| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 12801 |
\begin{align*}
y^{\prime }&=t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.093 |
|
| 12802 |
\begin{align*}
y^{\prime \prime }&=y^{\prime } \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.093 |
|
| 12803 |
\begin{align*}
\cos \left (x \right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.094 |
|
| 12804 |
\begin{align*}
m y^{\prime \prime }+a y^{\prime }+k y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.094 |
|
| 12805 |
\begin{align*}
x_{1}^{\prime }&=-3 x_{1}+\sqrt {2}\, x_{2}+{\mathrm e}^{-t} \\
x_{2}^{\prime }&=\sqrt {2}\, x_{1}-2 x_{2}-{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.095 |
|
| 12806 |
\begin{align*}
\left (-t^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } t +2 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.095 |
|
| 12807 |
\begin{align*}
y^{\prime \prime }-y^{\prime }&={\mathrm e}^{2 x} \sin \left (x \right ) x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.095 |
|
| 12808 |
\begin{align*}
3 y^{\prime \prime }+\cos \left (x \right ) y^{\prime }+\sin \left (y\right ) {y^{\prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.095 |
|
| 12809 |
\begin{align*}
x^{2} y^{\prime \prime }-\left (a \,x^{2}+2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.095 |
|
| 12810 |
\begin{align*}
x^{\prime }&=-\frac {x}{2}+2 y-3 z \\
y^{\prime }&=y-\frac {z}{2} \\
z^{\prime }&=-2 x+z \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.095 |
|
| 12811 |
\begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=\tan \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.095 |
|
| 12812 |
\begin{align*}
2 y^{\prime \prime } x +y^{\prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.095 |
|
| 12813 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x -4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.096 |
|
| 12814 |
\begin{align*}
\left (x +3\right ) x^{2} y^{\prime \prime }+5 x \left (x +1\right ) y^{\prime }-\left (1-4 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.096 |
|
| 12815 |
\begin{align*}
{y^{\prime \prime }}^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.097 |
|
| 12816 |
\begin{align*}
{y^{\prime }}^{2}-y^{2} a^{2}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.098 |
|
| 12817 |
\begin{align*}
x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x^{2}-2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.098 |
|
| 12818 |
\begin{align*}
\left (x^{2}-25\right )^{2} y^{\prime \prime }-\left (x +5\right ) y^{\prime }+10 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.098 |
|
| 12819 |
\begin{align*}
x^{\prime }&=2 x+y-2 z+2-t \\
y^{\prime }&=1-x \\
z^{\prime }&=x+y-z+1-t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.098 |
|
| 12820 |
\begin{align*}
x^{\prime }&=7 x+4 y-4 z \\
y^{\prime }&=4 x-8 y-z \\
z^{\prime }&=-4 x-y-8 z \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 3 \\
y \left (0\right ) &= 5 \\
z \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.098 |
|
| 12821 |
\begin{align*}
y^{\prime \prime }-y&=\operatorname {Heaviside}\left (t -1\right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.099 |
|
| 12822 |
\begin{align*}
2 y y^{\prime \prime }&=8 y^{3}-2 y^{2} \left (f \left (x \right )^{2}+f^{\prime }\left (x \right )\right )-3 f \left (x \right ) y y^{\prime }+{y^{\prime }}^{2} \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.099 |
|
| 12823 |
\begin{align*}
4 y^{3} {y^{\prime }}^{2}-4 y^{\prime } x +y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.100 |
|
| 12824 |
\begin{align*}
y^{\prime \prime }+y^{\prime }&=x +1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.100 |
|
| 12825 |
\begin{align*}
x \left (x -3\right ) y^{\prime \prime }+3 y^{\prime }&=x^{2} \\
y \left (5\right ) &= 0 \\
y^{\prime }\left (5\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.100 |
|
| 12826 |
\begin{align*}
4 y+y^{\prime \prime }&=\sin \left (2 x \right ) \sec \left (2 x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.101 |
|
| 12827 |
\begin{align*}
2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.101 |
|
| 12828 |
\begin{align*}
y^{\prime }+{y^{\prime }}^{3}+2 y^{\prime \prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.101 |
|
| 12829 |
\begin{align*}
-y^{\prime }+y^{\prime \prime } x&=x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.101 |
|
| 12830 |
\begin{align*}
{y^{\prime }}^{2}-y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.101 |
|
| 12831 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +7 y&=0 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
1.101 |
|
| 12832 |
\begin{align*}
y+2 y^{\prime }&=3 t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.102 |
|
| 12833 |
\begin{align*}
y^{\prime \prime }-y&={\mathrm e}^{-x} \sin \left ({\mathrm e}^{-x}\right )+\cos \left ({\mathrm e}^{-x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.102 |
|
| 12834 |
\begin{align*}
2 y^{3} y^{\prime \prime }+y^{4}-a^{2} x y^{2}-1&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.102 |
|
| 12835 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+13 y&=8 \sin \left (3 x \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.102 |
|
| 12836 |
\begin{align*}
2 x y^{\prime } y^{\prime \prime }&=-1+{y^{\prime }}^{2} \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= \sqrt {3} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.102 |
