| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 13901 |
\begin{align*}
x \left (-1+{y^{\prime }}^{2}\right )&=2 y^{\prime } y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.931 |
|
| 13902 |
\begin{align*}
y-1-y x +y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.931 |
|
| 13903 |
\begin{align*}
x {y^{\prime }}^{2}-2 y^{\prime } y+a x&=0 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
0.931 |
|
| 13904 |
\begin{align*}
4 x -2 y^{\prime } y+x {y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.931 |
|
| 13905 |
\begin{align*}
2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=\frac {-x^{2}+1}{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.931 |
|
| 13906 |
\begin{align*}
-y^{\prime }+y^{\prime \prime } x&=-\frac {2}{x}-\ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.931 |
|
| 13907 |
\begin{align*}
\left (2 x y^{3}+y\right ) y^{\prime }+2 y^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.931 |
|
| 13908 |
\begin{align*}
{y^{\prime \prime \prime }}^{2}+{y^{\prime \prime }}^{2}&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.931 |
|
| 13909 |
\begin{align*}
4 y^{\prime \prime }+y&=2 \sec \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.931 |
|
| 13910 |
\begin{align*}
\left (2 x^{2}+4 y x -y^{2}\right ) y^{\prime }&=x^{2}-4 y x -2 y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.932 |
|
| 13911 |
\begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}&=\ln \left (y\right ) y^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.932 |
|
| 13912 |
\begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.932 |
|
| 13913 |
\begin{align*}
3 y y^{\prime \prime }-5 {y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.932 |
|
| 13914 |
\begin{align*}
y^{\prime \prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.932 |
|
| 13915 |
\begin{align*}
x^{\prime }&=x+y-3 \\
y^{\prime }&=-x+y+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.933 |
|
| 13916 |
\begin{align*}
u^{\prime \prime }-\left (x +1\right ) u^{\prime }+\left (x -1\right ) u&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.933 |
|
| 13917 |
\begin{align*}
y^{\prime \prime }+a^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.933 |
|
| 13918 | \begin{align*}
y^{\prime \prime }+2 y&=4 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.934 |
|
| 13919 |
\begin{align*}
2 x^{2} y^{\prime \prime }+5 y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.934 |
|
| 13920 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.934 |
|
| 13921 |
\begin{align*}
y^{\prime \prime } x +\left (1-x \right ) y^{\prime }+k y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.934 |
|
| 13922 |
\begin{align*}
y^{\prime \prime }&=\sqrt {1+y^{\prime }} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.934 |
|
| 13923 |
\begin{align*}
2 y^{\prime } y+x {y^{\prime }}^{2}+x y y^{\prime \prime }&=0 \\
y \left (3\right ) &= 1 \\
y^{\prime }\left (3\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.934 |
|
| 13924 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }+x&=0 \\
y \left (2\right ) &= -1 \\
y^{\prime }\left (2\right ) &= -{\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.934 |
|
| 13925 |
\begin{align*}
\cos \left (x \right ) y^{\prime \prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.935 |
|
| 13926 |
\begin{align*}
y^{\prime \prime }+\left (a \,x^{3} b +b \,x^{2}+2 a \right ) y^{\prime }+a^{2} \left (b \,x^{3}+1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.935 |
|
| 13927 |
\begin{align*}
y+y^{\prime }&={\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.935 |
|
| 13928 |
\begin{align*}
4 y+2 x \left (x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.935 |
|
| 13929 |
\begin{align*}
2 x^{\prime }-x+7 y^{\prime }+3 y&=90 \sin \left (2 t \right ) \\
x^{\prime }-5 x+8 y^{\prime }-3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.935 |
|
| 13930 |
\begin{align*}
m y^{\prime \prime }+b y^{\prime }+k y&=\cos \left (\omega t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.936 |
|
| 13931 |
\begin{align*}
x^{\prime }+y^{\prime }-x-6 y&={\mathrm e}^{3 t} \\
x^{\prime }+2 y^{\prime }-2 x-6 y&=t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.936 |
|
| 13932 |
\begin{align*}
y^{\prime }&=3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.936 |
|
| 13933 |
\begin{align*}
y y^{\prime \prime }-y^{\prime } y&={y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.937 |
|
| 13934 |
\begin{align*}
{y^{\prime }}^{2}-\left (2 x +1\right ) y^{\prime }-x \left (1-x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.937 |
|
| 13935 |
\begin{align*}
a \left (a +1\right ) y-2 a x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.937 |
