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\[
{} y^{\prime \prime }-6 y^{\prime }-7 y = 0
\]
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\[
{} y^{\prime \prime }-y^{\prime }-12 y = 0
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\[
{} y^{\prime \prime }+5 y^{\prime }+6 y = 0
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+5 y = 0
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+y = 0
\]
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\[
{} y^{\prime \prime }+2 y = 0
\]
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\[
{} y^{\prime \prime }-y^{\prime }-6 y = {\mathrm e}^{4 t}
\]
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\[
{} y^{\prime \prime }+6 y^{\prime }+8 y = 2 \,{\mathrm e}^{-3 t}
\]
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\[
{} y^{\prime \prime }-y^{\prime }-2 y = 5 \,{\mathrm e}^{3 t}
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+13 y = {\mathrm e}^{-t}
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+13 y = -3 \,{\mathrm e}^{-2 t}
\]
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\[
{} y^{\prime \prime }+7 y^{\prime }+10 y = {\mathrm e}^{-2 t}
\]
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\[
{} y^{\prime \prime }-5 y^{\prime }+4 y = {\mathrm e}^{4 t}
\]
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\[
{} y^{\prime \prime }+y^{\prime }-6 y = 4 \,{\mathrm e}^{-3 t}
\]
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\[
{} y^{\prime \prime }+6 y^{\prime }+8 y = {\mathrm e}^{-t}
\]
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\[
{} y^{\prime \prime }+7 y^{\prime }+12 y = 3 \,{\mathrm e}^{-t}
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+13 y = -3 \,{\mathrm e}^{-2 t}
\]
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\[
{} y^{\prime \prime }+7 y^{\prime }+10 y = {\mathrm e}^{-2 t}
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+3 y = {\mathrm e}^{-\frac {t}{2}}
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+3 y = {\mathrm e}^{-2 t}
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+3 y = {\mathrm e}^{-4 t}
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-\frac {t}{2}}
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-2 t}
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-4 t}
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-t}
\]
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\[
{} y^{\prime \prime }-5 y^{\prime }+4 y = 5
\]
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\[
{} y^{\prime \prime }+5 y^{\prime }+6 y = 2
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+10 y = 10
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+6 y = -8
\]
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\[
{} y^{\prime \prime }+9 y = {\mathrm e}^{-t}
\]
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\[
{} y^{\prime \prime }+4 y = 2 \,{\mathrm e}^{-2 t}
\]
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\[
{} y^{\prime \prime }+2 y = -3
\]
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\[
{} y^{\prime \prime }+4 y = {\mathrm e}^{t}
\]
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\[
{} y^{\prime \prime }+9 y = 6
\]
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\[
{} y^{\prime \prime }+2 y = -{\mathrm e}^{t}
\]
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\[
{} y^{\prime \prime }+4 y = -3 t^{2}+2 t +3
\]
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\[
{} y^{\prime \prime }+2 y^{\prime } = 3 t +2
\]
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\[
{} y^{\prime \prime }+4 y^{\prime } = 3 t +2
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = t^{2}
\]
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\[
{} y^{\prime \prime }+4 y = t -\frac {1}{20} t^{2}
\]
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\[
{} y^{\prime \prime }+5 y^{\prime }+6 y = 4+{\mathrm e}^{-t}
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{-t}-4
\]
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\[
{} y^{\prime \prime }+6 y^{\prime }+8 y = 2 t +{\mathrm e}^{-t}
\]
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\[
{} y^{\prime \prime }+6 y^{\prime }+8 y = 2 t +{\mathrm e}^{t}
\]
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\[
{} y^{\prime \prime }+4 y = t +{\mathrm e}^{-t}
\]
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\[
{} y^{\prime \prime }+4 y = 6+t^{2}+{\mathrm e}^{t}
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = \cos \left (t \right )
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = 5 \cos \left (t \right )
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = \sin \left (t \right )
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = 2 \sin \left (t \right )
\]
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\[
{} y^{\prime \prime }+6 y^{\prime }+8 y = \cos \left (t \right )
\]
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\[
{} y^{\prime \prime }+6 y^{\prime }+8 y = -4 \cos \left (3 t \right )
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+13 y = 3 \cos \left (2 t \right )
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+20 y = -\cos \left (5 t \right )
