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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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\[
{} y^{\prime \prime }+6 y^{\prime }+13 y = 13 \operatorname {Heaviside}\left (-4+t \right )
\]
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\[
{} y^{\prime \prime }+4 y = \cos \left (2 t \right )
\]
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\[
{} y^{\prime \prime }+3 y = \operatorname {Heaviside}\left (-4+t \right ) \cos \left (-20+5 t \right )
\]
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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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\[
{} y^{\prime \prime }+2 y^{\prime }+3 y = \delta \left (t -1\right )-3 \delta \left (-4+t \right )
\]
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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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\[
{} y^{\prime \prime }+y^{\prime }+8 y = \left (1-\operatorname {Heaviside}\left (-4+t \right )\right ) \cos \left (-4+t \right )
\]
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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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\[
{} y^{\prime \prime }+4 y = \sin \left (2 t \right )
\]
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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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\[
{} y^{\prime \prime }+3 y^{\prime }+8 y = {\mathrm e}^{-x^{2}}
\]
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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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\[
{} y^{\prime \prime }+2 y^{\prime } = 8 \,{\mathrm e}^{2 x}
\]
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\[
{} y^{\prime \prime } = 2 y^{\prime }-6
\]
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\[
{} y^{\prime \prime }+4 y^{\prime } = 9 \,{\mathrm e}^{-3 x}
\]
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\[
{} y^{\prime \prime }+4 y^{\prime } = 9 \,{\mathrm e}^{-3 x}
\]
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\[
{} y^{\prime \prime }+2 y^{\prime } = 8 \,{\mathrm e}^{2 x}
\]
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\[
{} y^{\prime \prime } = 2 y^{\prime }-5 y+30 \,{\mathrm e}^{3 x}
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+3 y = 9 \,{\mathrm e}^{2 x}
\]
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\[
{} y^{\prime \prime }-6 y^{\prime }+8 y = {\mathrm e}^{4 x}
\]
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\[
{} y^{\prime \prime }+4 y = 24 \,{\mathrm e}^{2 x}
\]
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\[
{} y^{\prime \prime }+4 y = 24 \,{\mathrm e}^{2 x}
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }-8 y = 8 x^{2}-3
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }-8 y = 8 x^{2}-3
\]
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\[
{} y^{\prime \prime }-9 y = 36
\]
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\[
{} y^{\prime \prime }-3 y^{\prime }-10 y = -6 \,{\mathrm e}^{4 x}
\]
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\[
{} y^{\prime \prime }-3 y^{\prime }-10 y = 7 \,{\mathrm e}^{5 x}
\]
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\[
{} y^{\prime \prime }+6 y^{\prime }+9 y = 169 \sin \left (2 x \right )
\]
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\[
{} y^{\prime \prime }-3 y^{\prime }-10 y = {\mathrm e}^{4 x}
\]
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\[
{} y^{\prime \prime }-3 y^{\prime }-10 y = {\mathrm e}^{5 x}
\]
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\[
{} y^{\prime \prime }-3 y^{\prime }-10 y = -18 \,{\mathrm e}^{4 x}+14 \,{\mathrm e}^{5 x}
\]
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\[
{} y^{\prime \prime }-3 y^{\prime }-10 y = 35 \,{\mathrm e}^{5 x}+12 \,{\mathrm e}^{4 x}
\]
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\[
{} y^{\prime \prime }+9 y = 52 \,{\mathrm e}^{2 x}
\]
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\[
{} y^{\prime \prime }-6 y^{\prime }+9 y = 27 \,{\mathrm e}^{6 x}
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }-5 y = 30 \,{\mathrm e}^{-4 x}
\]
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\[
{} y^{\prime \prime }+3 y^{\prime } = {\mathrm e}^{\frac {x}{2}}
\]
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\[
{} y^{\prime \prime }-3 y^{\prime }-10 y = -5 \,{\mathrm e}^{3 x}
\]
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\[