|
| 13936 |
\begin{align*}
x^{\prime }&=a x+b y \\
y^{\prime }&=c x+b y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.937 |
|
| 13937 | \begin{align*}
y^{\prime }&=x +y \\
y \left (0\right ) &= 0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.937 |
|
| 13938 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }&=-2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.937 |
|
| 13939 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime }-\left (x^{2}+1\right ) y&={\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.937 |
|
| 13940 |
\begin{align*}
t y^{\prime \prime }-y^{\prime }&=3 t^{2}-1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.937 |
|
| 13941 |
\begin{align*}
-a y+y^{\prime }+2 y^{\prime \prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.938 |
|
| 13942 |
\begin{align*}
\left (x^{2}-x -6\right ) y^{\prime \prime }+\left (3 x +5\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=3\). |
✓ |
✓ |
✓ |
✓ |
0.938 |
|
| 13943 |
\begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.938 |
|
| 13944 |
\(\left [\begin {array}{cccc} 22 & -9 & -8 & -8 \\ 10 & -7 & -14 & 2 \\ 10 & 0 & 8 & -10 \\ 29 & -9 & -3 & -15 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.938 |
|
| 13945 |
\begin{align*}
4 y x -\left (x^{2}+7\right ) y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.939 |
|
| 13946 |
\begin{align*}
2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.939 |
|
| 13947 |
\begin{align*}
y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+a y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.939 |
|
| 13948 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }&=9 \,{\mathrm e}^{-3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.939 |
|
| 13949 |
\begin{align*}
y^{\prime \prime }+4 y&=\sec \left (2 t \right ) \tan \left (2 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.939 |
|
| 13950 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }&={\mathrm e}^{4 x} x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.939 |
|
| 13951 |
\begin{align*}
x^{\prime \prime }+\left (2+x\right ) x^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.939 |
|
| 13952 |
\begin{align*}
x^{\prime }+x+y&=t^{2} \\
y^{\prime }+y+z&=2 t \\
z^{\prime }+z&=t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.939 |
|
| 13953 |
\begin{align*}
y^{\prime \prime }+9 y&=0 \\
y \left (0\right ) &= 1 \\
y \left (\pi \right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.939 |
|
| 13954 |
\begin{align*}
y^{\prime \prime } x&=y^{\prime }+x^{5} \\
y \left (1\right ) &= {\frac {1}{2}} \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.939 |
|
| 13955 |
\begin{align*}
t^{2} y^{\prime \prime }+7 t y^{\prime }+10 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.940 |
|
| 13956 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +\alpha ^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.940 |
|
| 13957 | \begin{align*}
y^{\prime \prime }+6 y&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.940 |
|
| 13958 |
\begin{align*}
y^{\prime \prime }&=y^{\prime } y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.941 |
|
| 13959 |
\begin{align*}
y^{\prime }&=\frac {2 y}{\pi }-\sin \left (y\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.941 |
|
| 13960 |
\begin{align*}
x^{2} y^{\prime }&=a \,x^{2} y^{2}+b x y+c \,x^{n}+s \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.941 |
|
| 13961 |
\begin{align*}
y^{\prime \prime }+9 y&=9 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.941 |
|
| 13962 |
\begin{align*}
x^{\prime }&=x+y+z-2 \,{\mathrm e}^{-t} \\
y^{\prime }&=2 x+y-z-2 \,{\mathrm e}^{-t} \\
z^{\prime }&=-3 x+2 y+4 z+3 \,{\mathrm e}^{-t} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
z \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.942 |
|
| 13963 |
\begin{align*}
x_{1}^{\prime }&=7 x_{1}-x_{4} \\
x_{2}^{\prime }&=6 x_{2} \\
x_{3}^{\prime }&=-x_{3} \\
x_{4}^{\prime }&=2 x_{1}+5 x_{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.942 |
|
| 13964 |
\begin{align*}
x^{\prime }&=2 x-y+{\mathrm e}^{t} \\
y^{\prime }&=3 x-2 y+t \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.942 |
|
| 13965 |
\begin{align*}
y^{\prime \prime }+2 y&=x^{3}+x^{2}+{\mathrm e}^{-2 x}+\cos \left (3 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.943 |
|
| 13966 |
\begin{align*}
x {y^{\prime }}^{3}&=a +b y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.943 |
|
| 13967 |
\begin{align*}
2 y+y^{\prime }&=3 \,{\mathrm e}^{-2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.944 |
|
| 13968 |
\begin{align*}
y^{\prime \prime }+\lambda y&=0 \\
y^{\prime }\left (0\right ) &= 0 \\
y \left (L \right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.945 |
