| # | ODE | Mathematica | Maple | Sympy |
| \[
{} y^{\prime \prime }-\left (a +b \right ) y^{\prime }+a b y = f \left (t \right )
\]
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| \[
{} y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 4 & 0\le t <2 \\ 8 t & 2\le t <\infty \end {array}\right .
\]
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| \[
{} y^{\prime \prime }-3 y^{\prime }+2 y = \left \{\begin {array}{cc} {\mathrm e}^{t} & 0\le t <1 \\ {\mathrm e}^{2 t} & 1\le t <\infty \end {array}\right .
\]
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| \[
{} -y+y^{\prime } = \left \{\begin {array}{cc} 1 & 0\le t <2 \\ -1 & 2\le t <4 \\ 0 & 4\le t <\infty \end {array}\right .
\]
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| \[
{} 3 y+y^{\prime } = \left \{\begin {array}{cc} t & 0\le t <1 \\ 1 & 1\le t <\infty \end {array}\right .
\]
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| \[
{} -y+y^{\prime } = \left \{\begin {array}{cc} 0 & 0\le t <1 \\ t -1 & 1\le t <2 \\ -t +3 & 2\le t <3 \\ 0 & 3\le t <\infty \end {array}\right .
\]
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| \[
{} y+y^{\prime } = \left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t <\infty \end {array}\right .
\]
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| \[
{} y^{\prime \prime }-y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t <\infty \end {array}\right .
\]
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| \[
{} y^{\prime \prime }-4 y^{\prime }+4 y = \left \{\begin {array}{cc} 0 & 0\le t <2 \\ 4 & 2\le t <\infty \end {array}\right .
\]
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| \[
{} y^{\prime } = \left \{\begin {array}{cc} 0 & t =0 \\ \sin \left (\frac {1}{t}\right ) & \operatorname {otherwise} \end {array}\right .
\]
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| \[
{} y^{\prime }+2 y = \left \{\begin {array}{cc} 0 & 0\le t <1 \\ -3 & 1\le t \end {array}\right .
\]
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| \[
{} y^{\prime }+5 y = \left \{\begin {array}{cc} -5 & 0\le t <1 \\ 5 & 1\le t \end {array}\right .
\]
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| \[
{} y^{\prime }-3 y = \left \{\begin {array}{cc} 0 & 0\le t <2 \\ 2 & 2\le t <3 \\ 0 & 3\le t \end {array}\right .
\]
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| \[
{} y^{\prime }+2 y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right .
\]
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| \[
{} y^{\prime }-4 y = \left \{\begin {array}{cc} 12 \,{\mathrm e}^{t} & 0\le t <1 \\ 12 \,{\mathrm e} & 1\le t \end {array}\right .
\]
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| \[
{} 3 y+y^{\prime } = \left \{\begin {array}{cc} 10 \sin \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right .
\]
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| \[
{} y^{\prime \prime }+9 y = \operatorname {Heaviside}\left (t -3\right )
\]
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| \[
{} y^{\prime \prime }-5 y^{\prime }+4 y = \left \{\begin {array}{cc} 1 & 0\le t <5 \\ 0 & 5\le t \end {array}\right .
\]
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| \[
{} y^{\prime \prime }+5 y^{\prime }+6 y = \left \{\begin {array}{cc} 0 & 0\le t <1 \\ 6 & 1\le t <3 \\ 0 & 3\le t \end {array}\right .
\]
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| \[
{} y^{\prime \prime }+9 y = \operatorname {Heaviside}\left (t -2 \pi \right ) \sin \left (t \right )
\]
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| \[
{} y^{\prime \prime }+2 y^{\prime }+y = \operatorname {Heaviside}\left (t -3\right )
\]
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| \[
{} y^{\prime \prime }+2 y^{\prime }+y = \left \{\begin {array}{cc} {\mathrm e}^{-t} & 0\le t <4 \\ 0 & 4\le t \end {array}\right .
