| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 3901 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }-8 x y^{\prime }+20 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.317 |
|
| 3902 |
\begin{align*}
2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }-x \left (-7 x^{2}+12\right ) y^{\prime }+\left (3 x^{2}+7\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.317 |
|
| 3903 |
\begin{align*}
y^{\prime \prime }+7 y^{\prime }+10 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.317 |
|
| 3904 |
\begin{align*}
y^{\prime \prime }+8 y^{\prime }+25 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.317 |
|
| 3905 |
\begin{align*}
x^{\prime }&=5 x-6 y \\
y^{\prime }&=6 x-7 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.317 |
|
| 3906 |
\begin{align*}
x^{2} y^{\prime \prime }-x \left (2 x -1\right ) y^{\prime }+\left (x^{2}-x -1\right ) y&={\mathrm e}^{x} x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.318 |
|
| 3907 |
\begin{align*}
y x -1+x^{2} y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.318 |
|
| 3908 |
\begin{align*}
x^{2} \left (x +2\right ) y^{\prime \prime }+5 x \left (1-x \right ) y^{\prime }-\left (2-8 x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.318 |
|
| 3909 |
\begin{align*}
y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y&=3 \,{\mathrm e}^{x} x^{2}-7 \,{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.318 |
|
| 3910 |
\begin{align*}
x^{\left (6\right )}-x^{\prime \prime \prime \prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.318 |
|
| 3911 |
\begin{align*}
y^{\prime \prime \prime }&=x +\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.318 |
|
| 3912 |
\begin{align*}
x_{1}^{\prime }&=-3 x_{1}+\frac {5 x_{2}}{2} \\
x_{2}^{\prime }&=-\frac {5 x_{1}}{2}+2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.318 |
|
| 3913 |
\begin{align*}
x^{\prime }&=2 x \\
y^{\prime }&=3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.318 |
|
| 3914 |
\begin{align*}
x^{\prime \prime }-2 x^{\prime }+x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.318 |
|
| 3915 |
\begin{align*}
x_{1}^{\prime }&=4 x_{1}-x_{2} \\
x_{2}^{\prime }&=x_{1}+2 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.318 |
|
| 3916 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+2 y&=2 x \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.319 |
|
| 3917 |
\begin{align*}
y^{\prime \prime }+2 i y^{\prime }+3 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.319 |
|
| 3918 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.319 |
|
| 3919 |
\begin{align*}
y^{\prime \prime }+\left (x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.319 |
|
| 3920 |
\begin{align*}
16 y^{\prime \prime }+24 y^{\prime }+9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.319 |
|
| 3921 |
\begin{align*}
y^{\prime \prime }-x y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.319 |
|
| 3922 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-4 x_{2} \\
x_{2}^{\prime }&=4 x_{1}-7 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.319 |
|
| 3923 |
\begin{align*}
y^{\prime \prime \prime }-y^{\prime }&=-2 x -2+4 \,{\mathrm e}^{x}-6 \,{\mathrm e}^{-x}+96 \,{\mathrm e}^{3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.319 |
|
| 3924 |
\begin{align*}
2 y^{\prime \prime }+y^{\prime }-y&={\mathrm e}^{3 t} \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.319 |
|
| 3925 |
\begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=\frac {2 \,{\mathrm e}^{x}}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.319 |
|
| 3926 |
\begin{align*}
y^{\prime \prime }+4 k y^{\prime }-12 k^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.319 |
|
| 3927 |
\begin{align*}
x^{\prime }&=\cos \left (y \right )-x \tan \left (y \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.319 |
|
| 3928 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.319 |
|
| 3929 |
\begin{align*}
y^{\prime \prime }-5 y^{\prime }+6 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.319 |
|
| 3930 |
\begin{align*}
y^{\prime \prime }+2 x^{2} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.319 |
|
| 3931 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.319 |
|
| 3932 |
\begin{align*}
x \left (x^{2}+1\right ) y^{\prime \prime }+\left (7 x^{2}+4\right ) y^{\prime }+8 y x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.319 |
|
| 3933 |
\(\left [\begin {array}{cc} 0 & 1 \\ -1 & 0 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.319 |