|
| 13969 |
\begin{align*}
{y^{\prime }}^{3}+\left (1-3 x \right ) {y^{\prime }}^{2}-x \left (1-3 x \right ) y^{\prime }-1-x^{3}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.945 |
|
| 13970 |
\begin{align*}
y^{\prime }&=\frac {y}{x}+2 x +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.945 |
|
| 13971 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (3 x +2\right ) y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.945 |
|
| 13972 |
\begin{align*}
t^{2} x^{\prime \prime }+3 t x^{\prime }+x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.945 |
|
| 13973 |
\begin{align*}
y y^{\prime \prime }+{y^{\prime }}^{2}&=2 y^{\prime } y \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.945 |
|
| 13974 |
\begin{align*}
y^{\prime }+\frac {4 y}{3}&=1-\frac {t}{4} \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.945 |
|
| 13975 |
\begin{align*}
x^{\prime }&=-x-4 y-4 \\
y^{\prime }&=x-y-6 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.945 |
|
| 13976 | \begin{align*}
x^{\prime }&=\frac {x \sqrt {6 x-9}}{3} \\
x \left (0\right ) &= 3 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.945 |
|
| 13977 |
\begin{align*}
x^{\prime \prime }+\frac {x^{\prime }}{t}+q \left (t \right ) x&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.945 |
|
| 13978 |
\begin{align*}
y^{\prime }-a y&={\mathrm e}^{c t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.945 |
|
| 13979 |
\begin{align*}
2 y^{\prime \prime } x -\left (x^{3}+1\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.946 |
|
| 13980 |
\begin{align*}
y y^{\prime \prime }&={y^{\prime }}^{2} \left (1-y^{\prime } \cos \left (y\right )+y y^{\prime } \sin \left (y\right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.946 |
|
| 13981 |
\begin{align*}
2 y^{\prime \prime }-7 y^{\prime }+3&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.946 |
|
| 13982 |
\begin{align*}
x_{1}^{\prime }&=-7 x_{1}+6 x_{2}-6 x_{3} \\
x_{2}^{\prime }&=-9 x_{1}+5 x_{2}-9 x_{3} \\
x_{3}^{\prime }&=-x_{2}-x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.946 |
|
| 13983 |
\begin{align*}
4 y+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.946 |
|
| 13984 |
\begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x -8 y&={\mathrm e}^{x} \left (x^{2}+2\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.946 |
|
| 13985 |
\begin{align*}
\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=2 \left (x -1\right )^{2} {\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.947 |
|
| 13986 |
\begin{align*}
1-y^{\prime }&=x +y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.947 |
|
| 13987 |
\begin{align*}
-\left (4 x^{2}+1\right ) y+4 y^{\prime } x +4 x^{2} y^{\prime \prime }&=4 x^{{3}/{2}} {\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.947 |
|
| 13988 |
\begin{align*}
1+{y^{\prime }}^{2}+2 y y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.947 |
|
| 13989 |
\begin{align*}
4 y+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (\pi \right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.947 |
|
| 13990 |
\begin{align*}
y^{\prime \prime }&=-\frac {b y}{x^{2} \left (x -a \right )^{2}}+c \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.947 |
|
| 13991 |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (\sin \left (x \right )^{2}-\cos \left (x \right )\right ) y^{\prime }}{\sin \left (x \right )}-y \sin \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.947 |
|
| 13992 |
\begin{align*}
y^{\prime }&=\frac {y^{2}+5}{y} \\
y \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.947 |
|
| 13993 |
\begin{align*}
y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.947 |
|
| 13994 |
\begin{align*}
\left (y-x \right ) y^{\prime }&=y-x +8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.947 |
|
| 13995 |
\begin{align*}
y^{\prime \prime }&=\operatorname {c1} \,{\mathrm e}^{a x}+\operatorname {c2} \,{\mathrm e}^{-b x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.948 |
|
| 13996 | \begin{align*}
y^{\prime \prime }-y&=0 \\
\end{align*} | ✓ | ✓ | ✓ | ✓ | 0.948 |
|
| 13997 |
\begin{align*}
y^{\prime \prime }&=\frac {y}{{\mathrm e}^{x}+1} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.948 |
|
| 13998 |
\begin{align*}
y^{\prime }&=y^{2} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.948 |
|
| 13999 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{t} \left (t^{2}+1\right ) \sin \left (2 t \right )+3 \,{\mathrm e}^{-t} \cos \left (t \right )+4 \,{\mathrm e}^{t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.948 |
|
| 14000 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (x +3\right ) y^{\prime }+\left (x^{2}+x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.948 |
|