\]
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| \[
{} y^{\prime }+2 y = \delta \left (t -1\right )
\]
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| \[
{} y^{\prime }-3 y = 3+\delta \left (t -2\right )
\]
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| \[
{} y^{\prime }-4 y = \delta \left (t -4\right )
\]
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| \[
{} y+y^{\prime } = \delta \left (t -1\right )-\delta \left (t -3\right )
\]
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| \[
{} y^{\prime \prime }+4 y = \delta \left (t -\pi \right )
\]
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| \[
{} y^{\prime \prime }-y = \delta \left (t -1\right )-\delta \left (t -2\right )
\]
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| \[
{} y^{\prime \prime }+4 y^{\prime }+3 y = 2 \delta \left (t -2\right )
\]
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| \[
{} y^{\prime \prime }+4 y = \delta \left (t -\pi \right )-\delta \left (t -2 \pi \right )
\]
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| \[
{} y^{\prime \prime }+4 y^{\prime }+4 y = 3 \delta \left (t -1\right )
\]
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| \[
{} y^{\prime \prime }+4 y^{\prime }+5 y = 3 \delta \left (t -\pi \right )
\]
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| \[
{} y^{\prime }-3 y = \operatorname {Heaviside}\left (t -2\right )
\]
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| \[
{} y^{\prime }+4 y = \delta \left (t -3\right )
\]
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| \[
{} y^{\prime \prime }-y = \delta \left (t -1\right )-\delta \left (t -2\right )
\]
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| \[
{} y^{\prime \prime }-6 y^{\prime }+9 y = \delta \left (t -3\right )
\]
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| \[
{} y^{\prime \prime }+9 y = 0
\]
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| \[
{} y^{\prime \prime }-2 y^{\prime }+y = 0
\]
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| \[
{} y^{\prime \prime }+4 y^{\prime }+3 y = 0
\]
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| \[
{} y^{\prime \prime \prime }+y^{\prime } = 0
\]
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| \[
{} y^{\prime \prime }-y = 0
\]
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| \[
{} y^{\prime \prime }-2 y^{\prime }+y = 0
\]
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| \[
{} y^{\prime \prime }+k^{2} y = 0
\]
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| \[
{} y^{\prime \prime }-3 y^{\prime }+2 y = 0
\]
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| \[
{} \left (-t^{2}+1\right ) y^{\prime \prime }+2 y = 0
\]
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| \[
{} \left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y = 0
\]
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| \[
{} \left (t -1\right ) y^{\prime \prime }-t y^{\prime }+y = 0
\]
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| \[
{} \left (t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y = 0
\]
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| \[
{} \left (t^{2}+1\right ) y^{\prime \prime }-4 t y^{\prime }+6 y = 0
\]
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| \[
{} \left (-t^{2}+1\right ) y^{\prime \prime }-6 t y^{\prime }-4 y = 0
\]
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| \[
{} y^{\prime \prime }+\frac {t y^{\prime }}{-t^{2}+1}+\frac {y}{t +1} = 0
\]
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| \[
{} y^{\prime \prime }+\frac {\left (1-t \right ) y^{\prime }}{t}+\frac {\left (1-\cos \left (t \right )\right ) y}{t^{3}} = 0
\]
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| \[
{} y^{\prime \prime }+3 t \left (1-t \right ) y^{\prime }+\frac {\left (1-{\mathrm e}^{t}\right ) y}{t} = 0
\]
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| \[
{} y^{\prime \prime }+\frac {y^{\prime }}{t}+\frac {\left (1-t \right ) y}{t^{3}} = 0
\]
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| \[
{} t y^{\prime \prime }+\left (1-t \right ) y^{\prime }+4 t y = 0
\]
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✓ |
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| \[
{} 2 t y^{\prime \prime }+y^{\prime }+t y = 0
\]
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| \[
{} t^{2} y^{\prime \prime }+2 t y^{\prime }+t^{2} y = 0
\]
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| \[
{} t^{2} y^{\prime \prime }+t \,{\mathrm e}^{t} y^{\prime }+4 \left (1-4 t \right ) y = 0
\]
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| \[
{} t y^{\prime \prime }+\left (1-t \right ) y^{\prime }+\lambda y = 0
\]
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| \[
{} t^{2} y^{\prime \prime }+3 t \left (1+3 t \right ) y^{\prime }+\left (-t^{2}+1\right ) y = 0
\]
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| \[
{} t^{2} y^{\prime \prime }+5 t y^{\prime }+4 y = 0
\]
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| \[
{} t y^{\prime \prime }-2 y^{\prime }+t y = 0
\]
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| \[
{} 2 t^{2} y^{\prime \prime }-t y^{\prime }+\left (t +1\right ) y = 0
\]
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| \[
{} t^{2} y^{\prime \prime }-t \left (t +1\right ) y^{\prime }+y = 0
\]
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| \[
{} 2 t^{2} y^{\prime \prime }-t y^{\prime }+\left (1-t \right ) y = 0
\]
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| \[
{} t^{2} y^{\prime \prime }+t^{2} y^{\prime }-2 y = 0
\]
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| \[
{} t^{2} y^{\prime \prime }+2 t y^{\prime }-a \,t^{2} y = 0
\]
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| \[
{} t y^{\prime \prime }+\left (t -1\right ) y^{\prime }-2 y = 0
\]
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✓ |
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| \[
{} t y^{\prime \prime }-4 y = 0
\]
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✓ |
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✓ |
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| \[
{} t^{2} \left (1-t \right ) y^{\prime \prime }+\left (t^{2}+t \right ) y^{\prime }+\left (1-2 t \right ) y = 0
\]
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| \[
