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\[
{} y^{\prime \prime }+4 y^{\prime }-12 y = \delta \left (t -3\right )
\]
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\[
{} y^{\prime \prime }+6 y^{\prime }+9 y = \delta \left (t -4\right )
\]
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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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\[
{} x {y^{\prime \prime }}^{2}+2 y = 2 x
\]
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\[
{} x^{\prime \prime }+2 \sin \left (x\right ) = \sin \left (2 t \right )
\]
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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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\[
{} y^{\prime \prime }-\frac {y^{\prime }}{t}+\frac {y}{t^{2}} = \frac {1}{t}
\]
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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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\[
{} y^{\prime \prime }-6 y^{\prime }+13 y = 25 \sin \left (2 t \right )
\]
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\[
{} y^{\prime \prime }-9 y = 54 t \sin \left (2 t \right )
\]
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\[
{} y^{\prime \prime }-5 y^{\prime }+6 y = -78 \cos \left (3 t \right )
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+4 y = -32 t^{2} \cos \left (2 t \right )
\]
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\[
{} y^{\prime \prime }-y^{\prime }-20 y = -2 \,{\mathrm e}^{t}
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }-5 y = -648 t^{2} {\mathrm e}^{5 t}
\]
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\[
{} y^{\prime \prime }-7 y^{\prime }+12 y = -2 t^{3} {\mathrm e}^{4 t}
\]
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\[
{} y^{\prime \prime }+4 y^{\prime } = 8 \,{\mathrm e}^{4 t}-4 \,{\mathrm e}^{-4 t}
\]
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\[
{} y^{\prime \prime }-3 y^{\prime } = t^{2}-{\mathrm e}^{3 t}
\]
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\[
{} y^{\prime \prime }+4 y^{\prime } = -24 t -6-4 t \,{\mathrm e}^{-4 t}+{\mathrm e}^{-4 t}
\]
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\[
{} y^{\prime \prime }-3 y^{\prime } = t^{2}-{\mathrm e}^{3 t}
\]
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\[
{} y^{\prime \prime } = t^{2}+{\mathrm e}^{t}+\sin \left (t \right )
\]
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\[
{} y^{\prime \prime }+3 y^{\prime } = 18
\]
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\[
{} y^{\prime \prime }-y = 4
\]
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\[
{} y^{\prime \prime }-4 y = 32 t
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }-3 y = -2
\]
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\[
{} y^{\prime \prime }+y^{\prime }-6 y = 3 t
\]
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\[
{} y^{\prime \prime }+8 y^{\prime }+16 y = 4
\]
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\[
{} y^{\prime \prime }+7 y^{\prime }+10 y = t \,{\mathrm e}^{-t}
\]
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\[
{} y^{\prime \prime }+6 y^{\prime }+25 y = -1
\]
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\[
{} y^{\prime \prime }-3 y^{\prime } = -{\mathrm e}^{3 t}-2 t
\]
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\[
{} y^{\prime \prime }-y^{\prime } = -3 t -4 t^{2} {\mathrm e}^{2 t}
\]
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\[
{} y^{\prime \prime }-2 y^{\prime } = 2 t^{2}
\]
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\[
{} y^{\prime \prime }+4 y^{\prime } = -24 t -6-4 t \,{\mathrm e}^{-4 t}+{\mathrm e}^{-4 t}
\]
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\[
{} y^{\prime \prime }-3 y^{\prime } = {\mathrm e}^{-3 t}-{\mathrm e}^{3 t}
\]
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\[
{} y^{\prime \prime }+9 y = \left \{\begin {array}{cc} 2 t & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+9 \pi ^{2} y = \left \{\begin {array}{cc} 2 t & 0\le t <\pi \\ -2 \pi +2 t & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 10 & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+y^{\prime }-2 y = f \left (t \right )
\]
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\[
{} x^{\prime \prime }+9 x = \sin \left (3 t \right )
\]
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\[