|
| 12837 |
\begin{align*}
\left (x -2\right ) y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.103 |
|
| 12838 |
\begin{align*}
\left (x^{2}-1\right )^{2} y^{\prime \prime }+a y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.103 |
|
| 12839 |
\begin{align*}
2 x^{\prime }+y^{\prime }-x-y&=-2 t \\
x^{\prime }+y^{\prime }+x-y&=t^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.103 |
|
| 12840 |
\begin{align*}
y^{\prime }&=5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.103 |
|
| 12841 |
\begin{align*}
y^{\prime \prime } x -3 y^{\prime }&=5 x \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.104 |
|
| 12842 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (\frac {5}{3} x +x^{2}\right ) y^{\prime }-\frac {y}{3}&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.104 |
|
| 12843 |
\begin{align*}
y^{\prime }&=y^{2}-4 y+2 \\
y \left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✗ |
✓ |
1.104 |
|
| 12844 |
\begin{align*}
x^{\prime }&=3 x-y \\
y^{\prime }&=x+2 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.104 |
|
| 12845 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (a +2 b \right ) x^{2} y^{\prime }+\left (\left (a +b \right ) b \,x^{2}-2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.105 |
|
| 12846 |
\begin{align*}
x y y^{\prime \prime }-x {y^{\prime }}^{2}+y y^{\prime }+x \left (d +a y^{4}\right )+y \left (c +b y^{2}\right )&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
1.105 |
|
| 12847 |
\begin{align*}
y^{\prime }+y&={\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.105 |
|
| 12848 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}-3 x \right ) y^{\prime }+\left (3 x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.105 |
|
| 12849 |
\begin{align*}
y^{\prime \prime }-y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.106 |
|
| 12850 |
\begin{align*}
y^{\prime }&=y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.106 |
|
| 12851 |
\begin{align*}
x^{\prime }&=-x-y \\
y^{\prime }&=\frac {3 x}{4}-\frac {3 y}{2}+3 z \\
z^{\prime }&=\frac {x}{8}+\frac {y}{4}-\frac {z}{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.106 |
|
| 12852 |
\begin{align*}
y^{\prime \prime }&=2 a \left (c +b x +y\right ) \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\
\end{align*} |
✗ |
✓ |
✓ |
✗ |
1.106 |
|
| 12853 |
\begin{align*}
2 y y^{\prime }&=1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.106 |
|
| 12854 |
\begin{align*}
y^{\prime }&=-\frac {4}{x^{2}} \\
y \left (1\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.106 |
|
| 12855 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=3 \,{\mathrm e}^{2 t} t -4 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.106 |
|
| 12856 |
\begin{align*}
\left (x \sin \left (x \right )+\cos \left (x \right )\right ) y^{\prime \prime }-x \cos \left (x \right ) y^{\prime }+\cos \left (x \right ) y&=x \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.107 |
|
| 12857 |
\begin{align*}
2 y^{\prime \prime } x +\left (-2 x^{2}+1\right ) y^{\prime }-4 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.107 |
|
| 12858 |
\begin{align*}
y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c \left (a x +b -c \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.107 |
|
| 12859 |
\begin{align*}
4 \left (x^{2}+1\right )^{2} y^{\prime \prime }+\left (a \,x^{2}+a -3\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.107 |
|
| 12860 |
\begin{align*}
y^{\prime \prime }+7 y^{\prime }+10 y&=3 \,{\mathrm e}^{-2 t}-6 \,{\mathrm e}^{-5 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.108 |
|
| 12861 |
\begin{align*}
y^{\prime \prime }-2 \left (2+x \right ) y^{\prime }+4 y&=0 \\
y \left (-2\right ) &= 1 \\
y^{\prime }\left (-2\right ) &= 0 \\
\end{align*} Series expansion around \(x=-2\). |
✓ |
✓ |
✓ |
✓ |
1.108 |
|
| 12862 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=g \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.109 |
|
| 12863 |
\begin{align*}
1+\frac {y^{2}}{x^{2}}-\frac {2 y y^{\prime }}{x}&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.109 |
|
| 12864 |
\begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=\cos \left (x \right ) \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
1.109 |
|
| 12865 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}-x \right ) y^{\prime }+\left (1-x \right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.109 |
|
| 12866 |
\begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+2 y^{\prime }-2 y&={\mathrm e}^{2 x} \left (\left (-x^{2}+5 x +27\right ) \cos \left (x \right )+\left (9 x^{2}+13 x +2\right ) \sin \left (x \right )\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.110 |
|
| 12867 |
\begin{align*}
y&=x {y^{\prime }}^{2}+{y^{\prime }}^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.110 |
|
| 12868 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (\frac {t}{2}\right )+\csc \left (\frac {t}{2}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.110 |
|
| 12869 |
\begin{align*}
L i^{\prime }+R i&=e \\
i \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.110 |
|
| 12870 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x -4 y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.111 |
|
| 12871 |
\begin{align*}
