| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 21901 |
\begin{align*}
y^{\prime }&=1-y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.798 |
|
| 21902 |
\begin{align*}
y^{\prime } x -y \left (\ln \left (y x \right )-1\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.801 |
|
| 21903 |
\begin{align*}
y^{\prime }&=\frac {y-\ln \left (\frac {x +1}{x -1}\right ) x^{3}+\ln \left (\frac {x +1}{x -1}\right ) x y^{2}}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.803 |
|
| 21904 |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (-\left (a^{2} b^{2}-\left (1+a \right )^{2}\right ) \sin \left (x \right )^{2}-a \left (1+a \right ) b \sin \left (2 x \right )-a \left (-1+a \right )\right ) y}{\sin \left (x \right )^{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
8.803 |
|
| 21905 |
\begin{align*}
y^{\prime }+\frac {2 y}{x}&=6 y^{2} x^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.809 |
|
| 21906 |
\begin{align*}
\left (2 y-6 x \right ) y^{\prime }-y+3 x +2&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.812 |
|
| 21907 |
\begin{align*}
-y+y^{\prime }&=t y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.812 |
|
| 21908 |
\begin{align*}
1+\ln \left (y x \right )+\frac {x y^{\prime }}{y}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.815 |
|
| 21909 |
\begin{align*}
y^{\prime }&=\frac {-3 x^{2}-2 y^{2}}{4 y x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.818 |
|
| 21910 |
\begin{align*}
x^{3} y^{\prime \prime }+3 x^{2} y^{\prime }+y x -1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.818 |
|
| 21911 |
\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*} |
✓ |
✓ |
✓ |
✓ |
8.827 |
|
| 21912 |
\begin{align*}
x^{\prime \prime }+4 x&=\delta \left (-2+t \right )-\delta \left (t -5\right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
8.828 |
|
| 21913 |
\begin{align*}
\left (a b x +a n +b m \right ) y+\left (m +n +\left (a +b \right ) x \right ) y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
8.834 |
|
| 21914 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-4\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
8.836 |
|
| 21915 |
\begin{align*}
x \left (3-2 x^{2} y\right ) y^{\prime }&=4 x -3 y+3 y^{2} x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.839 |
|
| 21916 |
\begin{align*}
y^{\prime }&=\frac {1}{x -3 y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.839 |
|
| 21917 |
\begin{align*}
y^{\prime }&=-\frac {x}{2}+1+x \sqrt {x^{2}-4 x +4 y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.840 |
|
| 21918 |
\begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }+2 \left (1-x \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
8.841 |
|
| 21919 |
\begin{align*}
\frac {r \tan \left (\theta \right ) r^{\prime }}{a^{2}-r^{2}}&=1 \\
r \left (\frac {\pi }{4}\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.843 |
|
| 21920 |
\begin{align*}
x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=64 \ln \left (x \right ) x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.845 |
|
| 21921 |
\begin{align*}
y \ln \left (y^{\prime }\right )+y^{\prime }-y \ln \left (y\right )-y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.847 |
|
| 21922 |
\begin{align*}
y^{\prime }&={\mathrm e}^{x -y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.847 |
|
| 21923 |
\begin{align*}
y^{\prime }&=\frac {y x}{x^{2}+y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.848 |
|
| 21924 |
\begin{align*}
y^{\prime } x&=y+2 \,{\mathrm e}^{-\frac {y}{x}} x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.851 |
|
| 21925 |
\begin{align*}
y \left (2-3 y x \right )-y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.854 |
|
| 21926 |
\begin{align*}
x^{2} y^{\prime }+2+x y \left (4+y x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.855 |
|
| 21927 |
\begin{align*}
\left (-t^{2}+1\right ) y^{\prime }-t y&=5 t y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.856 |
|
| 21928 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (4 x^{2}-1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
8.861 |
|
| 21929 |
\begin{align*}
x^{2}-y^{\prime } x&=y \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.862 |
|
| 21930 |
\begin{align*}
\left (x +2 y+1\right ) y^{\prime }+1-x -2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.864 |
|
| 21931 |
\begin{align*}
\left (\cos \left (x \right )-\sin \left (x \right )\right ) y^{\prime }+\left (\cos \left (x \right )+\sin \left (x \right )\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.865 |
|
| 21932 |
\begin{align*}
y^{\prime } x&=2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.867 |
|
| 21933 |
\begin{align*}
y+x y^{2}-y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.870 |
|
| 21934 |
\begin{align*}