|
| 3934 |
\begin{align*}
x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-10 x y^{\prime }-8 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.319 |
|
| 3935 |
\begin{align*}
2 y^{\prime \prime }-5 y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.319 |
|
| 3936 |
\begin{align*}
12 y^{\prime \prime }+8 y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.319 |
|
| 3937 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-12 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.319 |
|
| 3938 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.319 |
|
| 3939 |
\begin{align*}
9 y^{\prime \prime }-12 y^{\prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.320 |
|
| 3940 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+13 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.320 |
|
| 3941 |
\begin{align*}
y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y&=8 \,{\mathrm e}^{-x \left (x +2\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.320 |
|
| 3942 |
\begin{align*}
y^{\prime \prime \prime \prime }&={\mathrm e}^{x} \cos \left (x \right )+y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.320 |
|
| 3943 |
\begin{align*}
y^{\prime \prime }-y&=3 \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.320 |
|
| 3944 |
\begin{align*}
x^{\prime }&=x \\
y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.320 |
|
| 3945 |
\begin{align*}
3 t \left (t +1\right ) y^{\prime \prime }+t y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.320 |
|
| 3946 |
\begin{align*}
x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.320 |
|
| 3947 |
\begin{align*}
t y^{\prime \prime }+y^{\prime }+y t&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.320 |
|
| 3948 |
\begin{align*}
y^{\prime \prime }+9 y&=27 t^{3} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.320 |
|
| 3949 |
\begin{align*}
x^{\prime }&=2 x \\
y^{\prime }&=3 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.320 |
|
| 3950 |
\begin{align*}
\left (x^{3}+x^{2}-3 x +1\right ) y^{\prime \prime \prime }+\left (9 x^{2}+6 x -9\right ) y^{\prime \prime }+\left (18 x +6\right ) y^{\prime }+6 y&=x^{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.320 |
|
| 3951 |
\begin{align*}
x^{\prime }+x^{2}&=0 \\
x \left (-\frac {1}{2}\right ) &= 0 \\
\end{align*}
Series expansion around \(t=-{\frac {1}{2}}\). |
✓ |
✓ |
✓ |
✓ |
0.320 |
|
| 3952 |
\begin{align*}
y^{\prime \prime }+10 y^{\prime }+26 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.320 |
|
| 3953 |
\(\left [\begin {array}{cc} -3 & 5 \\ 5 & 4 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.320 |
|
| 3954 |
\(\left [\begin {array}{cc} -3 & 5 \\ 5 & 4 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.320 |
|
| 3955 |
\begin{align*}
{y^{\prime \prime }}^{2}+y^{\prime }&=x y^{\prime \prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.320 |
|
| 3956 |
\begin{align*}
y^{\prime }&=y \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.321 |
|
| 3957 |
\begin{align*}
y^{\prime \prime }+x^{2} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.321 |
|
| 3958 |
\begin{align*}
4 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+x \left (-19 x^{2}+7\right ) y^{\prime }-\left (14 x^{2}+1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.321 |
|
| 3959 |
\begin{align*}
y^{\prime \prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.321 |
|
| 3960 |
\begin{align*}
x^{2} \left (x -2\right ) y^{\prime \prime }+4 \left (x -2\right ) y^{\prime }+3 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
0.321 |
|
| 3961 |
\begin{align*}
2 y-3 x y^{\prime \prime }+4 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.321 |
|
| 3962 |
\begin{align*}
3 y^{\prime \prime }+x y^{\prime }-4 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.322 |
|
| 3963 |
\begin{align*}
y^{\prime \prime }+x y^{\prime }+y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.322 |
|
| 3964 |
\begin{align*}
y^{\prime \prime }+\sqrt {x}\, y^{\prime }+\left (\frac {1}{4 \sqrt {x}}+\frac {x}{4}-9\right ) y-x \,{\mathrm e}^{-\frac {x^{{3}/{2}}}{3}}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.322 |
|
| 3965 |
\(\left [\begin {array}{cc} 7 & 1 \\ -4 & 11 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.322 |
|
| 3966 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.322 |
|
| 3967 |
\begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }-3 y&=5 x^{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.322 |
|
