| # |
ID |
ODE |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| 9101 |
\begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| 9102 |
\begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (x^{2}+6\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| 9103 |
\begin{align*}
x^{\prime }&=\frac {1}{\sqrt {t^{2}+1}} \\
x \left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| 9104 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&=16 x^{3} {\mathrm e}^{3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| 9105 |
\begin{align*}
y^{\prime }&=t \,{\mathrm e}^{-t} \\
y \left (0\right ) &= -1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| 9106 |
\begin{align*}
r^{\prime \prime }+r^{\prime }+r&=1 \\
r \left (0\right ) &= 0 \\
r^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| 9107 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }-3 y&=-12 x +8 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| 9108 |
\begin{align*}
8 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+2 x \left (-21 x^{2}+10\right ) y^{\prime }-\left (35 x^{2}+2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.672 |
|
| 9109 |
\begin{align*}
y^{\prime \prime }-5 y^{\prime }-6 y&={\mathrm e}^{3 x} \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.672 |
|
| 9110 |
\begin{align*}
f^{\prime \prime }+8 f^{\prime }+12 f&=12 \,{\mathrm e}^{-4 t} \\
f \left (0\right ) &= 0 \\
f^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.672 |
|
| 9111 |
\begin{align*}
y^{\prime \prime }-y x -x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.672 |
|
| 9112 |
\begin{align*}
\left (-a^{2}+x^{2}\right )^{2} y^{\prime \prime }+b^{2} y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.672 |
|
| 9113 |
\begin{align*}
n \left (n +1\right ) y-2 y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.672 |
|
| 9114 |
\begin{align*}
x^{\prime }&=-3 x-5 y \\
y^{\prime }&=3 x+y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 4 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.672 |
|
| 9115 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+20 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.672 |
|
| 9116 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=0 \\
y \left (0\right ) &= 2 \\
y \left (2\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.672 |
|
| 9117 |
\begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{3 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.672 |
|
| 9118 |
\begin{align*}
t^{2} y^{\prime \prime }+2 y^{\prime } t -a \,t^{2} y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✓ |
0.672 |
|
| 9119 |
\begin{align*}
6 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (50 x^{2}+1\right ) y^{\prime }+\left (30 x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.673 |
|
| 9120 |
\begin{align*}
y^{\prime \prime }-y&=9 x \,{\mathrm e}^{2 x} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 7 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.673 |
|
| 9121 |
\begin{align*}
y^{\prime \prime }+y&={\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.673 |
|
| 9122 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y&=16 x^{2} {\mathrm e}^{-x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.673 |
|
| 9123 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.673 |
|
| 9124 |
\begin{align*}
\left (x^{2}+x -6\right ) y^{\prime \prime }+\left (x +3\right ) y^{\prime }+\left (x -2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.673 |
|
| 9125 |
\begin{align*}
\left (2+x \right ) y^{\prime \prime }+3 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.673 |
|
| 9126 |
\begin{align*}
y^{\prime } x -\sin \left (x \right )&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.673 |
|
| 9127 |
\begin{align*}
y^{\prime \prime } x +y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.673 |
|
| 9128 |
\begin{align*}
x^{\prime }-y^{\prime }+y&=-{\mathrm e}^{t} \\
x+y^{\prime }-y&={\mathrm e}^{2 t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.674 |
|
| 9129 |
\begin{align*}
y^{\prime }-2 y&=x^{2} \\
y \left (1\right ) &= 1 \\
\end{align*} Series expansion around \(x=1\). |
✓ |
✓ |
✓ |
✓ |
0.674 |
|
| 9130 |
\begin{align*}
y^{\prime \prime }-y^{\prime } x -y x -x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.674 |
|
| 9131 |
\begin{align*}
x y y^{\prime \prime }-x {y^{\prime }}^{2}+a y y^{\prime }+y^{3} b x&=0 \\
\end{align*} |
✗ |
✗ |
✗ |
✗ |
0.674 |
|
| 9132 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+3 y&=9 x^{2}+4 \\
y \left (0\right ) &= 6 \\
y^{\prime }\left (0\right ) &= 8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.674 |
|
| 9133 |
\begin{align*}
5 x^{\prime }-3 y^{\prime }&=x+y \\
3 x^{\prime }-y^{\prime }&=t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.674 |
|
| 9134 |
\begin{align*}
x^{\prime }&=-2 x-2 y \\
y^{\prime }&=-2 x+y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.674 |
|
| 9135 |
\begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.674 |
|
| 9136 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.674 |
|
| 9137 |
\begin{align*}
