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\[
{} y^{\prime \prime }-5 y^{\prime }+6 y = x^{2} {\mathrm e}^{3 x}
\]
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\[
{} y^{\prime \prime }-5 y^{\prime }+6 y = x^{2} \cos \left (2 x \right )
\]
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\[
{} y^{\prime \prime }-5 y^{\prime }+6 y = x^{2} {\mathrm e}^{3 x} \sin \left (2 x \right )
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+20 y = {\mathrm e}^{4 x} \sin \left (2 x \right )
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+20 y = {\mathrm e}^{2 x} \sin \left (4 x \right )
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+20 y = x^{3} \sin \left (4 x \right )
\]
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\[
{} y^{\prime \prime }-10 y^{\prime }+25 y = 3 x^{2} {\mathrm e}^{5 x}
\]
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\[
{} y^{\prime \prime }-10 y^{\prime }+25 y = 3 x^{4}
\]
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\[
{} y^{\prime \prime }-6 y^{\prime }+9 y = 27 \,{\mathrm e}^{6 x}+25 \sin \left (6 x \right )
\]
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\[
{} y^{\prime \prime }+9 y = 25 x \cos \left (2 x \right )+3 \sin \left (3 x \right )
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+5 y = 5 \sin \left (x \right )^{2}
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+5 y = 20 \sinh \left (x \right )
\]
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\[
{} y^{\prime \prime }+y = \cot \left (x \right )
\]
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\[
{} y^{\prime \prime }+4 y = \csc \left (2 x \right )
\]
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\[
{} y^{\prime \prime }-7 y^{\prime }+10 y = 6 \,{\mathrm e}^{3 x}
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+4 y = \left (24 x^{2}+2\right ) {\mathrm e}^{2 x}
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+4 y = \frac {{\mathrm e}^{-2 x}}{x^{2}+1}
\]
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\[
{} y^{\prime \prime }-y^{\prime }-6 y = 12 \,{\mathrm e}^{2 x}
\]
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\[
{} 2 y^{\prime \prime }-7 y^{\prime }+3 = 0
\]
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\[
{} y^{\prime \prime }-9 y^{\prime }+14 y = 98 x^{2}
\]
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\[
{} y^{\prime \prime }-12 y^{\prime }+36 y = 25 \sin \left (3 x \right )
\]
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\[
{} y^{\prime \prime }-9 y^{\prime }+14 y = 576 x^{2} {\mathrm e}^{-x}
\]
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\[
{} y^{\prime \prime }-12 y^{\prime }+36 y = 81 \,{\mathrm e}^{3 x}
\]
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\[
{} y^{\prime \prime }-12 y^{\prime }+36 y = 3 x \,{\mathrm e}^{6 x}-2 \,{\mathrm e}^{6 x}
\]
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\[
{} y^{\prime \prime }+36 y = 6 \sec \left (6 x \right )
\]
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\[
{} y^{\prime \prime }+6 y^{\prime }+9 y = 10 \,{\mathrm e}^{-3 x}
\]
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\[
{} y^{\prime \prime }+6 y^{\prime }+9 y = 2 \cos \left (2 x \right )
\]
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\[
{} 4 y^{\prime \prime }-12 y^{\prime }+9 y = x \,{\mathrm e}^{\frac {3 x}{2}}
\]
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\[
{} 3 y^{\prime \prime }+8 y^{\prime }-3 y = 123 x \sin \left (3 x \right )
\]
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\[
{} y^{\prime \prime }-4 y = t^{3}
\]
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\[
{} y^{\prime \prime }+4 y = 20 \,{\mathrm e}^{4 t}
\]
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\[
{} y^{\prime \prime }+4 y = \sin \left (2 t \right )
\]
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\[
{} y^{\prime \prime }+4 y = 3 \operatorname {Heaviside}\left (t -2\right )
\]
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\[
{} y^{\prime \prime }+5 y^{\prime }+6 y = {\mathrm e}^{4 t}
\]
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\[
{} y^{\prime \prime }-5 y^{\prime }+6 y = t^{2} {\mathrm e}^{4 t}
\]
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\[
{} y^{\prime \prime }-5 y^{\prime }+6 y = 7
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+13 y = {\mathrm e}^{2 t} \sin \left (3 t \right )
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+13 y = 4 t +2 \,{\mathrm e}^{2 t} \sin \left (3 t \right )
\]
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\[
{} y^{\prime \prime }+9 y = 27 t^{3}
\]
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\[
{} y^{\prime \prime }+8 y^{\prime }+7 y = 165 \,{\mathrm e}^{4 t}
\]
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\[
{} y^{\prime \prime }-6 y^{\prime }+9 y = t^{2} {\mathrm e}^{3 t}
\]
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\[
{} y^{\prime \prime } = {\mathrm e}^{t} \sin \left (t \right )
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+40 y = 122 \,{\mathrm e}^{-3 t}
\]
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\[
{} y^{\prime \prime }-9 y = 24 \,{\mathrm e}^{-3 t}
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+13 y = {\mathrm e}^{2 t} \sin \left (3 t \right )
\]
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\[
{} y^{\prime \prime }+4 y = 1
\]
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\[
{} y^{\prime \prime }+4 y = t
\]
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\[
{} y^{\prime \prime }+4 y = {\mathrm e}^{3 t}
\]
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\[
{} y^{\prime \prime }+4 y = \sin \left (2 t \right )
\]
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\[
{} y^{\prime \prime }+4 y = \sin \left (t \right )
\]
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\[
{} y^{\prime \prime }-6 y^{\prime }+9 y = 1
\]
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\[
{} y^{\prime \prime }-6 y^{\prime }+9 y = t
\]
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\[
{} y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{3 t}
\]
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\[
{} y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{-3 t}
\]
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\[
{} y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{t}
\]
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\[
{} y^{\prime \prime } = \operatorname {Heaviside}\left (t -2\right )
\]
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\[
{} y^{\prime \prime } = \operatorname {Heaviside}\left (t -2\right )
\]
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\[
{} y^{\prime \prime }+9 y = \operatorname {Heaviside}\left (t -10\right )
\]
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\[
{} y^{\prime \prime } = \left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+9 y = \left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right .