x^{2} y^{\prime \prime }+\left (2 x^{2}+x \right ) y^{\prime }-4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.111 |
|
| 12872 |
\begin{align*}
2 \left (1-x \right ) x^{2} y^{\prime \prime }-x \left (1+7 x \right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.111 |
|
| 12873 |
\begin{align*}
y^{\prime \prime }+y&=\frac {\operatorname {Heaviside}\left (t -4+k \right )-\operatorname {Heaviside}\left (t -4-k \right )}{2 k} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.112 |
|
| 12874 |
\begin{align*}
2 x^{2} y^{\prime \prime }-3 y^{\prime } x -18 y&=\ln \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.112 |
|
| 12875 |
\begin{align*}
9 x^{2} y^{\prime \prime }+9 x^{2} y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.112 |
|
| 12876 |
\begin{align*}
\left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2}+\left (1-\ln \left (y\right )\right ) y y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.112 |
|
| 12877 |
\begin{align*}
y^{\prime }&=x +y \\
y \left (1\right ) &= -3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.113 |
|
| 12878 |
\begin{align*}
\cos \left (x \right ) y^{\prime \prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.113 |
|
| 12879 |
\begin{align*}
y^{\prime \prime } x +\left (x^{3}-1\right ) y^{\prime }+x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.113 |
|
| 12880 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime } x +4 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.113 |
|
| 12881 |
\begin{align*}
y^{\prime }&=y-1 \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.113 |
|
| 12882 |
\begin{align*}
y^{\prime }+20 y&=24 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.113 |
|
| 12883 |
\begin{align*}
y^{\prime \prime }+9 y&=9 \sec \left (3 t \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.114 |
|
| 12884 |
\begin{align*}
2 y^{\prime \prime }+3 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
1.114 |
|
| 12885 |
\begin{align*}
2 x^{2} y^{\prime \prime }+\left (x^{2}+5 x \right ) y^{\prime }+\left (x^{2}-2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.114 |
|
| 12886 |
\begin{align*}
x \left (x^{2}-2\right ) y^{\prime \prime }-\left (x^{3}+3 x^{2}-2 x -2\right ) y^{\prime }+\left (x^{2}+4 x +2\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.114 |
|
| 12887 |
\begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
1.114 |
|
| 12888 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&=24 \cosh \left (t \right ) \\
y \left (0\right ) &= 6 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
1.114 |
|
| 12889 |
\begin{align*}
y^{\prime \prime }-y^{\prime }-6 y&=\cos \left (t \right )+57 \sin \left (t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 7 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
1.114 |
|
| 12890 |
\begin{align*}
y^{2} {y^{\prime }}^{3}+2 y^{\prime } x -y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
1.115 |
|
| 12891 |
\begin{align*}
5 {y^{\prime }}^{2}+6 y^{\prime } x -2 y&=0 \\
\end{align*} |
✓ |
✓ |
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1.115 |
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| 12892 |
\begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +\left (x^{3}+x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
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1.115 |
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| 12893 |
\begin{align*}
y^{\prime \prime }-y^{\prime }&=-5 \,{\mathrm e}^{-x} \left (\cos \left (x \right )+\sin \left (x \right )\right ) \\
y \left (0\right ) &= -4 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*} |
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1.115 |
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| 12894 |
\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*} |
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1.115 |
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| 12895 |
\begin{align*}
-5 y-3 y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
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1.115 |
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| 12896 |
\begin{align*}
x^{\prime \prime }+\lambda ^{2} x&=0 \\
x \left (0\right ) &= 0 \\
x \left (\pi \right ) &= 0 \\
\end{align*} |
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1.115 |
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| 12897 |
\begin{align*}
x^{\prime }&=3 x-2 y \\
y^{\prime }&=17 x-7 y \\
\end{align*} |
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1.115 |
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| 12898 |
\begin{align*}
y_{1}^{\prime }&=-7 y_{1}-4 y_{2}+4 y_{3} \\
y_{2}^{\prime }&=y_{1}+y_{3} \\
y_{3}^{\prime }&=-9 y_{1}-5 y_{2}+6 y_{3} \\
\end{align*} With initial conditions \begin{align*}
y_{1} \left (0\right ) &= -6 \\
y_{2} \left (0\right ) &= 9 \\
y_{3} \left (0\right ) &= -1 \\
\end{align*} |
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1.116 |
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| 12899 |
\begin{align*}
x^{\prime \prime }+k^{2} x&=0 \\
\end{align*} |
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1.116 |
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| 12900 |
\begin{align*}
2 {y^{\prime }}^{3}-3 {y^{\prime }}^{2}+x&=y \\
\end{align*} |
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1.116 |
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