{} 4 y^{\prime \prime }+4 y^{\prime }+37 y = \cos \left (3 t \right )
\]
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\[
{} y^{\prime \prime }+4 y = 1
\]
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\[
{} y^{\prime \prime }+16 y^{\prime } = t
\]
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\[
{} y^{\prime \prime }-7 y^{\prime }+10 y = {\mathrm e}^{3 t}
\]
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\[
{} y^{\prime \prime }+16 y = 2 \cos \left (4 t \right )
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+20 y = 2 t \,{\mathrm e}^{-2 t}
\]
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\[
{} y^{\prime \prime }+\frac {y}{4} = \sec \left (\frac {t}{2}\right )+\csc \left (\frac {t}{2}\right )
\]
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\[
{} y^{\prime \prime }+16 y = \csc \left (4 t \right )
\]
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\[
{} y^{\prime \prime }+16 y = \cot \left (4 t \right )
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+50 y = {\mathrm e}^{-t} \csc \left (7 t \right )
\]
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\[
{} y^{\prime \prime }+6 y^{\prime }+25 y = {\mathrm e}^{-3 t} \left (\sec \left (4 t \right )+\csc \left (4 t \right )\right )
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+26 y = {\mathrm e}^{t} \left (\sec \left (5 t \right )+\csc \left (5 t \right )\right )
\]
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\[
{} y^{\prime \prime }+12 y^{\prime }+37 y = {\mathrm e}^{-6 t} \csc \left (t \right )
\]
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\[
{} y^{\prime \prime }-6 y^{\prime }+34 y = {\mathrm e}^{3 t} \tan \left (5 t \right )
\]
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\[
{} y^{\prime \prime }-10 y^{\prime }+34 y = {\mathrm e}^{5 t} \cot \left (3 t \right )
\]
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\[
{} y^{\prime \prime }-12 y^{\prime }+37 y = {\mathrm e}^{6 t} \sec \left (t \right )
\]
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\[
{} y^{\prime \prime }-8 y^{\prime }+17 y = {\mathrm e}^{4 t} \sec \left (t \right )
\]
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\[
{} y^{\prime \prime }-9 y = \frac {1}{1+{\mathrm e}^{3 t}}
\]
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\[
{} y^{\prime \prime }-25 y = \frac {1}{1-{\mathrm e}^{5 t}}
\]
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\[
{} y^{\prime \prime }-y = 2 \sinh \left (t \right )
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{t}}{t}
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+4 y = \frac {{\mathrm e}^{2 t}}{t^{2}}
\]
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\[
{} y^{\prime \prime }+8 y^{\prime }+16 y = \frac {{\mathrm e}^{-4 t}}{t^{4}}
\]
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\[
{} y^{\prime \prime }+6 y^{\prime }+9 y = \frac {{\mathrm e}^{-3 t}}{t}
\]
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\[
{} y^{\prime \prime }+6 y^{\prime }+9 y = {\mathrm e}^{-3 t} \ln \left (t \right )
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = \cos \left ({\mathrm e}^{t}\right )
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+4 y = {\mathrm e}^{-2 t} \sqrt {-t^{2}+1}
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{t} \sqrt {-t^{2}+1}
\]
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\[
{} y^{\prime \prime }-10 y^{\prime }+25 y = {\mathrm e}^{5 t} \ln \left (2 t \right )
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{2 t} \arctan \left (t \right )
\]
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\[
{} y^{\prime \prime }+8 y^{\prime }+16 y = \frac {{\mathrm e}^{-4 t}}{t^{2}+1}
\]
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\[
{} y^{\prime \prime }+y = \sec \left (\frac {t}{2}\right )+\csc \left (\frac {t}{2}\right )
\]
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\[
{} y^{\prime \prime }+9 y = \tan \left (3 t \right )^{2}
\]
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\[
{} y^{\prime \prime }+9 y = \sec \left (3 t \right )
\]
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\[
{} y^{\prime \prime }+9 y = \tan \left (3 t \right )
\]
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\[
{} y^{\prime \prime }+4 y = \tan \left (2 t \right )
\]
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\[
{} y^{\prime \prime }+16 y = \tan \left (2 t \right )
\]
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