin{align*}
y \left (3 x^{2}+y\right )-x \left (x^{2}-y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
63.698 |
|
| 26934 |
\begin{align*}
\left (3 x +2 y+1\right ) y^{\prime }+4 x +3 y+2&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
63.796 |
|
| 26935 |
\begin{align*}
y y^{\prime }+a \left (2 b x +1\right ) {\mathrm e}^{b x} y&=-a^{2} b \,x^{2} {\mathrm e}^{2 b x} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
63.804 |
|
| 26936 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=1+y^{2}-2 x y \left (1+y^{2}\right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
63.955 |
|
| 26937 |
\begin{align*}
2 y-4 \left (1-x \right ) y^{\prime }+\left (1-x \right )^{2} y^{\prime \prime }&=\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
63.993 |
|
| 26938 |
\begin{align*}
x \left (2 a x y+b \right ) y^{\prime }&=-4 a \,x^{2} y^{2}-3 b x y+c \,x^{2}+k \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
64.003 |
|
| 26939 |
\begin{align*}
\left (x^{2} y-1\right ) y^{\prime }-x y^{2}+1&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
64.009 |
|
| 26940 |
\begin{align*}
\left (x +\frac {2}{y}\right ) y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
64.098 |
|
| 26941 |
\begin{align*}
y x +\left (x^{2}+y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
64.186 |
|
| 26942 |
\begin{align*}
\left (1+{y^{\prime }}^{2}\right ) y^{\prime \prime \prime }&=\left (a +3 y^{\prime }\right ) {y^{\prime \prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
64.355 |
|
| 26943 |
\begin{align*}
6 y^{2}-x \left (2 x^{3}+y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
64.366 |
|
| 26944 |
\begin{align*}
9 y^{4} \left (x^{2}-1\right ) {y^{\prime }}^{2}-6 x y^{5} y^{\prime }-4 x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
64.535 |
|
| 26945 |
\begin{align*}
\left (b x +a \right ) y+2 \left (1-2 x \right ) y^{\prime }+4 x \left (1-x \right ) y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
64.611 |
|
| 26946 |
\begin{align*}
x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y&=x^{2} \left (x^{2}-1\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
64.735 |
|
| 26947 |
\begin{align*}
y y^{\prime }-y&=\frac {6}{25} x -A \,x^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
64.764 |
|
| 26948 |
\begin{align*}
x^{2}-3 y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
64.792 |
|
| 26949 |
\begin{align*}
x -y+\left (x -4 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
64.798 |
|
| 26950 |
\begin{align*}
\left (c \,x^{2}+b x +a \right ) y+x^{2} y^{\prime }+x^{3} y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
64.802 |
|
| 26951 |
\begin{align*}
x^{2} y^{\prime \prime }-3 x y^{\prime }+5 y&=x^{2} \sin \left (\ln \left (x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
64.819 |
|
| 26952 |
\begin{align*}
t \left (t^{2}-4\right ) y^{\prime \prime }+y&={\mathrm e}^{t} \\
y \left (1\right ) &= y_{1} \\
y^{\prime }\left (1\right ) &= y_{1} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
64.867 |
|
| 26953 |
\begin{align*}
y y^{\prime }-y&=-\frac {6}{25} x -A \,x^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
64.923 |
|
| 26954 |
\begin{align*}
y^{\prime }&=\frac {y-x y^{2}}{x +x^{2} y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
65.319 |
|
| 26955 |
\begin{align*}
y^{\prime }&=\frac {x +3 y}{x -3 y} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
65.322 |
|
| 26956 |
\begin{align*}
\left (x y^{\prime }-y\right ) \left (x -y y^{\prime }\right )&=2 y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
65.365 |
|
| 26957 |
\begin{align*}
x^{2}+y^{2}+1+x \left (x -2 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
65.442 |
|
| 26958 |
\begin{align*}
y^{\prime }&=\frac {3 y^{2}-t^{2}}{2 y t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
65.507 |
|
| 26959 |
\begin{align*}
y^{\prime }&=\frac {2 x +7 y}{2 x -2 y} \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
65.532 |
|
| 26960 |
\begin{align*}
x^{\prime }&=\frac {x^{2}+t \sqrt {t^{2}+x^{2}}}{x t} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
65.538 |
|
| 26961 |
\begin{align*}
x^{2}+2 y x -y^{2}+\left (y^{2}+2 y x -x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
65.674 |
|
| 26962 |
\begin{align*}
\left (6 x -5 y+4\right ) y^{\prime }+y-2 x -1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
65.970 |
|
| 26963 |
\begin{align*}
{y^{\prime }}^{2} x^{2}+\left (2 x +y\right ) y y^{\prime }+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
66.009 |
|
| 26964 |
\begin{align*}
\left (2 x +3 x^{2} y\right ) y^{\prime }+y+2 x y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
66.040 |
|
| 26965 |
\begin{align*}
\left (a \,x^{2}+b x +c \right )^{{3}/{2}} y^{\prime \prime }-F \left (\frac {y}{\sqrt {a \,x^{2}+b x +c}}\right )&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
66.072 |
|
| 26966 |
\begin{align*}