5 y+2 y^{\prime }+y^{\prime \prime }&=4 \cos \left (2 x \right )+\sin \left (2 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.674 |
|
| 9138 |
\begin{align*}
y^{\prime \prime }-\sin \left (x \right ) y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.674 |
|
| 9139 |
\begin{align*}
y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y&=0 \\
y \left (0\right ) &= 1 \\
y \left (2\right ) &= 0 \\
y \left (\infty \right ) &= 0 \\
\end{align*} |
✗ |
✓ |
✓ |
✓ |
0.674 |
|
| 9140 |
\begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right )^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.674 |
|
| 9141 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=\sin \left ({\mathrm e}^{-x}\right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.675 |
|
| 9142 |
\begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+4 y^{\prime }-4 y&=10 \,{\mathrm e}^{-t} \\
y \left (0\right ) &= 5 \\
y^{\prime }\left (0\right ) &= -2 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.675 |
|
| 9143 |
\begin{align*}
x_{1}^{\prime }&=x_{1}-3 x_{2} \\
x_{2}^{\prime }&=3 x_{1}+x_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.675 |
|
| 9144 |
\begin{align*}
y^{\prime \prime }+{\mathrm e}^{x} y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.675 |
|
| 9145 |
\begin{align*}
y^{\prime \prime }&=x {y^{\prime }}^{2} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.675 |
|
| 9146 |
\begin{align*}
y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime }&=x \,{\mathrm e}^{x}-3 x^{2} \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.675 |
|
| 9147 |
\begin{align*}
y^{\prime \prime }+\frac {2 y^{\prime }}{2+x}+y&=0 \\
\end{align*} Series expansion around \(x=-2\). |
✓ |
✓ |
✓ |
✓ |
0.675 |
|
| 9148 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }-3 y&=-2 \\
y \left (0\right ) &= {\frac {2}{3}} \\
y^{\prime }\left (0\right ) &= 8 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.675 |
|
| 9149 |
\begin{align*}
y^{\prime \prime }+2 y^{\prime }-3 y&=x \,{\mathrm e}^{x} \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✗ |
0.675 |
|
| 9150 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }+2 y&=t^{2} {\mathrm e}^{t}+7 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.675 |
|
| 9151 |
\begin{align*}
y^{\prime }+2 y&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✗ |
0.675 |
|
| 9152 |
\begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=4 \cos \left (x \right )-2 \sin \left (x \right ) \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.676 |
|
| 9153 |
\begin{align*}
x \left (-x^{2}+1\right )^{2} y^{\prime \prime }+\left (-x^{2}+1\right ) \left (3 x^{2}+1\right ) y^{\prime }+4 x \left (x^{2}+1\right ) y&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.676 |
|
| 9154 |
\begin{align*}
y^{\prime }-a \left (t \right ) y&=\delta \left (t \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.676 |
|
| 9155 |
\begin{align*}
f^{\prime \prime }+2 \left (z -1\right ) f^{\prime }+4 f&=0 \\
\end{align*} Series expansion around \(z=0\). |
✓ |
✓ |
✓ |
✓ |
0.677 |
|
| 9156 |
\begin{align*}
x^{\prime \prime }+4 x^{\prime }+3 x&={\mathrm e}^{-3 t} \\
x \left (0\right ) &= {\frac {1}{2}} \\
x^{\prime }\left (0\right ) &= -2 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.677 |
|
| 9157 |
\begin{align*}
y^{\prime \prime }+y&={\mathrm e}^{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.677 |
|
| 9158 |
\begin{align*}
y^{\prime \prime }+y&=\sin \left (x \right ) \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.677 |
|
| 9159 |
\begin{align*}
x^{\prime \prime }-3 x^{\prime }-40 x&=2 \,{\mathrm e}^{-t} \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.677 |
|
| 9160 |
\(\left [\begin {array}{ccc} 1 & -1 & -1 \\ 1 & 3 & 1 \\ -3 & -6 & 6 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.677 |
|
| 9161 |
\(\left [\begin {array}{ccc} -5 & -12 & 6 \\ 1 & 5 & -1 \\ -7 & -10 & 8 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.677 |
|
| 9162 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }-10 y&=35 \,{\mathrm e}^{5 x}+12 \,{\mathrm e}^{4 x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.677 |
|
| 9163 |
\begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (-x^{2}+2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.677 |
|
| 9164 |
\begin{align*}
4 x^{2} y^{\prime \prime }+8 y^{\prime } x +\left (1-4 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.677 |
|
| 9165 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime }+8 y&=\sin \left (t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.677 |
|
| 9166 |
\begin{align*}
x^{\prime }&=4 x-y \\
y^{\prime }&=-4 x+4 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.677 |
|
| 9167 |
\begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=x^{2} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.677 |
|
| 9168 |
\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*} |
✓ |
✓ |
✓ |
✓ |
0.677 |
|
| 9169 |
\begin{align*}
y^{\prime \prime }-y&=\frac {2}{{\mathrm e}^{x}-{\mathrm e}^{-x}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.677 |
|
| 9170 |
\begin{align*}
x_{1}^{\prime }&=-2 x_{1}-x_{3} \\
x_{2}^{\prime }&=-x_{2} \\
