| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 23901 |
\begin{align*}
2 x \left (x^{3}+y^{4}\right ) y^{\prime }&=\left (x^{3}+2 y^{4}\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.668 |
|
| 23902 |
\begin{align*}
y^{\prime }&=\frac {\left (x^{4}+3 x y^{2}+3 y^{2}\right ) y}{\left (x +6 y^{2}\right ) x \left (x +1\right )} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.671 |
|
| 23903 |
\begin{align*}
2 {y^{\prime }}^{3}+y^{\prime } x -2 y&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
9.672 |
|
| 23904 |
\begin{align*}
y^{\prime }&=a x y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.675 |
|
| 23905 |
\begin{align*}
y^{\prime }&=\frac {y}{x}+\sin \left (\frac {y}{x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.675 |
|
| 23906 |
\begin{align*}
y^{\prime }-\frac {3 y}{x}&=x^{4} y^{{1}/{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.677 |
|
| 23907 |
\begin{align*}
y^{\prime }&=x y^{3} \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.682 |
|
| 23908 |
\begin{align*}
y^{\prime }&=\sqrt {25-y^{2}} \\
y \left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.682 |
|
| 23909 |
\begin{align*}
y \left ({\mathrm e}^{x}+2 y x \right )-{\mathrm e}^{x} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.683 |
|
| 23910 |
\begin{align*}
y^{\prime \prime }+y^{\prime }+y&=\operatorname {Heaviside}\left (t -\pi \right )-\operatorname {Heaviside}\left (t -2 \pi \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
9.687 |
|
| 23911 |
\begin{align*}
y^{\prime } x&=k +a \,x^{n}+b y+c y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.687 |
|
| 23912 |
\begin{align*}
x^{2} {y^{\prime }}^{2}-\left (a +2 y x \right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.690 |
|
| 23913 |
\begin{align*}
\left (-x^{2}+1\right ) z^{\prime }-x z&=a x z^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.694 |
|
| 23914 |
\begin{align*}
a^{2} {y^{\prime \prime }}^{2}&=1+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.697 |
|
| 23915 |
\begin{align*}
\left (1-y^{2} x^{4}\right ) y^{\prime }&=x^{3} y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.703 |
|
| 23916 |
\begin{align*}
x \left (y^{2}+x^{2}-a \right ) y^{\prime }-\left (a +x^{2}+y^{2}\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.704 |
|
| 23917 |
\begin{align*}
y^{\prime }&={\mathrm e}^{t}+y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.705 |
|
| 23918 |
\begin{align*}
\left (1-3 x -y\right )^{2} y^{\prime }&=\left (1-2 y\right ) \left (3-6 x -4 y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.708 |
|
| 23919 |
\begin{align*}
2 \sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y&=y^{3} \sin \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.711 |
|
| 23920 |
\begin{align*}
y&=y^{\prime } x +\sqrt {b^{2}-a^{2} {y^{\prime }}^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.711 |
|
| 23921 |
\begin{align*}
y^{\prime }&=1+y+y^{2} \cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
9.712 |
|
| 23922 |
\begin{align*}
y^{\prime \prime }+a y^{\prime }-\left (b \,x^{2}+c \right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.715 |
|
| 23923 |
\begin{align*}
y^{\prime }&=\frac {y \left (1+\ln \left (y\right )-\ln \left (x \right )\right )}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.715 |
|
| 23924 |
\begin{align*}
y^{\prime }&=\frac {2 a \left (x y^{2}-4 a +x \right )}{-x^{3} y^{3}+4 a \,x^{2} y-x^{3} y+2 a y^{6} x^{3}-24 y^{4} a^{2} x^{2}+96 y^{2} x \,a^{3}-128 a^{4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.717 |
|
| 23925 |
\begin{align*}
3 x^{2} y+y^{3}+\left (x^{3}+3 x y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.725 |
|
| 23926 |
\begin{align*}
x y \left (x^{2}+1\right ) y^{\prime }-1-y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.728 |
|
| 23927 |
\begin{align*}
y^{\prime }+\frac {y}{\left (-x^{2}+1\right )^{{3}/{2}}}&=\frac {x +\sqrt {-x^{2}+1}}{\left (-x^{2}+1\right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.728 |
|
| 23928 |
\begin{align*}
x -y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.728 |
|
| 23929 |
\begin{align*}
y^{\prime }&=a y+b y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.730 |
|
| 23930 |
\begin{align*}
\left (1+y\right ) y^{\prime } \sqrt {x^{2}+1}&=y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.731 |
|
| 23931 |
\begin{align*}
y^{\prime }&=-\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.735 |
|
| 23932 |
\begin{align*}
y y^{\prime } x&=y^{2}+9 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.737 |
|
| 23933 |
\begin{align*}
y^{2}+2 t y y^{\prime }+3 t^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.747 |
|
| 23934 |
\begin{align*}
y^{\prime }&=\frac {2 y}{x} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.758 |
|
| 23935 |
\begin{align*}