y^{\prime }&=\frac {x \left (-2+3 x \sqrt {x^{2}+3 y}\right )}{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.870 |
|
| 21935 |
\begin{align*}
y^{\prime }&=\frac {t}{y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.871 |
|
| 21936 |
\begin{align*}
y^{\prime \prime } x +\left (x^{n}+1-n \right ) y^{\prime }+b \,x^{2 n -1} y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
8.874 |
|
| 21937 |
\begin{align*}
y^{\prime }+\frac {2 y}{x}&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.875 |
|
| 21938 |
\begin{align*}
x \cos \left (x \right ) y^{\prime }+y \left (x \sin \left (x \right )+\cos \left (x \right )\right )&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.876 |
|
| 21939 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=1-y x -3 x^{2}+2 x^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.877 |
|
| 21940 |
\begin{align*}
y^{\prime }&=-\frac {16 x y^{3}-8 y^{3}-8 y+8 x y^{2}-2 x^{2} y^{3}-8+12 y x -6 y^{2} x^{2}+x^{3} y^{3}}{32 y x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.881 |
|
| 21941 |
\begin{align*}
1+y-y^{\prime } t&=\ln \left (y^{\prime }\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.882 |
|
| 21942 |
\begin{align*}
y-2 x -y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.882 |
|
| 21943 |
\begin{align*}
y^{\prime }-\sqrt {\frac {b_{4} y^{4}+b_{3} y^{3}+b_{2} y^{2}+b_{1} y+b_{0}}{a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0}}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.885 |
|
| 21944 |
\begin{align*}
y^{\prime }&=\frac {y^{2}+2 y x}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.885 |
|
| 21945 |
\begin{align*}
x^{\left (5\right )}+x&=0 \\
x \left (\infty \right ) &= 0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
8.886 |
|
| 21946 |
\begin{align*}
x \left (a +y\right )^{2} y^{\prime }&=b y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.891 |
|
| 21947 |
\begin{align*}
y^{\prime \prime }-x^{2} y-x^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.898 |
|
| 21948 |
\begin{align*}
x {y^{\prime }}^{2}+x -2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.902 |
|
| 21949 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (3 x^{2}-4\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
8.907 |
|
| 21950 |
\begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime }-y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.912 |
|
| 21951 |
\begin{align*}
\left (4 y-2 x -3\right ) y^{\prime }+2 y-x -1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.913 |
|
| 21952 |
\begin{align*}
y^{\prime }&=-\frac {y \left (\ln \left (x -1\right )+\coth \left (x +1\right ) x -\coth \left (x +1\right ) x^{2} y\right )}{x \ln \left (x -1\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.915 |
|
| 21953 |
\begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
y \left (\frac {1}{2}\right ) &= -4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.918 |
|
| 21954 |
\begin{align*}
y^{\prime }&=a \left (t \right ) y \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.923 |
|
| 21955 |
\begin{align*}
\left (x^{2}-y^{2}\right ) y^{\prime }&=2 y x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.925 |
|
| 21956 |
\begin{align*}
y^{\prime }-5 y&=3 x^{3}+4 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.928 |
|
| 21957 |
\begin{align*}
y^{\prime }&=\frac {-30 x^{3} y+12 x^{6}+70 x^{{7}/{2}}-30 x^{3}-25 \sqrt {x}\, y+50 x -25 \sqrt {x}-25}{5 \left (-5 y+2 x^{3}+10 \sqrt {x}-5\right ) x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.930 |
|
| 21958 |
\begin{align*}
y^{\prime \prime }&=x {y^{\prime }}^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.932 |
|
| 21959 |
\begin{align*}
y^{\prime }&=t^{2}+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.934 |
|
| 21960 |
\begin{align*}
3 y^{\prime } x&=\left (3 y^{3} \ln \left (x \right ) x +1\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.940 |
|
| 21961 |
\begin{align*}
2 y y^{\prime } x&=x^{2}+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.941 |
|
| 21962 |
\begin{align*}
2 \cos \left (x \right ) y^{\prime }&=\sin \left (x \right ) y-y^{3} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.941 |
|
| 21963 |
\begin{align*}
\left (3 x^{2}+2 y x +4 y^{2}\right ) y^{\prime }+2 x^{2}+6 y x +y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.941 |
|
| 21964 |
\begin{align*}
y^{\prime }&=a \,{\mathrm e}^{\lambda x} y^{2}+a \,{\mathrm e}^{\lambda x} f \left (x \right ) y+\lambda f \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.947 |
|
| 21965 |
\begin{align*}
x^{\prime }&=-\frac {x+t +1}{x-t +1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.947 |
|
| 21966 |
\begin{align*}
x +3 y+\left (3 x +y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.951 |
|
| 21967 |
\begin{align*}
y^{\prime }&=-\frac {x}{y} \\
y \left (0\right ) &= a_{0} \\
