| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 22901 |
\begin{align*}
y^{\prime }-\frac {2 y}{x}&=0 \\
y \left (1\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.174 |
|
| 22902 |
\begin{align*}
1+{y^{\prime }}^{2}+2 y y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.174 |
|
| 22903 |
\begin{align*}
y^{\prime }&=\frac {y^{2}-4 y t +6 t^{2}}{t^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.174 |
|
| 22904 |
\begin{align*}
2 x^{2} y^{\prime \prime }-x y^{\prime }+y&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.175 |
|
| 22905 |
\begin{align*}
y^{\prime }&=x y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.175 |
|
| 22906 |
\begin{align*}
x \left (x -1\right )^{2} \left (x +2\right ) y^{\prime \prime }+x^{2} y^{\prime }-\left (x^{3}+2 x -1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
8.177 |
|
| 22907 |
\begin{align*}
y^{\prime }+\frac {4 y}{x}&=x^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.181 |
|
| 22908 |
\begin{align*}
y+\left (y^{n} a \,x^{2}-2 x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.182 |
|
| 22909 |
\begin{align*}
y^{\prime }&=\frac {\left ({\mathrm e}^{-\frac {y}{x}} y x +{\mathrm e}^{-\frac {y}{x}} y+{\mathrm e}^{-\frac {y}{x}} x^{2}+x \,{\mathrm e}^{-\frac {y}{x}}+x^{4}\right ) {\mathrm e}^{\frac {y}{x}}}{x \left (x +1\right )} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
8.187 |
|
| 22910 |
\begin{align*}
x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.188 |
|
| 22911 |
\begin{align*}
x \left (x^{2}+y^{2}\right )^{2} \left (-x y^{\prime }+y\right )+y^{6} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.188 |
|
| 22912 |
\begin{align*}
{b^{\prime }}^{7}&=3 p \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.191 |
|
| 22913 |
\begin{align*}
c y^{\prime }&=\frac {a x +b y^{2}}{r \,x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.192 |
|
| 22914 |
\begin{align*}
3 x y^{\prime }-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.202 |
|
| 22915 |
\begin{align*}
y^{\prime }+\frac {x +2 y}{x}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.204 |
|
| 22916 |
\begin{align*}
x^{\prime }&=x^{3}-x \\
x \left (0\right ) &= a \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.207 |
|
| 22917 |
\begin{align*}
\cosh \left (6 t \right )+5 \sinh \left (4 t \right )+20 \sinh \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.209 |
|
| 22918 |
\begin{align*}
y \left (x^{2} y^{2}-m \right )+x \left (x^{2} y^{2}+n \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.223 |
|
| 22919 |
\begin{align*}
8 x y^{\prime }-y&=-\frac {1}{y^{3} \sqrt {x +1}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.224 |
|
| 22920 |
\begin{align*}
y^{\prime }+\frac {4 y}{x}&=x^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.229 |
|
| 22921 |
\begin{align*}
y-4 \left (x +y^{6}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.239 |
|
| 22922 |
\begin{align*}
y^{\prime }&=\frac {a^{3}+y^{2} a^{3}+2 y a^{2} b x +b^{2} x^{2} a +y^{3} a^{3}+3 a^{2} b x y^{2}+3 a \,b^{2} x^{2} y+b^{3} x^{3}}{a^{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.240 |
|
| 22923 |
\begin{align*}
y^{\prime }&=\left (1-x \right ) y^{2}+\left (2 x -1\right ) y-x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.241 |
|
| 22924 |
\begin{align*}
2 x y y^{\prime }+3 x^{2}-y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.243 |
|
| 22925 |
\begin{align*}
y^{\prime }&=\frac {x y}{1-y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.243 |
|
| 22926 |
\begin{align*}
\left (1-x^{2} y\right ) y^{\prime }+1-x y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.244 |
|
| 22927 |
\begin{align*}
y^{3} {y^{\prime \prime }}^{2}+y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.245 |
|
| 22928 |
\begin{align*}
y^{\prime }&=\frac {x +y+2}{x +1} \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.246 |
|
| 22929 |
\begin{align*}
y^{\prime }&=\frac {y+\cos \left (\frac {y}{x}\right )^{2}}{x} \\
y \left (1\right ) &= \frac {\pi }{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.254 |
|
| 22930 |
\begin{align*}
\left (x +y\right ) \left (x y^{\prime }-y\right )^{3}+x^{3} y^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
8.257 |
|
| 22931 |
\begin{align*}
\sin \left (y x \right )+x y \cos \left (y x \right )+x^{2} \cos \left (y x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.257 |
|
| 22932 |
\begin{align*}
2 x^{2}-y \,{\mathrm e}^{x}-{\mathrm e}^{x} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.259 |
|
| 22933 |
\begin{align*}
x y^{3} y^{\prime }&=\left (-x^{2}+1\right ) \left (1+y^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.263 |