\frac {y \left (2+x^{3} y\right )}{x^{3}}&=\frac {\left (1-2 x^{3} y\right ) y^{\prime }}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.760 |
|
| 23936 |
\begin{align*}
y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.760 |
|
| 23937 |
\begin{align*}
y^{\prime }&=y^{3}+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.764 |
|
| 23938 |
\begin{align*}
s^{\prime }+2 s&=s t^{2} \\
s \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.768 |
|
| 23939 |
\begin{align*}
y^{\prime }&=\sqrt {\frac {y-4}{x}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.773 |
|
| 23940 |
\begin{align*}
-y+y^{\prime } x&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.781 |
|
| 23941 |
\begin{align*}
y+x y^{2}-y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.782 |
|
| 23942 |
\begin{align*}
\frac {2 x}{y^{3}}+\frac {\left (y^{2}-3 x^{2}\right ) y^{\prime }}{y^{4}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.788 |
|
| 23943 |
\begin{align*}
2 y y^{\prime } x^{3}+3 y^{2} x^{2}+7&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.790 |
|
| 23944 |
\begin{align*}
b y+a y {y^{\prime }}^{2}+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.800 |
|
| 23945 |
\begin{align*}
y^{\prime }&=\sqrt {x +y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.802 |
|
| 23946 |
\begin{align*}
y^{3} \left (x +y y^{\prime }\right )&=\left (x^{2}+y^{2}\right )^{3} y^{\prime } \\
\end{align*} |
✓ |
✗ |
✗ |
✗ |
9.812 |
|
| 23947 |
\begin{align*}
x^{3}+y^{3}-y^{2} y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.816 |
|
| 23948 |
\begin{align*}
\frac {2 t}{t^{2}+1}+y+\left ({\mathrm e}^{y}+t \right ) y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
9.822 |
|
| 23949 |
\begin{align*}
y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=8 x^{3} \sin \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.824 |
|
| 23950 |
\begin{align*}
\frac {x}{\sqrt {x^{2}+y^{2}}}+\frac {1}{x}+\frac {1}{y}+\left (\frac {y}{\sqrt {x^{2}+y^{2}}}+\frac {1}{y}-\frac {x}{y^{2}}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
9.826 |
|
| 23951 |
\begin{align*}
9 {y^{\prime }}^{4}+8 y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.834 |
|
| 23952 |
\begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{x}}{{\mathrm e}^{-x} y+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.842 |
|
| 23953 |
\begin{align*}
\left (a y-b x \right )^{2} \left (a^{2} {y^{\prime }}^{2}+b^{2}\right )-c^{2} \left (a y^{\prime }+b \right )^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.845 |
|
| 23954 |
\begin{align*}
2 x +y-\left (4 x +2 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.845 |
|
| 23955 |
\begin{align*}
y^{\prime }&=\frac {\left (-256 a \,x^{2} y-32 a^{2} x^{6}-256 a \,x^{2}+512 y^{3}+192 x^{4} a y^{2}+24 y a^{2} x^{8}+a^{3} x^{12}\right ) x}{512 y+64 a \,x^{4}+512} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.849 |
|
| 23956 |
\begin{align*}
y^{\prime }&=3 x^{2} \left (y+2\right ) \\
y \left (2\right ) &= 8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.849 |
|
| 23957 |
\begin{align*}
2 {y^{\prime }}^{3} x +1&=y {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.860 |
|
| 23958 |
\begin{align*}
x {y^{\prime }}^{2}-y y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.860 |
|
| 23959 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.867 |
|
| 23960 |
\begin{align*}
y^{\prime }&=y^{2}+a \lambda +a \left (\lambda -a \right ) \tan \left (\lambda x \right )^{2} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.871 |
|
| 23961 |
\begin{align*}
y^{\prime }&=-\frac {\left (-\frac {1}{x}-\textit {\_F1} \left (y^{2}-2 x \right )\right ) x}{\sqrt {y^{2}}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.874 |
|
| 23962 |
\begin{align*}
y^{\prime }&=\frac {2 x}{y} \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.876 |
|
| 23963 |
\begin{align*}
\cos \left (x \right ) y^{\prime \prime }+\sin \left (x \right ) y^{\prime }-2 \cos \left (x \right )^{3} y&=2 \cos \left (x \right )^{5} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.876 |
|
| 23964 |
\begin{align*}
y^{\prime }&=\sigma y^{2}+a +b \,{\mathrm e}^{\lambda x}+c \,{\mathrm e}^{2 \lambda x} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.879 |
|
| 23965 |
\begin{align*}
y^{\prime }&=y^{3}+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.880 |
|
| 23966 |
\begin{align*}
2 x \left (y+2 \sqrt {x}\right ) y^{\prime }&=\left (y+\sqrt {x}\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.889 |
|
| 23967 |
\begin{align*}
x \tan \left (\frac {y}{x}\right )+y-y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.895 |
|
| 23968 |
\begin{align*}
y^{\prime }&=-\left (-\ln \left (\ln \left (y\right )\right )+\ln \left (x \right )\right ) y \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.908 |
|
| 23969 |
\begin{align*}
