| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 10901 |
\begin{align*}
b \,{\mathrm e}^{2 a x} y+a y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.839 |
|
| 10902 |
\begin{align*}
2 y-2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.839 |
|
| 10903 |
\begin{align*}
y^{\prime \prime }+y&=\cot \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.839 |
|
| 10904 |
\begin{align*}
-3 y+3 x y^{\prime }+\left (2 x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.839 |
|
| 10905 |
\begin{align*}
y+2 x y^{2}-x^{2} y^{3}+2 x^{2} y y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.839 |
|
| 10906 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+5 y&=x^{3} {\mathrm e}^{2 x} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.839 |
|
| 10907 |
\begin{align*}
x^{\prime \prime }+9 x&=\sin \left (3 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.839 |
|
| 10908 |
\begin{align*}
x^{2} y^{\prime \prime }-2 x y^{\prime }+7 y&=0 \\
\end{align*}
Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.839 |
|
| 10909 |
\begin{align*}
y^{\prime }+y^{2}-2 y \sin \left (x \right )+\sin \left (x \right )^{2}-\cos \left (x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.839 |
|
| 10910 |
\begin{align*}
x^{\prime }&=2 x+y \\
y^{\prime }&=x-3 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.839 |
|
| 10911 |
\begin{align*}
x^{\prime }+3 x&={\mathrm e}^{-2 t} \\
x \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.839 |
|
| 10912 |
\begin{align*}
x {y^{\prime }}^{3}-2 y {y^{\prime }}^{2}+4 x^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.839 |
|
| 10913 |
\begin{align*}
y_{1}^{\prime }&=2 y_{1}-y_{2}+{\mathrm e}^{t} \\
y_{2}^{\prime }&=3 y_{1}-2 y_{2}+{\mathrm e}^{t} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.839 |
|
| 10914 |
\begin{align*}
y^{2} x^{4}-y+\left (x^{2} y^{4}-x \right ) y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.840 |
|
| 10915 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 7 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.840 |
|
| 10916 |
\begin{align*}
x_{1}^{\prime }&=5 x_{1}-6 x_{3} \\
x_{2}^{\prime }&=2 x_{1}-x_{2}-2 x_{3} \\
x_{3}^{\prime }&=4 x_{1}-2 x_{2}-4 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.841 |
|
| 10917 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1} \\
x_{2}^{\prime }&=x_{1}+3 x_{2} \\
x_{3}^{\prime }&=3 x_{3} \\
x_{4}^{\prime }&=2 x_{3}+3 x_{4} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 1 \\
x_{3} \left (0\right ) &= 1 \\
x_{4} \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.841 |
|
| 10918 |
\begin{align*}
4 y+y^{\prime \prime }&=\ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.841 |
|
| 10919 |
\begin{align*}
y^{\prime \prime }-\frac {y^{\prime }}{x}+\left (1+\frac {1}{x^{2}}\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.841 |
|
| 10920 |
\begin{align*}
y^{\prime \prime }&=-\frac {2 y^{\prime }}{x}-\frac {c y}{x^{2} \left (a x +b \right )^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.841 |
|
| 10921 |
\begin{align*}
y^{\prime }&=\frac {1}{x -1} \\
y \left (2\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.841 |
|
| 10922 |
\begin{align*}
x^{\prime }&=-3 x+2 y \\
y^{\prime }&=-x-y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.841 |
|
| 10923 |
\begin{align*}
x^{\prime }&=3 x \\
y^{\prime }&=2 x+3 y \\
z^{\prime }&=3 y-2 z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.841 |
|
| 10924 |
\begin{align*}
x^{\prime }&=x+2 y+z \\
y^{\prime }&=6 x-y \\
z^{\prime }&=-x-2 y-z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.842 |
|
| 10925 |
\begin{align*}
x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-3 x \left (-x^{2}+1\right ) y^{\prime }+4 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.842 |
|
| 10926 |
\begin{align*}
4 y+y^{\prime \prime }&=2 \tan \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.842 |
|
| 10927 |
\begin{align*}
y^{\prime \prime }+y&=a x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.842 |
|
| 10928 |
\begin{align*}
y^{\prime }&=2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.842 |
|
| 10929 |
\begin{align*}
\left (x +1\right ) \left (x^{2}+1\right ) y^{\prime }&=2 x^{2}+x \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.842 |
|
| 10930 |
\begin{align*}
\left (x -1\right ) y^{\prime \prime }+3 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.842 |
|
| 10931 |
\begin{align*}
2 x^{2} y^{\prime \prime }+2 x y^{\prime }-y x&=\sin \left (x \right ) \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.842 |
|
| 10932 |
\begin{align*}
x y y^{\prime \prime }-{y^{\prime }}^{2} x +y y^{\prime }+x \left (d +y^{4} a \right )+y \left (c +b y^{2}\right )&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.842 |
|
| 10933 |
\begin{align*}
x^{\prime \prime }-4 x^{\prime }+6 x&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.842 |
|
| 10934 |
\begin{align*}
2 \left (x +3\right )^{2} y^{\prime \prime }-\left (x^{2}+5 x +6\right ) y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=-3\). |