|
| 22934 |
\begin{align*}
y^{2} {y^{\prime \prime }}^{2}+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.263 |
|
| 22935 |
\begin{align*}
x^{\prime }&=\frac {2 x}{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.268 |
|
| 22936 |
\begin{align*}
4 y+3 \left (2 x -1\right ) \left (y^{\prime }+y^{4}\right )&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.272 |
|
| 22937 |
\begin{align*}
y^{\prime }&=2 y^{2}+x y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.276 |
|
| 22938 |
\begin{align*}
x^{2}+y^{2}-2 x y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.276 |
|
| 22939 |
\begin{align*}
4 y^{6}+x^{3}&=6 x y^{5} y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.277 |
|
| 22940 |
\begin{align*}
y^{\prime } y^{\prime \prime }&=x \left (x +1\right ) \\
y \left (1\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.279 |
|
| 22941 |
\begin{align*}
\frac {y^{2}-y x}{x y^{2}}+\frac {x y^{\prime }}{y^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.280 |
|
| 22942 |
\begin{align*}
y^{\prime }&=t y^{{1}/{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.281 |
|
| 22943 |
\begin{align*}
9 x^{2}+y-1-\left (4 y-x \right ) y^{\prime }&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.283 |
|
| 22944 |
\begin{align*}
y^{\prime }&=6 x y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.284 |
|
| 22945 |
\begin{align*}
x \left (1+x y^{2}\right ) y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.285 |
|
| 22946 |
\begin{align*}
y^{\prime }&=\left (\frac {\ln \left (-1+y\right ) y}{\left (1-y\right ) \ln \left (x \right ) x}-\frac {\ln \left (-1+y\right )}{\left (1-y\right ) \ln \left (x \right ) x}-f \left (x \right )\right ) \left (1-y\right ) \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
8.295 |
|
| 22947 |
\begin{align*}
2 y^{\prime \prime }+3 y^{\prime }+4 x^{2} y&=1 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
8.295 |
|
| 22948 |
\begin{align*}
x y^{\prime }&=2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.296 |
|
| 22949 |
\begin{align*}
2 x^{2} y^{\prime }&=x^{2}+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.297 |
|
| 22950 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime }-y x&=a x y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.297 |
|
| 22951 |
\begin{align*}
y^{\prime }&=-\left (n +1\right ) x^{n} y^{2}+x^{n +1} f \left (x \right ) y-f \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
8.298 |
|
| 22952 |
\begin{align*}
\frac {2 x}{y^{3}}+\frac {\left (y^{2}-3 x^{2}\right ) y^{\prime }}{y^{4}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.301 |
|
| 22953 |
\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. |
✓ |
✓ |
✓ |
✓ |
8.302 |
|
| 22954 |
\begin{align*}
x y^{\prime }+y \ln \left (x \right )&=\ln \left (y\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.302 |
|
| 22955 |
\begin{align*}
x^{3} y^{\prime \prime }-x^{2} y^{\prime }+y x -\ln \left (x \right )^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.311 |
|
| 22956 |
\begin{align*}
y^{\prime }&=-\frac {a x}{2}-\frac {b}{2}+x^{2} \sqrt {a^{2} x^{2}+2 a b x +b^{2}+4 a y-4 c} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.319 |
|
| 22957 |
\begin{align*}
x^{4} {y^{\prime }}^{2}+x y^{2} y^{\prime }-y^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.329 |
|
| 22958 |
\begin{align*}
y^{\prime }&=-\frac {a x}{2}-\frac {b}{2}+x \sqrt {a^{2} x^{2}+2 a b x +b^{2}+4 a y-4 c} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.330 |
|
| 22959 |
\begin{align*}
x^{\prime }&=t^{2} {\mathrm e}^{-x} \\
x \left (0\right ) &= \ln \left (2\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.334 |
|
| 22960 |
\begin{align*}
y^{\prime }&=x^{2}+y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.335 |
|
| 22961 |
\begin{align*}
y^{\prime }&=y^{3} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.336 |
|
| 22962 |
\begin{align*}
y^{\prime }&=\frac {2 \cos \left (2 x \right )}{10+2 y} \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.336 |
|
| 22963 |
\begin{align*}
x^{2} y^{\prime }+2+x y \left (4+y x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.341 |
|
| 22964 |
\begin{align*}
{\mathrm e}^{y t}+\frac {t \,{\mathrm e}^{y t} y^{\prime }}{y}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.341 |
|
| 22965 |
\begin{align*}
\left (1-\sin \left (x \right )\right ) y^{\prime }+\cos \left (x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.343 |
|
| 22966 |
\begin{align*}
3 x^{2} y^{2}-y^{3}+2 x +\left (2 x^{3} y-3 x y^{2}+1\right ) y^{\prime }&=0 \\
