| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 19901 |
\begin{align*}
{y^{\prime }}^{2}&=y+x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.034 |
|
| 19902 |
\begin{align*}
t y^{\prime }+y&=t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.035 |
|
| 19903 |
\begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{x +y}}{y-1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.036 |
|
| 19904 |
\begin{align*}
y^{\prime }&=-\frac {y}{t +1}+t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.036 |
|
| 19905 |
\begin{align*}
y^{\prime }&=3 y^{{2}/{3}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.037 |
|
| 19906 |
\begin{align*}
y^{\prime } x&=y+\left (x^{2}-y^{2}\right ) f \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.040 |
|
| 19907 |
\begin{align*}
\sqrt {t}\, \sin \left (t \right ) y+y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.041 |
|
| 19908 |
\begin{align*}
y^{\prime }&=1-\frac {\sin \left (x +y\right )}{\cos \left (x \right ) \sin \left (y\right )} \\
y \left (\frac {\pi }{4}\right ) &= \frac {\pi }{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.043 |
|
| 19909 |
\begin{align*}
y^{\prime }&=\frac {4 y^{2}-x^{4}}{4 y x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.044 |
|
| 19910 |
\begin{align*}
4 {y^{\prime }}^{2}-2 \left (y+3 y^{\prime } x \right ) y^{\prime \prime }+3 x^{2} {y^{\prime \prime }}^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
3.046 |
|
| 19911 |
\begin{align*}
a y+b x y+\left (c x +d x y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.047 |
|
| 19912 |
\begin{align*}
y^{\prime }&=3 x^{2} \left (1+y^{2}\right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.048 |
|
| 19913 |
\begin{align*}
y {y^{\prime }}^{2}+2 y^{\prime } x -9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.049 |
|
| 19914 |
\begin{align*}
y^{\prime }&=\frac {-3+x +y}{y-x +1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.049 |
|
| 19915 |
\begin{align*}
\cos \left (x \right ) \sin \left (x \right ) y^{\prime }&=y+\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.049 |
|
| 19916 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime }+2 x y^{2}&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.050 |
|
| 19917 |
\begin{align*}
\left (x^{2} y^{3}+y x \right ) y^{\prime }-1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.050 |
|
| 19918 | \begin{align*}
y^{\prime }&=\frac {1+y^{2}}{x^{2}+1} \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 3.051 |
|
| 19919 |
\begin{align*}
c y^{\prime }&=\frac {a x +b y^{2}}{r} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.052 |
|
| 19920 |
\begin{align*}
y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+\cot \left (x \right ) y&=0 \\
y \left (\frac {\pi }{4}\right ) &= 1 \\
y^{\prime }\left (\frac {\pi }{4}\right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
3.052 |
|
| 19921 |
\begin{align*}
y^{\prime }&=\frac {x -y \cos \left (x \right )}{y+\sin \left (x \right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.052 |
|
| 19922 |
\begin{align*}
y^{\prime }+y&=\frac {2 x \,{\mathrm e}^{-x}}{1+{\mathrm e}^{x} y} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.055 |
|
| 19923 |
\begin{align*}
\left (-x^{2}+1\right ) {y^{\prime }}^{2}&=1-y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.055 |
|
| 19924 |
\begin{align*}
y^{\prime }+\frac {x y}{x^{2}+1}&=\frac {1}{x \left (x^{2}+1\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.056 |
|
| 19925 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (-x^{2}+3\right ) y^{\prime }-3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.057 |
|
| 19926 |
\begin{align*}
y^{\prime \prime } x -\left (3 x -2\right ) y^{\prime }-\left (2 x -3\right ) y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
3.057 |
|
| 19927 |
\begin{align*}
2 y^{\prime \prime } x -\left (x -1\right ) y^{\prime }+a y&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
3.058 |
|
| 19928 |
\begin{align*}
y^{\prime }&=\frac {2 x +y}{3-x +3 y^{2}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.059 |
|
| 19929 |
\begin{align*}
6 y^{2} y^{\prime } x +x +2 y^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.059 |
|
| 19930 |
\begin{align*}
\frac {1}{2 \sqrt {t}}+y^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.059 |
|
| 19931 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y-3 x^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.060 |
|
| 19932 |
\begin{align*}
y^{\prime }&=y^{2} \cos \left (t \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.060 |
|
| 19933 |
\begin{align*}
x^{{10}/{3}}-2 y+y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.062 |
|
| 19934 |
\begin{align*}
x^{\prime }-2 x&={\mathrm e}^{2 t} t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.062 |
|
| 19935 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=\left (1+y\right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.063 |
|
| 19936 |
\begin{align*}