✓ |
✓ |
✓ |
✓ |
0.842 |
|
| 10935 |
\begin{align*}
y^{\prime \prime }+16 y&=\sin \left (4 x +\alpha \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.842 |
|
| 10936 |
\begin{align*}
2 x y^{\prime \prime }-y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.843 |
|
| 10937 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-2 x_{2} \\
x_{2}^{\prime }&=4 x_{1}-2 x_{2}+\delta \left (t -\pi \right ) \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.843 |
|
| 10938 |
\begin{align*}
\sin \left (x \right ) y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.843 |
|
| 10939 |
\begin{align*}
y^{\prime }-2 y&=\left \{\begin {array}{cc} 1 & x \le 1 \\ 0 & 1<x \end {array}\right . \\
y \left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.843 |
|
| 10940 |
\begin{align*}
\left (b +c \,{\mathrm e}^{x}\right ) y+a y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.843 |
|
| 10941 |
\begin{align*}
2 x^{2} y^{\prime \prime }+2 x y^{\prime }-y x&=x^{3}+x \sin \left (x \right ) \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.843 |
|
| 10942 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-5 x_{2}-\cos \left (t \right ) \\
x_{2}^{\prime }&=x_{1}-2 x_{2}+\sin \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.844 |
|
| 10943 |
\begin{align*}
y-\left (x +1\right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.844 |
|
| 10944 |
\begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{x^{2}+1} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.844 |
|
| 10945 |
\(\left [\begin {array}{ccc} \frac {\sqrt {2}}{2} & \frac {i \sqrt {2}}{2} & 0 \\ -\frac {\sqrt {2}}{2} & \frac {i \sqrt {2}}{2} & 0 \\ 0 & 0 & 1 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.844 |
|
| 10946 |
\begin{align*}
x_{1}^{\prime }&=-x_{1}-x_{2}-1 \\
x_{2}^{\prime }&=2 x_{1}-x_{2}+5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.845 |
|
| 10947 |
\begin{align*}
y^{\prime }&=2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.845 |
|
| 10948 |
\begin{align*}
x^{2} y^{\prime \prime }+x \left (3-2 x \right ) y^{\prime }+\left (1-2 x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.845 |
|
| 10949 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=x^{3} {\mathrm e}^{2 x}+x \,{\mathrm e}^{2 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.845 |
|
| 10950 |
\begin{align*}
{y^{\prime }}^{3}-x y^{4} y^{\prime }-y^{5}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.845 |
|
| 10951 |
\begin{align*}
a x^{\prime }+b y^{\prime }&=\alpha x+\beta y \\
b x^{\prime }-a y^{\prime }&=\beta x-\alpha y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.845 |
|
| 10952 |
\begin{align*}
4 y+y^{\prime \prime }&=\sin \left (x \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.845 |
|
| 10953 |
\begin{align*}
w^{\prime }-y&=0 \\
w+y^{\prime }+z&=1 \\
w-y+z^{\prime }&=2 \sin \left (t \right ) \\
\end{align*}
With initial conditions \begin{align*}
y \left (0\right ) &= 1 \\
w \left (0\right ) &= 1 \\
z \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.845 |
|
| 10954 |
\begin{align*}
2 x \left (x -1\right ) y^{\prime \prime }+3 \left (x -1\right ) y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.845 |
|
| 10955 |
\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*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.846 |
|
| 10956 |
\begin{align*}
2 x^{2} \left (x +2\right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (x +1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.846 |
|
| 10957 |
\begin{align*}
t y^{\prime \prime }+y^{\prime }-4 y&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.846 |
|
| 10958 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=\cos \left (a x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.846 |
|
| 10959 |
\begin{align*}
4 y^{\prime \prime }-12 y^{\prime }+9 y&=0 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 9 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.846 |
|
| 10960 |
\begin{align*}
x^{\prime }&=-x+a y \\
y^{\prime }&=-x-y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.846 |
|
| 10961 |
\begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.846 |
|
| 10962 |
\begin{align*}
y^{\prime }+y&=x^{2} \\
y \left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.846 |
|
| 10963 |
\begin{align*}
8 x^{2} y^{\prime \prime }+x \left (x^{2}+2\right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.847 |
|
| 10964 |
\begin{align*}
9 x^{2} y^{\prime \prime }+\left (3 x +2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.847 |
|
| 10965 |
\begin{align*}
{y^{\prime }}^{2} x -2 y y^{\prime }-x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.847 |
|
| 10966 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&={\mathrm e}^{x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.847 |
|
| 10967 |
\begin{align*}
2 x y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.848 |
|
| 10968 |
\begin{align*}