y \left (-2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.343 |
|
| 22967 |
\begin{align*}
x^{2} y+\left (x +1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.343 |
|
| 22968 |
\begin{align*}
x y^{\prime \prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
8.344 |
|
| 22969 |
\begin{align*}
y^{\prime }&=x^{2} y^{2}-4 x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.346 |
|
| 22970 |
\begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+y&=\sec \left (\ln \left (x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.349 |
|
| 22971 |
\begin{align*}
x y^{\prime }+\left (a +b \,x^{n} y\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.353 |
|
| 22972 |
\begin{align*}
y^{\prime } \sin \left (2 x \right )&=2 y+2 \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.355 |
|
| 22973 |
\begin{align*}
x^{\prime }+\frac {\left (t +1\right ) x}{2 t}&=\frac {t +1}{x t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.355 |
|
| 22974 |
\begin{align*}
3 x +2 y+1-\left (3 x +2 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.356 |
|
| 22975 |
\begin{align*}
x^{n} y^{\prime \prime }+a x y^{\prime }-\left (b^{2} x^{n}+2 b \,x^{n -1}+a b x +a \right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
8.356 |
|
| 22976 |
\begin{align*}
x y^{\prime }+y&=x^{3} y^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.360 |
|
| 22977 |
\begin{align*}
y^{\prime }&=\frac {\left (x +y-1\right )^{2}}{2 \left (x +2\right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.361 |
|
| 22978 |
\begin{align*}
y^{\prime }&=\frac {x^{2}+3 y^{2}}{2 x y} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.362 |
|
| 22979 |
\begin{align*}
2 x^{3}-y+x y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.362 |
|
| 22980 |
\begin{align*}
y^{\prime }&=\left (1-12 x \right ) y^{2} \\
y \left (0\right ) &= -{\frac {1}{8}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.377 |
|
| 22981 |
\begin{align*}
y y^{\prime \prime }&=a \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.378 |
|
| 22982 |
\begin{align*}
2 y^{\prime }+y-2 y^{\prime } \ln \left (y^{\prime }\right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.387 |
|
| 22983 |
\begin{align*}
3 x y^{\prime }+5 y&=10 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.391 |
|
| 22984 |
\begin{align*}
1&=\frac {y}{1-x^{2} y^{2}}+\frac {x y^{\prime }}{1-x^{2} y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.398 |
|
| 22985 |
\begin{align*}
1+y+\left (x -y \left (y+1\right )^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.401 |
|
| 22986 |
\begin{align*}
y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }-x^{2}+2 y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.401 |
|
| 22987 |
\begin{align*}
x^{2} y^{\prime }&=x^{2}-y x +y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.401 |
|
| 22988 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 0 & 0\le t <1 \\ 1 & 1\le t <2 \\ -1 & 2\le t \end {array}\right . \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
8.405 |
|
| 22989 |
\begin{align*}
y^{\prime }&=\frac {y^{2} \left (-2 y+2 x^{2}+2 x^{2} y+x^{4} y\right )}{x^{3} \left (x^{2}-y+x^{2} y\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.408 |
|
| 22990 |
\begin{align*}
x \left (1-y^{2}\right ) y^{\prime }&=\left (x^{2}+1\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.415 |
|
| 22991 |
\begin{align*}
y^{\prime }-\frac {y}{x}&=-\frac {y^{2}}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.415 |
|
| 22992 |
\begin{align*}
x \csc \left (\frac {y}{x}\right )-y+x y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.421 |
|
| 22993 |
\begin{align*}
y^{\prime }&=\frac {y \ln \left (y\right )}{\sin \left (x \right )} \\
y \left (\frac {\pi }{2}\right ) &= {\mathrm e}^{{\mathrm e}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.427 |
|
| 22994 |
\begin{align*}
y^{\prime }&=\frac {y}{-x +y} \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.429 |
|
| 22995 |
\begin{align*}
y^{\prime }&=\frac {x +y-2}{y-x -4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.429 |
|
| 22996 |
\begin{align*}
y^{\prime }&=\frac {2 y}{x} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.431 |
|
| 22997 |
\begin{align*}
y^{\prime }-y^{2}-x -x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.433 |
|
| 22998 |
\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*} |
✓ |
✓ |
✓ |
✗ |
8.435 |
|
| 22999 |
\begin{align*}
y^{\prime }&={\mathrm e}^{\frac {x y^{\prime }}{y}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
8.436 |
|
| 23000 |
\begin{align*}
y^{\prime }+y x&=x y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
8.438 |
|