y^{\prime } x&=2 y+\cos \left (x \right ) x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.063 |
|
| 19937 | \begin{align*}
\cos \left (x \right )+\ln \left (y\right )+\left (\frac {x}{y}+{\mathrm e}^{y}\right ) y^{\prime }&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✗ | 3.063 |
|
| 19938 |
\begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{-2 y} \sin \left (x \right )}{x^{2}+1} \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.065 |
|
| 19939 |
\begin{align*}
y^{\prime }&=\frac {x +y+F \left (-\frac {-y+x \ln \left (x \right )}{x}\right ) x^{2}}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.065 |
|
| 19940 |
\begin{align*}
x&=y-{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.065 |
|
| 19941 |
\begin{align*}
y^{\prime \prime }&=-\frac {\cos \left (x \right ) y^{\prime }}{\sin \left (x \right )}-\frac {\left (v \left (v +1\right ) \sin \left (x \right )^{2}-n^{2}\right ) y}{\sin \left (x \right )^{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
3.066 |
|
| 19942 |
\begin{align*}
\left (x +a \right ) y^{\prime }&=b x -n y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.067 |
|
| 19943 |
\begin{align*}
x^{\prime \prime \prime }+a x^{\prime \prime }+b x^{\prime }+c x&=0 \\
x \left (\infty \right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
3.068 |
|
| 19944 |
\begin{align*}
y^{\prime }-\frac {y}{x}&=y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.068 |
|
| 19945 |
\begin{align*}
y^{\prime } \sin \left (2 x \right )&=2 y+2 \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.069 |
|
| 19946 |
\begin{align*}
y^{\prime \prime }&=\frac {\left (2 b c \,x^{c} \left (x^{2}-1\right )+2 \left (a -1\right ) x^{2}-2 a \right ) y^{\prime }}{x \left (x^{2}-1\right )}-\frac {\left (b^{2} c^{2} x^{2 c} \left (x^{2}-1\right )+b c \,x^{c +2} \left (2 a -c -1\right )-b c \,x^{c} \left (2 a -c +1\right )+x^{2} \left (a \left (a -1\right )-v \left (v +1\right )\right )-a \left (a +1\right )\right ) y}{x^{2} \left (x^{2}-1\right )} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
3.069 |
|
| 19947 |
\begin{align*}
y^{\prime }-\frac {2 y}{x}&=x^{2} \sin \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.069 |
|
| 19948 |
\begin{align*}
y^{\prime } x&=\sqrt {1-y^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.070 |
|
| 19949 |
\begin{align*}
x \ln \left (x \right )^{2} y^{\prime }&=-4 \ln \left (x \right )^{2}+y \ln \left (x \right )+y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.070 |
|
| 19950 |
\begin{align*}
y^{\prime }&=\cos \left (y\right ) \\
y \left (0\right ) &= -\frac {\pi }{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.071 |
|
| 19951 |
\begin{align*}
y^{\prime }&=-{\mathrm e}^{-t^{2}} y+\cos \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.072 |
|
| 19952 |
\begin{align*}
2 x^{2} y^{\prime \prime }-3 y^{\prime } x +2 y&=\ln \left (x^{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.073 |
|
| 19953 |
\begin{align*}
a y y^{\prime }+b y^{2}+f \left (x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.073 |
|
| 19954 |
\begin{align*}
\left (a +x^{2}+y^{2}\right ) y y^{\prime }+x \left (y^{2}+x^{2}-a \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.073 |
|
| 19955 |
\begin{align*}
\frac {3 t^{2}}{y}-\frac {t^{3} y^{\prime }}{y^{2}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.073 |
|
| 19956 | \begin{align*}
{y^{\prime }}^{3} \sin \left (x \right )-\left (y \sin \left (x \right )-\cos \left (x \right )^{2}\right ) {y^{\prime }}^{2}-\left (y \cos \left (x \right )^{2}+\sin \left (x \right )\right ) y^{\prime }+y \sin \left (x \right )&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✗ | 3.074 |
|
| 19957 |
\begin{align*}
y^{4} x^{3}+x^{2} y^{3}+x y^{2}+y+\left (y^{3} x^{4}-x^{3} y^{2}-x^{3} y+x \right ) y^{\prime }&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
3.075 |
|
| 19958 |
\begin{align*}
x y^{\prime } y-y^{2}&=x^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.076 |
|
| 19959 |
\begin{align*}
y+\left (y x -x -y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.078 |
|
| 19960 |
\begin{align*}
\sin \left (\theta \right ) \cos \left (\theta \right ) r^{\prime }-\sin \left (\theta \right )^{2}&=r \cos \left (\theta \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.078 |
|
| 19961 |
\begin{align*}
y^{\prime }+y^{3}+a x y^{2}&=0 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
3.081 |
|
| 19962 |
\begin{align*}
y&=2 y^{\prime }+3 {y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.081 |
|
| 19963 |
\begin{align*}
y \left (1+y^{2}\right )+x \left (y^{2}-x +1\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.082 |
|
| 19964 |
\begin{align*}
y^{\prime }&=\frac {\sqrt {y}}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.082 |
|
| 19965 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime }+2 y x&=\cot \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.084 |
|
| 19966 |
\begin{align*}
y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+y \cos \left (x \right )^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.085 |