3 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.848 |
|
| 10969 |
\begin{align*}
x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-2 x \left (-x^{2}+2\right ) y^{\prime }+4 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.848 |
|
| 10970 |
\begin{align*}
4 x^{2} y^{\prime \prime }+x \left (x^{2}-4\right ) y^{\prime }+3 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.848 |
|
| 10971 |
\begin{align*}
x y^{\prime \prime }+y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.848 |
|
| 10972 |
\begin{align*}
x^{\prime }&=-2 x+5 y \\
y^{\prime }&=-2 x+4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.848 |
|
| 10973 |
\begin{align*}
x^{\prime }&=\frac {3 x}{4}-2 y \\
y^{\prime }&=x-\frac {5 y}{4} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.848 |
|
| 10974 |
\begin{align*}
y_{1}^{\prime }&=-4 y_{1}-y_{2} \\
y_{2}^{\prime }&=y_{1}-2 y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 1 \\
y_{2} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.848 |
|
| 10975 |
\begin{align*}
x^{\prime }&=x+3 y+a \\
y^{\prime }&=x-y+b \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.848 |
|
| 10976 |
\begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y&=6 x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.848 |
|
| 10977 |
\begin{align*}
x \left (x^{2}+3\right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-8 y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.849 |
|
| 10978 |
\begin{align*}
\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.849 |
|
| 10979 |
\begin{align*}
2 y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.849 |
|
| 10980 |
\begin{align*}
\sqrt {x}\, y^{\prime \prime }+y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.849 |
|
| 10981 |
\begin{align*}
4 y^{\prime \prime }+4 y^{\prime }+37 y&=\cos \left (3 t \right ) \\
y \left (0\right ) &= a \\
y^{\prime }\left (\pi \right ) &= a \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.849 |
|
| 10982 |
\begin{align*}
y \left (1+{y^{\prime }}^{2}\right )&=2 x y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.850 |
|
| 10983 |
\begin{align*}
x^{2} y^{\prime \prime }&=y^{\prime } \left (2 x -y^{\prime }\right ) \\
y \left (-1\right ) &= 5 \\
y^{\prime }\left (-1\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.850 |
|
| 10984 |
\begin{align*}
2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=1 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.850 |
|
| 10985 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.850 |
|
| 10986 |
\begin{align*}
x^{\prime \prime }+7 x&=t \,{\mathrm e}^{3 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.850 |
|
| 10987 |
\begin{align*}
x^{\prime }&=x+5 y \\
y^{\prime }&=-x-3 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= -2 \\
y \left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.850 |
|
| 10988 |
\begin{align*}
x x^{\prime \prime }-{x^{\prime }}^{2}+{\mathrm e}^{t} x^{2}&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
0.850 |
|
| 10989 |
\begin{align*}
\sin \left (t \right ) y^{\prime \prime }+\cos \left (t \right ) y^{\prime }+\frac {y}{t}&=0 \\
\end{align*}
Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✗ |
0.851 |
|
| 10990 |
\begin{align*}
\left (1-x \right ) y^{\prime \prime }&=y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.851 |
|
| 10991 |
\begin{align*}
x_{1}^{\prime }&=2 x_{1}-x_{2}+3 x_{3} \\
x_{2}^{\prime }&=3 x_{1}+x_{2} \\
x_{3}^{\prime }&=2 x_{1}-x_{2}+3 x_{3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.851 |
|
| 10992 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-x_{2}+x_{3} \\
x_{2}^{\prime }&=x_{1}+x_{2}-x_{3} \\
x_{3}^{\prime }&=-2 x_{2}+2 x_{3} \\
\end{align*}
With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= -2 \\
x_{3} \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.851 |
|
| 10993 |
\begin{align*}
x^{3} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=\infty \). |
✓ |
✓ |
✓ |
✓ |
0.851 |
|
| 10994 |
\begin{align*}
2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y&=\cos \left (x \right ) \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.851 |
|
| 10995 |
\begin{align*}
2 x^{2} y^{\prime \prime }+2 x y^{\prime }-y x&=\sin \left (x \right ) \cos \left (x \right ) \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.851 |
|
| 10996 |
\begin{align*}
y y^{\prime }&=\left (x -b \right ) {y^{\prime }}^{2}+a \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.851 |
|
| 10997 |
\begin{align*}
\left (x^{2}-x \right ) y^{\prime \prime }+2 \left (2 x +1\right ) y^{\prime }+2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.851 |
|
| 10998 |
\begin{align*}
y^{\prime \prime }+9 y&=20 \,{\mathrm e}^{-t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.851 |
|
| 10999 |
\begin{align*}
3 x y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.852 |
|
| 11000 |
\begin{align*}
x y^{\prime \prime }+\left (-x +3\right ) y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.852 |
|