{} y^{\prime \prime }+9 y = 10 \cos \left (2 x \right )+15 \sin \left (2 x \right )
\]
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\[
{} y^{\prime \prime }-6 y^{\prime }+9 y = 25 \sin \left (6 x \right )
\]
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\[
{} y^{\prime \prime }+3 y^{\prime } = 26 \cos \left (\frac {x}{3}\right )-12 \sin \left (\frac {x}{3}\right )
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }-5 y = \cos \left (x \right )
\]
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\[
{} y^{\prime \prime }-3 y^{\prime }-10 y = -4 \cos \left (x \right )+7 \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }-3 y^{\prime }-10 y = -200
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }-5 y = x^{3}
\]
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\[
{} y^{\prime \prime }-6 y^{\prime }+9 y = 18 x^{2}+3 x +4
\]
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\[
{} y^{\prime \prime }+9 y = 9 x^{4}-9
\]
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\[
{} y^{\prime \prime }+9 y = x^{3}
\]
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\[
{} y^{\prime \prime }+9 y = 25 x \cos \left (2 x \right )
\]
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\[
{} y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{2 x} \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }+9 y = 54 x^{2} {\mathrm e}^{3 x}
\]
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\[
{} y^{\prime \prime } = 6 x \,{\mathrm e}^{x} \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = \left (-6 x -8\right ) \cos \left (2 x \right )+\left (8 x -11\right ) \sin \left (2 x \right )
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = \left (12 x -4\right ) {\mathrm e}^{-5 x}
\]
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\[
{} y^{\prime \prime }+9 y = 39 x \,{\mathrm e}^{2 x}
\]
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\[
{} y^{\prime \prime }-3 y^{\prime }-10 y = -3 \,{\mathrm e}^{-2 x}
\]
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\[
{} y^{\prime \prime }+4 y^{\prime } = 20
\]
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\[
{} y^{\prime \prime }+4 y^{\prime } = x^{2}
\]
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\[
{} y^{\prime \prime }+9 y = 3 \sin \left (3 x \right )
\]
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\[
{} y^{\prime \prime }-6 y^{\prime }+9 y = 10 \,{\mathrm e}^{3 x}
\]
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\[
{} y^{\prime \prime }-3 y^{\prime }-10 y = \left (72 x^{2}-1\right ) {\mathrm e}^{2 x}
\]
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\[
{} y^{\prime \prime }-3 y^{\prime }-10 y = 4 x \,{\mathrm e}^{6 x}
\]
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\[
{} y^{\prime \prime }-10 y^{\prime }+25 y = 6 \,{\mathrm e}^{5 x}
\]
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\[
{} y^{\prime \prime }-10 y^{\prime }+25 y = 6 \,{\mathrm e}^{-5 x}
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+5 y = 24 \sin \left (3 x \right )
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+5 y = 8 \,{\mathrm e}^{-3 x}
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+5 y = {\mathrm e}^{2 x} \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+5 y = {\mathrm e}^{-x} \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+5 y = 100
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+5 y = {\mathrm e}^{-x}
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+5 y = 10 x^{2}+4 x +8
\]
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\[
{} y^{\prime \prime }+9 y = {\mathrm e}^{2 x} \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }+y = 6 \cos \left (x \right )-3 \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }+y = 6 \cos \left (2 x \right )-3 \sin \left (2 x \right )
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+5 y = x^{3} {\mathrm e}^{-x} \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+5 y = x^{3} {\mathrm e}^{2 x} \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }-5 y^{\prime }+6 y = x^{2} {\mathrm e}^{-7 x}+2 \,{\mathrm e}^{-7 x}
\]
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\[
{} y^{\prime \prime }-5 y^{\prime }+6 y = x^{2}
\]
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\[
{} y^{\prime \prime }-5 y^{\prime }+6 y = 4 \,{\mathrm e}^{-8 x}
\]
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\[
{} y^{\prime \prime }-5 y^{\prime }+6 y = 4 \,{\mathrm e}^{3 x}
\]
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