{} t^{2} y^{\prime \prime }+t \left (t +1\right ) y^{\prime }-y = 0
\]
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| \[
{} t^{2} y^{\prime \prime }+t \left (1-2 t \right ) y^{\prime }+\left (t^{2}-t +1\right ) y = 0
\]
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✓ |
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| \[
{} t^{2} \left (t +1\right ) y^{\prime \prime }-t \left (2 t +1\right ) y^{\prime }+\left (2 t +1\right ) y = 0
\]
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✓ |
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| \[
{} t y^{\prime \prime }+2 \left (i t -k \right ) y^{\prime }-2 i k y = 0
\]
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✓ |
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| \[
{} [y_{1}^{\prime }\left (t \right ) = y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right ) y_{2} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = y_{1} \left (t \right )+y_{2} \left (t \right )+t^{2}, y_{2}^{\prime }\left (t \right ) = -y_{1} \left (t \right )+y_{2} \left (t \right )+1]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = \sin \left (t \right ) y_{1} \left (t \right ), y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right )+\cos \left (t \right ) y_{2} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = t \sin \left (y_{1} \left (t \right )\right )-y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right )+t \cos \left (y_{2} \left (t \right )\right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = y_{1} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )+y_{4} \left (t \right ), y_{3}^{\prime }\left (t \right ) = y_{4} \left (t \right ), y_{4}^{\prime }\left (t \right ) = y_{2} \left (t \right )+2 y_{3} \left (t \right )]
\]
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| \[
{} \left [y_{1}^{\prime }\left (t \right ) = \frac {y_{1} \left (t \right )}{2}-y_{2} \left (t \right )+5, y_{2}^{\prime }\left (t \right ) = -y_{1} \left (t \right )+\frac {y_{2} \left (t \right )}{2}-5\right ]
\]
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✓ |
✓ |
✓ |
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| \[
{} [y_{1}^{\prime }\left (t \right ) = 5 y_{1} \left (t \right )-2 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 4 y_{1} \left (t \right )-y_{2} \left (t \right )]
\]
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✓ |
✓ |
✓ |
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| \[
{} [y_{1}^{\prime }\left (t \right ) = 3 y_{1} \left (t \right )-y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 4 y_{1} \left (t \right )-y_{2} \left (t \right )]
\]
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✓ |
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| \[
{} [y_{1}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )-y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 3 y_{1} \left (t \right )-2 y_{2} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = y_{2} \left (t \right )+t, y_{2}^{\prime }\left (t \right ) = -y_{1} \left (t \right )-t]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = -y_{1} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 3 y_{2} \left (t \right )]
\]
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✓ |
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| \[
{} [y_{1}^{\prime }\left (t \right ) = y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -2 y_{1} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )+y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 2 y_{2} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = -y_{1} \left (t \right )+2 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -2 y_{1} \left (t \right )-y_{2} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )-y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 3 y_{1} \left (t \right )-2 y_{2} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )-5 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right )-2 y_{2} \left (t \right )]
\]
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✓ |
✓ |
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| \[
{} [y_{1}^{\prime }\left (t \right ) = 3 y_{1} \left (t \right )-4 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right )-y_{2} \left (t \right )]
\]
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✓ |
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| \[
{} [y_{1}^{\prime }\left (t \right ) = -y_{1} \left (t \right )+3 y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 2 y_{2} \left (t \right ), y_{3}^{\prime }\left (t \right ) = y_{3} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = 4 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -y_{1} \left (t \right ), y_{3}^{\prime }\left (t \right ) = y_{1} \left (t \right )+4 y_{2} \left (t \right )-y_{3} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )-y_{2} \left (t \right )+{\mathrm e}^{t}, y_{2}^{\prime }\left (t \right ) = 3 y_{1} \left (t \right )-2 y_{2} \left (t \right )+{\mathrm e}^{t}]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = -y_{1} \left (t \right )+2 y_{2} \left (t \right )+5, y_{2}^{\prime }\left (t \right ) = -2 y_{1} \left (t \right )-y_{2} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )-5 y_{2} \left (t \right )+2 \cos \left (t \right ), y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right )-2 y_{2} \left (t \right )+\cos \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = -y_{1} \left (t \right )-4 y_{2} \left (t \right )+4, y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right )-y_{2} \left (t \right )+1]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )+y_{2} \left (t \right )+{\mathrm e}^{t}, y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right )+2 y_{2} \left (t \right )-{\mathrm e}^{t}]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = 5 y_{1} \left (t \right )+2 y_{2} \left (t \right )+t, y_{2}^{\prime }\left (t \right ) = -8 y_{1} \left (t \right )-3 y_{2} \left (t \right )-2 t]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = -2 y_{1} \left (t \right )+2 y_{2} \left (t \right )+y_{3} \left (t \right )+{\mathrm e}^{-2 t}, y_{2}^{\prime }\left (t \right ) = -y_{2} \left (t \right ), y_{3}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )-2 y_{2} \left (t \right )-y_{3} \left (t \right )-{\mathrm e}^{-2 t}]
\]
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|