y y^{\prime }-\frac {a \left (x \left (m -1\right )+1\right ) y}{x}&=\frac {a^{2} \left (m x +1\right ) \left (x -1\right )}{x} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
66.132 |
|
| 26967 |
\begin{align*}
{y^{\prime }}^{2}+a y+b \,x^{2}&=0 \\
\end{align*} |
✓ |
✗ |
✓ |
✗ |
66.390 |
|
| 26968 |
\begin{align*}
\left (x -y^{\prime }-y\right )^{2}&=x^{2} \left (2 y x -x^{2} y^{\prime }\right ) \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
66.469 |
|
| 26969 |
\begin{align*}
2 x^{2}+y x +y^{2}+2 x^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
66.481 |
|
| 26970 |
\begin{align*}
U^{\prime }&=\frac {U+1}{\sqrt {s}+\sqrt {s U}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
66.487 |
|
| 26971 |
\begin{align*}
y y^{\prime }-y&=\frac {2 a^{2}}{\sqrt {8 a^{2}+x^{2}}} \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
66.569 |
|
| 26972 |
\begin{align*}
y+x y^{2}+\left (x -x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
66.776 |
|
| 26973 |
\begin{align*}
-x^{\prime \prime }+x&={\mathrm e}^{-x} \\
x \left (a \right ) &= 0 \\
x \left (b \right ) &= 0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
67.083 |
|
| 26974 |
\begin{align*}
3 y^{2}+4 y x +\left (x^{2}+2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
67.201 |
|
| 26975 |
\begin{align*}
x y {y^{\prime }}^{2}+\left (x^{22}-y^{2}+a \right ) y^{\prime }-y x&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
67.270 |
|
| 26976 |
\begin{align*}
\left (x -3 y\right ) y^{\prime }+4+3 x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
67.437 |
|
| 26977 |
\begin{align*}
x y^{\prime }&=a \sin \left (\lambda x \right )^{m} y^{2}+k y+a \,b^{2} x^{2 k} \sin \left (\lambda x \right )^{m} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
67.467 |
|
| 26978 |
\begin{align*}
y^{\prime }&=\frac {-3+x +y}{x -y-1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
67.729 |
|
| 26979 |
\begin{align*}
x^{3}+y^{2}+\left (y x -3 x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
67.807 |
|
| 26980 |
\begin{align*}
y^{\prime }&=a +b y-\sqrt {A +B y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
67.823 |
|
| 26981 |
\begin{align*}
x \left (x^{2}-y x +y^{2}\right ) y^{\prime }+\left (x^{2}+y x +y^{2}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
67.832 |
|
| 26982 |
\begin{align*}
y^{\prime }&=\frac {x -2 y}{y-2 x} \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
67.833 |
|
| 26983 |
\begin{align*}
y^{\prime }&=y^{2}+2 a \lambda x \,{\mathrm e}^{\lambda \,x^{2}}-a^{2} {\mathrm e}^{2 \lambda \,x^{2}} \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
68.014 |
|
| 26984 |
\begin{align*}
y^{\prime }&=\frac {y^{2}}{y x -x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
68.040 |
|
| 26985 |
\begin{align*}
x y^{\prime }&=a \cos \left (\lambda x \right )^{m} y^{2}+k y+a \,b^{2} x^{2 k} \cos \left (\lambda x \right )^{m} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
68.044 |
|
| 26986 |
\begin{align*}
x^{\prime }&=\frac {2 x}{3 t}+\frac {2 t}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
68.100 |
|
| 26987 |
\begin{align*}
x +y-1-\left (x -y-1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
68.105 |
|
| 26988 |
\begin{align*}
y {y^{\prime \prime }}^{4}+{y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
68.113 |
|
| 26989 |
\begin{align*}
x +y+2-\left (x -y-4\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
68.154 |
|
| 26990 |
\begin{align*}
{y^{\prime }}^{3}+{y^{\prime }}^{2} x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
68.173 |
|
| 26991 |
\begin{align*}
x&=y y^{\prime }+a {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
68.192 |
|
| 26992 |
\begin{align*}
\frac {8 x^{4} y+12 x^{3} y^{2}+2}{2 x +3 y}+\frac {\left (2 x^{5}+3 x^{4} y+3\right ) y^{\prime }}{x^{2} y^{4}+1}&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
68.326 |
|
| 26993 |
\begin{align*}
2 y^{\prime }&=2 \sin \left (y\right )^{2} \tan \left (y\right )-x \sin \left (2 y\right ) \\
\end{align*} |
✗ |
✗ |
✓ |
✗ |
68.343 |
|
| 26994 |
\begin{align*}
x y y^{\prime }&=x^{2} y^{\prime }+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
68.481 |
|
| 26995 |
\begin{align*}
y^{\prime }-a \sqrt {1+y^{2}}-b&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
68.524 |
|
| 26996 |
\begin{align*}
3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
68.537 |
|
| 26997 |
\begin{align*}
{y^{\prime }}^{3}+y^{3}-3 y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
68.551 |
|
| 26998 |
\begin{align*}
y^{\prime \prime } y^{\prime \prime \prime }&=a \sqrt {1+b^{2} {y^{\prime \prime }}^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
68.554 |
|
| 26999 |
\begin{align*}
\left (x^{3}-y\right ) y-x \left (y+x^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
68.671 |
|
| 27000 |
\begin{align*}
x +2 y+\left (-1+y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
68.704 |
|