| 3968 |
\begin{align*}
s^{\prime \prime \prime \prime }-2 s^{\prime \prime }+s&=100 \cos \left (3 t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.322 |
|
| 3969 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.322 |
|
| 3970 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }-12 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.322 |
|
| 3971 |
\begin{align*}
y^{\prime }&={\mathrm e}^{y}-x^{2} y \\
y \left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.322 |
|
| 3972 |
\begin{align*}
4 y^{\prime \prime }+4 y^{\prime }+y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.323 |
|
| 3973 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+\frac {25 y}{4}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.323 |
|
| 3974 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }-4 x y^{\prime }+6 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.323 |
|
| 3975 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.323 |
|
| 3976 |
\begin{align*}
y^{\prime }+y \tan \left (x \right )&=\sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.323 |
|
| 3977 |
\begin{align*}
x^{\prime }&=x-3 y \\
y^{\prime }&=3 x+7 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.323 |
|
| 3978 |
\begin{align*}
y^{\prime }&=\operatorname {Heaviside}\left (-3+t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.323 |
|
| 3979 |
\begin{align*}
y^{\prime \prime }-x^{2} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.323 |
|
| 3980 |
\begin{align*}
20 y^{\prime \prime }+y^{\prime }-y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.323 |
|
| 3981 |
\begin{align*}
x^{\prime \prime }+x&=t \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.323 |
|
| 3982 |
\begin{align*}
\left (x^{3}-4 x \right ) y^{\prime \prime \prime }+\left (9 x^{2}-4\right ) y^{\prime \prime }+18 x y^{\prime }+6 y&=6 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.323 |
|
| 3983 |
\begin{align*}
y^{\prime \prime }-7 y^{\prime }+10 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.323 |
|
| 3984 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }-21 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.323 |
|
| 3985 |
\begin{align*}
4 y^{\prime \prime }-12 y^{\prime }+9 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.324 |
|
| 3986 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}-x_{2} \\
x_{2}^{\prime }&=x_{1}+5 x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.324 |
|
| 3987 |
\begin{align*}
y^{\prime \prime }+x^{2} y^{\prime }+x^{2} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.324 |
|
| 3988 |
\begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+12 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.324 |
|
| 3989 |
\begin{align*}
t^{3} x^{\prime \prime \prime }-3 t^{2} x^{\prime \prime }+6 x^{\prime } t -6 x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.324 |
|
| 3990 |
\begin{align*}
x^{\prime \prime \prime \prime }-4 x^{\prime \prime \prime }+8 x^{\prime \prime }-8 x^{\prime }+4 x&=\sin \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.324 |
|
| 3991 |
\begin{align*}
5 y+2 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.324 |
|
| 3992 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.324 |
|
| 3993 |
\begin{align*}
y^{\prime \prime \prime }+y&=x +\sin \left (x \right )+\cos \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.324 |
|
| 3994 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+7 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.324 |
|
| 3995 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-10 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.325 |
|
| 3996 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.325 |
|
| 3997 |
\begin{align*}
\frac {1}{y}-\left (3 y-\frac {x}{y^{2}}\right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.325 |
|
| 3998 |
\begin{align*}
x^{3} \left (x^{2}-25\right ) \left (x -2\right )^{2} y^{\prime \prime }+3 x \left (x -2\right ) y^{\prime }+7 \left (5+x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✗ |
✗ |
✓ |
✗ |
0.325 |
|
| 3999 |
\begin{align*}
3 x^{2} \left (x^{2}+3\right ) y^{\prime \prime }+x \left (11 x^{2}+3\right ) y^{\prime }+\left (5 x^{2}+1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.325 |
|
| 4000 |
\begin{align*}
y^{\prime \prime }&=\frac {\left (x^{2}-2\right ) y^{\prime }}{x \left (x^{2}-1\right )}-\frac {\left (x^{2}-2\right ) y}{x^{2} \left (x^{2}-1\right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.325 |
|