\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime }&=\alpha \,x^{k} y^{2}+\beta \,x^{s} y-\alpha \,\lambda ^{2} x^{k}+\beta \lambda \,x^{s} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.908 |
|
| 23970 |
\begin{align*}
u^{\prime \prime }+\frac {u^{\prime }}{4}+u&=k \left (\operatorname {Heaviside}\left (t -\frac {3}{2}\right )-\operatorname {Heaviside}\left (t -\frac {5}{2}\right )\right ) \\
u \left (0\right ) &= 0 \\
u^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
9.909 |
|
| 23971 |
\begin{align*}
2 n y-2 y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.914 |
|
| 23972 |
\begin{align*}
a^{2} {y^{\prime \prime }}^{2}&=1+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.915 |
|
| 23973 |
\begin{align*}
x^{n -1} {y^{\prime }}^{n}-n x y^{\prime }+y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.917 |
|
| 23974 |
\begin{align*}
u \left (1-v \right )+v^{2} \left (1-u\right ) u^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.921 |
|
| 23975 |
\begin{align*}
x \left (x +y\right ) y^{\prime }+y \left (3 x +y\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.925 |
|
| 23976 |
\begin{align*}
\left (b x +2 a \right ) y-2 \left (b x +a \right ) y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.932 |
|
| 23977 |
\begin{align*}
x^{2}+y^{2}&=2 y y^{\prime } x \\
y \left (-1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.936 |
|
| 23978 |
\begin{align*}
y^{\prime }&=\frac {x}{y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.940 |
|
| 23979 |
\begin{align*}
\left (y^{4}-3 x^{2}\right ) y^{\prime }&=-y x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.945 |
|
| 23980 |
\begin{align*}
\frac {2}{\sqrt {-x^{2}+1}}+y \cos \left (y x \right )+\left (x \cos \left (y x \right )-\frac {1}{y^{{1}/{3}}}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
9.952 |
|
| 23981 |
\begin{align*}
x +y+\left (2 x +2 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.957 |
|
| 23982 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=y x +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.957 |
|
| 23983 |
\begin{align*}
{y^{\prime }}^{2}-2 x^{2} y^{\prime }+2 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.957 |
|
| 23984 |
\begin{align*}
y^{\prime } x&=y^{2}-y \\
y \left (2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.958 |
|
| 23985 |
\begin{align*}
y y^{\prime \prime }+1&={y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.959 |
|
| 23986 |
\begin{align*}
\cos \left (x \right ) \cos \left (y\right )+2 x -\left (\sin \left (x \right ) \sin \left (y\right )+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.960 |
|
| 23987 |
\begin{align*}
x \cos \left (x \right ) y^{\prime }+y \left (x \sin \left (x \right )+\cos \left (x \right )\right )&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.966 |
|
| 23988 |
\begin{align*}
-y+y^{\prime } x&=y y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.970 |
|
| 23989 |
\begin{align*}
3 y y^{\prime \prime }&=36 y^{2}+2 {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.974 |
|
| 23990 |
\begin{align*}
x y \left (y-y^{\prime } x \right )&=x +y y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.974 |
|
| 23991 |
\begin{align*}
y^{\prime }&=\left (2 x +y-1\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.977 |
|
| 23992 |
\begin{align*}
y^{\prime }&=4 t^{2}-t y^{2} \\
y \left (2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.984 |
|
| 23993 |
\begin{align*}
y^{\prime }-\left (y-f \left (x \right )\right ) \left (y-g \left (x \right )\right ) \left (y-\frac {a f \left (x \right )+b g \left (x \right )}{a +b}\right ) h \left (x \right )-\frac {f^{\prime }\left (x \right ) \left (y-g \left (x \right )\right )}{f \left (x \right )-g \left (x \right )}-\frac {g^{\prime }\left (x \right ) \left (y-f \left (x \right )\right )}{g \left (x \right )-f \left (x \right )}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.986 |
|
| 23994 |
\begin{align*}
y^{\prime }&=-\frac {-x -\textit {\_F1} \left (y^{2}-2 x \right )}{\sqrt {y^{2}}\, x} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
9.987 |
|
| 23995 |
\begin{align*}
x^{2}+2 y y^{\prime }&=0 \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
9.988 |
|
| 23996 |
\begin{align*}
y^{\prime } x&=y-x \cot \left (\frac {y}{x}\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
9.997 |
|
| 23997 |
\begin{align*}
y \left (x +y\right )+\left (y x +1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.000 |
|
| 23998 |
\begin{align*}
y^{\prime }+b^{2} y^{2}&=a^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.001 |
|
| 23999 |
\begin{align*}
{y^{\prime }}^{2}+y^{\prime \prime \prime } y^{\prime }&=2 {y^{\prime \prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
10.003 |
|
| 24000 |
\begin{align*}
x^{\prime }&=\sqrt {x^{2}-1} \\
x \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
10.004 |
|