|
| 19967 |
\begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{5 t}}{y^{4}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.085 |
|
| 19968 |
\begin{align*}
y^{\prime }&=4 x^{3} y-y \\
y \left (1\right ) &= -3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.086 |
|
| 19969 |
\begin{align*}
y^{\prime }&=x +y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.086 |
|
| 19970 |
\begin{align*}
y^{\prime }+2 y x&={\mathrm e}^{-x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.086 |
|
| 19971 |
\begin{align*}
y^{\prime \prime }+\left (1+\frac {2 \cot \left (x \right )}{x}-\frac {2}{x^{2}}\right ) y&=\cos \left (x \right ) x \\
\end{align*} |
✗ |
✓ |
✗ |
✗ |
3.086 |
|
| 19972 |
\begin{align*}
y^{\prime \prime } x +\left (1-\cos \left (x \right )\right ) y^{\prime }+x^{2} y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
3.087 |
|
| 19973 |
\begin{align*}
\cos \left (y\right ) y^{\prime }&=8 \sin \left (8 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.087 |
|
| 19974 |
\begin{align*}
x^{3} y^{\prime }&=2 y^{2}+2 x^{2} y-2 x^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.089 |
|
| 19975 |
\begin{align*}
x^{4} \ln \left (x \right )-2 x y^{3}+3 x^{2} y^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.089 |
|
| 19976 | \begin{align*}
x y^{3}-y^{3}-{\mathrm e}^{x} x^{2}+3 y^{2} y^{\prime } x&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 3.090 |
|
| 19977 |
\begin{align*}
x y^{\prime } y&=\left (x +1\right ) \left (1+y\right ) \\
y \left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✗ |
✗ |
3.091 |
|
| 19978 |
\begin{align*}
x^{2} y^{\prime }-y^{2}-y x -x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.091 |
|
| 19979 |
\begin{align*}
y^{\prime }&=-3 y+{\mathrm e}^{-2 t}+t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.091 |
|
| 19980 |
\begin{align*}
2 x^{2} y^{\prime \prime }+5 y^{\prime } x +y&=85 \cos \left (2 \ln \left (x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.092 |
|
| 19981 |
\begin{align*}
y^{\prime } x&=\tan \left (\frac {y}{x}\right ) x +y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.093 |
|
| 19982 |
\begin{align*}
y^{\prime }&=\frac {y^{2}-1}{x^{2}-1} \\
y \left (2\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
3.093 |
|
| 19983 |
\begin{align*}
y^{\prime }&=\frac {t}{y-2} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.095 |
|
| 19984 |
\begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{t}}{y} \\
y \left (\ln \left (2\right )\right ) &= -8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.097 |
|
| 19985 |
\begin{align*}
\left (x +y\right ) y^{\prime }-1&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.100 |
|
| 19986 |
\begin{align*}
r^{2} \sin \left (t \right )&=\left (2 r \cos \left (t \right )+10\right ) r^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.100 |
|
| 19987 |
\begin{align*}
y^{\prime }&=2 y x +3 x^{2} {\mathrm e}^{x^{2}} \\
y \left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.101 |
|
| 19988 |
\begin{align*}
y+x^{2}&=y^{\prime } x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.101 |
|
| 19989 |
\begin{align*}
\frac {y^{5} x^{2}+y^{2}+y}{1+x^{2} y^{4}}+\frac {\left (y^{4} x^{3}+2 y x +x \right ) y^{\prime }}{1+x^{2} y^{4}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.101 |
|
| 19990 |
\begin{align*}
2 t y+y^{\prime }&=2 t \,{\mathrm e}^{-t^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.102 |
|
| 19991 |
\begin{align*}
x^{2}-\sin \left (y\right )^{2}+x \sin \left (2 y\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.102 |
|
| 19992 |
\begin{align*}
\left (a \,x^{n}+b \right ) y^{\prime \prime }+\left (c \,x^{n}+d \right ) y^{\prime }+\lambda \left (\left (-a \lambda +c \right ) x^{n}+d -b \lambda \right ) y&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
3.102 |
|
| 19993 |
\begin{align*}
x&={y^{\prime }}^{2}+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.102 |
|
| 19994 |
\begin{align*}
y^{\prime }&=\frac {\cos \left (x \right )+1}{2-\sin \left (y\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.103 |
|
| 19995 |
\begin{align*}
y^{\prime }+y&=2 x \,{\mathrm e}^{-x}+x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.103 |
|
| 19996 | \begin{align*}
\left (x^{2}-1\right ) y^{\prime }+2 y x -\cos \left (x \right )&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 3.105 |
|
| 19997 |
\begin{align*}
x^{\prime }&=2 t x \\
x \left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.105 |
|
| 19998 |
\begin{align*}
y^{\prime }-5 y&=\sin \left (x \right ) \left (x -1\right )+\left (x +1\right ) \cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.105 |
|
| 19999 |
\begin{align*}
y \,{\mathrm e}^{y x}-2 y^{3}+\left (x \,{\mathrm e}^{y x}-6 x y^{2}-2 y\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
3.105 |
|
| 20000 |
\begin{align*}
y^{\prime }&=\left (a +b y \cos \left (k x \right )\right ) y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
3.106 |
|