\]
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\[
{} y^{\prime \prime } = \delta \left (t -3\right )
\]
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\[
{} y^{\prime \prime } = \delta \left (t -1\right )-\delta \left (-4+t \right )
\]
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\[
{} y^{\prime \prime }+y = \delta \left (t \right )+\delta \left (t -\pi \right )
\]
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\[
{} y^{\prime \prime }+y = -2 \delta \left (t -\frac {\pi }{2}\right )
\]
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\[
{} y^{\prime \prime }+3 y^{\prime } = \delta \left (t \right )
\]
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\[
{} y^{\prime \prime }+3 y^{\prime } = \delta \left (t -1\right )
\]
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\[
{} y^{\prime \prime }+16 y = \delta \left (t -2\right )
\]
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\[
{} y^{\prime \prime }-16 y = \delta \left (t -10\right )
\]
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\[
{} y^{\prime \prime }+y = \delta \left (t \right )
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }-12 y = \delta \left (t \right )
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }-12 y = \delta \left (t -3\right )
\]
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\[
{} y^{\prime \prime }+6 y^{\prime }+9 y = \delta \left (-4+t \right )
\]
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\[
{} y^{\prime \prime }-12 y^{\prime }+45 y = \delta \left (t \right )
\]
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\[
{} y^{\prime \prime }+y^{\prime }-2 y = x^{3}
\]
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\[
{} x^{\prime \prime }+x = t \cos \left (t \right )-\cos \left (t \right )
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+2 y = x
\]
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\[
{} y^{\prime \prime }-7 y^{\prime }+12 y = 2
\]
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\[
{} y^{\prime \prime }+4 y = t
\]
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\[
{} y^{\prime \prime }+y = 2 \cos \left (t \right )
\]
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\[
{} y^{\prime \prime }+y = 8 \,{\mathrm e}^{2 t}
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+3 y = -{\mathrm e}^{-9 t}
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+3 y = 2 \,{\mathrm e}^{3 t}
\]
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\[
{} y^{\prime \prime }-y = 2 t -4
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = t^{2}
\]
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\[
{} y^{\prime \prime }+2 y^{\prime } = 3-4 t
\]
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\[
{} y^{\prime \prime }+y = \cos \left (2 t \right )
\]
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\[
{} y^{\prime \prime }+4 y = 4 \cos \left (t \right )-\sin \left (t \right )
\]
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\[
{} y^{\prime \prime }+4 y = \cos \left (2 t \right )+t
\]
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\[
{} y^{\prime \prime }+4 y = 3 t \,{\mathrm e}^{-t}
\]
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\[
{} y^{\prime \prime } = 3 t^{4}-2 t
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+13 y = 2 t \,{\mathrm e}^{-2 t} \sin \left (3 t \right )
\]
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\[
{} y^{\prime \prime }+y^{\prime }-2 y = -1
\]
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\[
{} 5 y^{\prime \prime }+y^{\prime }-4 y = -3
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }-8 y = 32 t
\]
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\[
{} 16 y^{\prime \prime }-8 y^{\prime }-15 y = 75 t
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+26 y = -338 t
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }-4 y = -32 t^{2}
\]
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\[
{} 8 y^{\prime \prime }+6 y^{\prime }+y = 5 t^{2}
\]
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\[
{} y^{\prime \prime }-6 y^{\prime }+8 y = -256 t^{3}
\]
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\[
{} y^{\prime \prime }-2 y^{\prime } = 52 \sin \left (3 t \right )
\]
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