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+20 y = -3 \sin \left (2 t \right )
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+y = \cos \left (3 t \right )
\]
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\[
{} y^{\prime \prime }+6 y^{\prime }+8 y = \cos \left (t \right )
\]
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\[
{} y^{\prime \prime }+6 y^{\prime }+8 y = 2 \cos \left (3 t \right )
\]
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\[
{} y^{\prime \prime }+6 y^{\prime }+20 y = -3 \sin \left (2 t \right )
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+y = 2 \cos \left (2 t \right )
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+y = \cos \left (3 t \right )
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+20 y = 3+2 \cos \left (2 t \right )
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-t} \cos \left (t \right )
\]
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\[
{} y^{\prime \prime }+9 y = \cos \left (t \right )
\]
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\[
{} y^{\prime \prime }+9 y = 5 \sin \left (2 t \right )
\]
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\[
{} y^{\prime \prime }+4 y = -\cos \left (\frac {t}{2}\right )
\]
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\[
{} y^{\prime \prime }+4 y = 3 \cos \left (2 t \right )
\]
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\[
{} y^{\prime \prime }+9 y = 2 \cos \left (3 t \right )
\]
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\[
{} y^{\prime \prime }+4 y = 8
\]
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\[
{} y^{\prime \prime }-4 y = {\mathrm e}^{2 t}
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+5 y = 2 \,{\mathrm e}^{t}
\]
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\[
{} y^{\prime \prime }+6 y^{\prime }+13 y = 13 \operatorname {Heaviside}\left (t -4\right )
\]
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\[
{} y^{\prime \prime }+4 y = \cos \left (2 t \right )
\]
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\[
{} y^{\prime \prime }+3 y = \operatorname {Heaviside}\left (t -4\right ) \cos \left (5 t -20\right )
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+9 y = 20 \operatorname {Heaviside}\left (t -2\right ) \sin \left (t -2\right )
\]
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\[
{} y^{\prime \prime }+3 y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 1 & 1\le t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+3 y = 5 \delta \left (t -2\right )
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+5 y = \delta \left (t -3\right )
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+2 y = -2 \delta \left (t -2\right )
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+3 y = \delta \left (t -1\right )-3 \delta \left (t -4\right )
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+2 y = {\mathrm e}^{-2 t} \sin \left (4 t \right )
\]
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\[
{} y^{\prime \prime }+y^{\prime }+5 y = \operatorname {Heaviside}\left (t -2\right ) \sin \left (4 t -8\right )
\]
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\[
{} y^{\prime \prime }+y^{\prime }+8 y = \left (1-\operatorname {Heaviside}\left (t -4\right )\right ) \cos \left (t -4\right )
\]
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\[
{} y^{\prime \prime }+y^{\prime }+3 y = \left (1-\operatorname {Heaviside}\left (t -2\right )\right ) {\mathrm e}^{-\frac {t}{10}+\frac {1}{5}} \sin \left (t -2\right )
\]
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\[
{} y^{\prime \prime }+16 y = 0
\]
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\[
{} y^{\prime \prime }+4 y = \sin \left (2 t \right )
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+y = 0
\]
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\[
{} y^{\prime \prime }+16 y = t
\]
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\[
{} y^{\prime \prime } = \frac {1+x}{x -1}
\]
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\[
{} x^{2} y^{\prime \prime } = 1
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+8 y = {\mathrm e}^{-x^{2}}
\]
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\[
{} x^{2} y^{\prime \prime }+3 x y^{\prime } = 0
\]
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\[
{} y^{\prime \prime } = \sin \left (2 x \right )
\]
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\[
{} y^{\prime \prime }-3 = x
\]
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\[
{} x y^{\prime \prime }+2 = \sqrt {x}
\]
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\[
{} x y^{\prime \prime }+4 y^{\prime } = 18 x^{2}
\]
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\[
{} x y^{\prime \prime } = 2 y^{\prime }
\]
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\[
{} y^{\prime \prime } = y^{\prime }
\]
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\[
{} y^{\prime \prime }+2 y^{\prime } = 8 \,{\mathrm e}^{2 x}
\]
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\[
{} x y^{\prime \prime } = y^{\prime }-2 x^{2} y^{\prime }
\]
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