x_{3}^{\prime }&=x_{1} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| 9171 |
\begin{align*}
\cos \left (x \right ) y^{\prime \prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| 9172 |
\(\left [\begin {array}{ccc} -2 & 6 & -18 \\ 12 & -23 & 66 \\ 5 & -10 & 29 \end {array}\right ]\) |
✓ |
N/A |
N/A |
N/A |
0.678 |
|
| 9173 |
\begin{align*}
y^{\prime \prime }+9 y&=24 \sin \left (t \right ) \left (\operatorname {Heaviside}\left (t \right )+\operatorname {Heaviside}\left (t -\pi \right )\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| 9174 |
\begin{align*}
y^{\prime \prime }-3 y^{\prime }-10 y&=-4 \cos \left (x \right )+7 \sin \left (x \right ) \\
y \left (0\right ) &= 8 \\
y^{\prime }\left (0\right ) &= -5 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| 9175 |
\begin{align*}
y^{\prime }&=x^{2} \sin \left (x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| 9176 |
\begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y&=-3 t \,{\mathrm e}^{-t} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| 9177 |
\begin{align*}
3 y-\left (x +3\right ) y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.678 |
|
| 9178 |
\begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=20 \,{\mathrm e}^{-2 x} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| 9179 |
\begin{align*}
2 y-y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=0\). |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| 9180 |
\begin{align*}
x^{\prime }&=2 x-7 y \\
y^{\prime }&=3 x-8 y \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| 9181 |
\begin{align*}
y^{\prime \prime }+10 y^{\prime }+25 y&=\frac {{\mathrm e}^{-5 x} \ln \left (x \right )}{x^{2}} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| 9182 |
\begin{align*}
x_{1}^{\prime }&=3 x_{1}-2 x_{2}+1 \\
x_{2}^{\prime }&=x_{1}+t \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| 9183 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=x^{3}+6 x^{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| 9184 |
\begin{align*}
y^{\prime \prime }+25 y&=\sin \left (5 x \right ) \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| 9185 |
\begin{align*}
y^{\prime \prime }-y&=5 \,{\mathrm e}^{x} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| 9186 |
\begin{align*}
y^{\prime \prime }-y^{\prime }+y&=x^{3}-2 x^{2}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| 9187 |
\begin{align*}
y^{\prime \prime }+5 y^{\prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.679 |
|
| 9188 |
\begin{align*}
y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y&=4 \,{\mathrm e}^{-x \left (2+x \right )} \\
\end{align*} |
✓ |
✓ |
✓ |
✗ |
0.679 |
|
| 9189 |
\begin{align*}
t^{2} y^{\prime \prime }+y^{\prime } t +\left (1+t \right ) y&=0 \\
\end{align*} Series expansion around \(t=0\). |
✓ |
✓ |
✓ |
✗ |
0.679 |
|
| 9190 |
\begin{align*}
x_{1}^{\prime }&=-7 x_{1}+6 x_{3} \\
x_{2}^{\prime }&=5 x_{2} \\
x_{3}^{\prime }&=6 x_{1}+2 x_{3} \\
\end{align*} |
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✓ |
✓ |
✓ |
0.679 |
|
| 9191 |
\begin{align*}
y_{1}^{\prime }&=y_{1}+y_{2} \\
y_{2}^{\prime }&=y_{1}-y_{2} \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.679 |
|
| 9192 |
\begin{align*}
y^{\prime \prime }&=0 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.679 |
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| 9193 |
\begin{align*}
x^{\prime }&=x \\
y^{\prime }&=3 y+z \\
z^{\prime }&=z-y \\
\end{align*} |
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✓ |
0.679 |
|
| 9194 |
\begin{align*}
y^{\prime \prime }+y&=\sin \left (x \right ) \\
y^{\prime }\left (1\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
✓ |
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✓ |
0.679 |
|
| 9195 |
\begin{align*}
y^{\prime \prime }&=-\frac {\left (x^{2} \sin \left (x \right )-2 \cos \left (x \right ) x \right ) y^{\prime }}{x^{2} \cos \left (x \right )}-\frac {\left (2 \cos \left (x \right )-x \sin \left (x \right )\right ) y}{x^{2} \cos \left (x \right )} \\
\end{align*} |
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✓ |
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0.679 |
|
| 9196 |
\begin{align*}
y^{\prime \prime }+3 y^{\prime } x -{\mathrm e}^{x} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
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0.679 |
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| 9197 |
\begin{align*}
y^{\prime \prime \prime }+4 y^{\prime }&=\sec \left (2 t \right ) \\
\end{align*} |
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0.679 |
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| 9198 |
\begin{align*}
y^{\prime \prime }+\frac {y}{4 x^{2}}&=0 \\
\end{align*} Series expansion around \(x=0\). |
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0.679 |
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| 9199 |
\begin{align*}
{y^{\prime }}^{2}-y^{\prime } x +y&=0 \\
\end{align*} |
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0.679 |
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| 9200 |
\begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=x^{2} {\mathrm e}^{-x}+1 \\
\end{align*} |
✓ |
✓ |
✓ |
✓ |
0.679 |
|