\end{align*} |
✓ |
✗ |
✓ |
✓ |
8.957 |
|
| 21968 |
\begin{align*}
y x +\left (x^{2}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.957 |
|
| 21969 |
\begin{align*}
y^{\prime } x +\left (1-\ln \left (x \right )-\ln \left (y\right )\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.960 |
|
| 21970 |
\begin{align*}
y^{\prime }&=y-x y^{3} {\mathrm e}^{-2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.961 |
|
| 21971 |
\begin{align*}
y^{\prime }&=-x^{3} \left (-y^{2}-2 y \ln \left (x \right )-\ln \left (x \right )^{2}\right )+\frac {y}{x \ln \left (x \right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.962 |
|
| 21972 |
\begin{align*}
\left (1-\sqrt {3}\right ) y^{\prime }+y \sec \left (x \right )&=y^{\sqrt {3}} \sec \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.963 |
|
| 21973 |
\begin{align*}
\ln \left (\cos \left (y^{\prime }\right )\right )+y^{\prime } \tan \left (y^{\prime }\right )&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.964 |
|
| 21974 |
\begin{align*}
\left (-y+y^{\prime } x \right ) y^{\prime \prime }+4 {y^{\prime }}^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
8.965 |
|
| 21975 |
\begin{align*}
x^{2}+y^{2}+\left (2 y x -3\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.968 |
|
| 21976 |
\begin{align*}
y y^{\prime }+f \left (x \right )&=g \left (x \right ) y \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
8.970 |
|
| 21977 |
\begin{align*}
y^{\prime }&=\frac {2 y^{3}}{1+2 F \left (\frac {1+4 x y^{2}}{y^{2}}\right ) y} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
8.970 |
|
| 21978 |
\begin{align*}
y^{\prime }&=\frac {x y^{2}}{x^{2} y+y^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.970 |
|
| 21979 |
\begin{align*}
y^{\prime \prime }-x^{3} y^{\prime }-x^{2} y-x^{3}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
8.972 |
|
| 21980 |
\begin{align*}
\left (x -a \right ) \left (-b +x \right ) y^{\prime }+k \left (x +y-a \right ) \left (x +y-b \right )+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.974 |
|
| 21981 |
\begin{align*}
y^{\prime }&=\frac {y \left (-\ln \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 \ln \left (\frac {1}{x}\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.977 |
|
| 21982 |
\begin{align*}
y y^{\prime }&=a x +b x y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.978 |
|
| 21983 |
\begin{align*}
y^{\prime } x +3 y&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.984 |
|
| 21984 |
\begin{align*}
y^{\prime }&=3 x^{2} y-3 x^{4}+2 x^{2}-2 y+2 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.985 |
|
| 21985 |
\begin{align*}
y^{\prime }&=x^{2}-y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.985 |
|
| 21986 |
\begin{align*}
y^{\prime }-\frac {y}{x}&=\frac {1}{y} \\
y \left (1\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.986 |
|
| 21987 |
\begin{align*}
y^{\prime }&=\frac {x^{2}+3 y^{2}}{2 y x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.987 |
|
| 21988 |
\begin{align*}
x y^{3}-1+x^{2} y^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.987 |
|
| 21989 |
\begin{align*}
y^{\prime \prime }+\frac {\left (x -1\right ) y^{\prime }}{x}+\frac {y}{x^{3}}&=\frac {{\mathrm e}^{-\frac {1}{x}}}{x^{3}} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
8.987 |
|
| 21990 |
\begin{align*}
y^{\prime }&=x +\frac {\sec \left (x \right ) y}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.988 |
|
| 21991 |
\begin{align*}
y^{\prime }&=1-\frac {y}{x} \\
y \left (-\frac {1}{2}\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.988 |
|
| 21992 |
\begin{align*}
\sin \left (3 x \right )+2 y \cos \left (3 x \right )^{3} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.989 |
|
| 21993 |
\begin{align*}
\left (y^{3}-x \right ) y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.992 |
|
| 21994 |
\begin{align*}
x -y+\left (3 x +y\right ) y^{\prime }&=0 \\
y \left (2\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.996 |
|
| 21995 |
\begin{align*}
y^{\prime }&=\sqrt {{| y|}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.997 |
|
| 21996 |
\begin{align*}
y^{\prime }&=\cos \left (y\right ) \\
y \left (0\right ) &= -\frac {\pi }{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.998 |
|
| 21997 |
\begin{align*}
y^{\prime }&=y^{2}+a x \cosh \left (b x \right )^{m} y+a \cosh \left (b x \right )^{m} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.999 |
|
| 21998 |
\begin{align*}
y^{\prime } x&=y+2 \,{\mathrm e}^{-\frac {y}{x}} x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.000 |
|
| 21999 |
\begin{align*}
y^{\prime }&=\frac {1}{y}-\frac {y}{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.002 |
|
| 22000 |
\begin{align*}
2 y \left (x +y+2\right )+\left (y^{2}-x^{2}-4 x -1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.005 |
|