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\[
{} y^{\prime \prime }+4 y = 0
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = 0
\]
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\[
{} y^{\prime \prime }-y^{\prime }-2 y = 0
\]
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\[
{} a y^{\prime \prime }+b y^{\prime }+c y = 0
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }-3 y = 0
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = 0
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+4 y = 0
\]
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\[
{} 9 y^{\prime \prime }+6 y^{\prime }+y = 0
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+2 y = 0
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+6 y = 0
\]
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\[
{} 4 y^{\prime \prime }-4 y^{\prime }+y = 0
\]
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\[
{} 2 y^{\prime \prime }-3 y^{\prime }+y = 0
\]
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\[
{} 6 y^{\prime \prime }-y^{\prime }-y = 0
\]
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\[
{} 9 y^{\prime \prime }+12 y^{\prime }+4 y = 0
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }-8 y = 0
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+2 y = 0
\]
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\[
{} y^{\prime \prime }+5 y^{\prime } = 0
\]
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\[
{} 4 y^{\prime \prime }-9 y = 0
\]
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\[
{} 25 y^{\prime \prime }-20 y^{\prime }+4 y = 0
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+16 y = 0
\]
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\[
{} y^{\prime \prime }+6 y^{\prime }+13 y = 0
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+\frac {5 y}{4} = 0
\]
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\[
{} y^{\prime \prime }-9 y^{\prime }+9 y = 0
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }-2 y = 0
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+4 y = 0
\]
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\[
{} 9 y^{\prime \prime }-24 y^{\prime }+16 y = 0
\]
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\[
{} 4 y^{\prime \prime }+9 y = 0
\]
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\[
{} 4 y^{\prime \prime }+9 y^{\prime }-9 y = 0
\]
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\[
{} y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = 0
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+\frac {25 y}{4} = 0
\]
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\[
{} y^{\prime \prime }+y^{\prime }-2 y = 0
\]
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\[
{} y^{\prime \prime }+16 y = 0
\]
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\[
{} 9 y^{\prime \prime }-12 y^{\prime }+4 y = 0
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = 0
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+5 y = 0
\]
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\[
{} 6 y^{\prime \prime }-5 y^{\prime }+y = 0
\]
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\[
{} y^{\prime \prime }+6 y^{\prime }+9 y = 0
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+5 y = 0
\]
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\[
{} y^{\prime \prime }+3 y^{\prime } = 0
\]
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\[
{} y^{\prime \prime }+y = 0
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+4 y = 0
\]
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\[
{} y^{\prime \prime }+6 y^{\prime }+3 y = 0
\]
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\[
{} y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = 0
\]
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\[
{} 2 y^{\prime \prime }+y^{\prime }-4 y = 0
\]
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\[
{} y^{\prime \prime }+8 y^{\prime }-9 y = 0
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+2 y = 0
\]
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\[
{} 4 y^{\prime \prime }-y = 0
\]
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\[
{} y^{\prime \prime }+2 y = 0
\]
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\[
{} y^{\prime \prime }+\frac {y^{\prime }}{4}+2 y = 0
\]
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\[
{} m y^{\prime \prime }+k y = 0
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }-3 y = 3 \,{\mathrm e}^{2 t}
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+5 y = 3 \sin \left (2 t \right )
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }-3 y = -3 t \,{\mathrm e}^{-t}
\]
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\[
{} y^{\prime \prime }+2 y^{\prime } = 3+4 \sin \left (2 t \right )
\]
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\[
{} y^{\prime \prime }+9 y = t^{2} {\mathrm e}^{3 t}+6
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+y = 2 \,{\mathrm e}^{-t}
\]
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\[
{} y^{\prime \prime }-5 y^{\prime }+4 y = 2 \,{\mathrm e}^{t}
\]
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\[
{} y^{\prime \prime }-y^{\prime }-2 y = 2 \,{\mathrm e}^{-t}
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+y = 3 \,{\mathrm e}^{-t}
\]
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\[
{} 4 y^{\prime \prime }-4 y^{\prime }+y = 16 \,{\mathrm e}^{\frac {t}{2}}
\]
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\[
{} 2 y^{\prime \prime }+3 y^{\prime }+y = t^{2}+3 \sin \left (t \right )
\]
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\[
{} y^{\prime \prime }+y = 3 \sin \left (2 t \right )+t \cos \left (2 t \right )
\]
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\[
{} u^{\prime \prime }+w_{0}^{2} u = \cos \left (w t \right )
\]
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\[
{} y^{\prime \prime }+y^{\prime }+4 y = 2 \sinh \left (t \right )
\]
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\[
{} y^{\prime \prime }-y^{\prime }-2 y = \cosh \left (2 t \right )
\]
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\[
{} y^{\prime \prime }+y^{\prime }-2 y = 2 t
\]
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\[
{} y^{\prime \prime }+4 y = t^{2}+3 \,{\mathrm e}^{t}
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = t \,{\mathrm e}^{t}+4
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }-3 y = 3 t \,{\mathrm e}^{2 t}
\]
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\[
{} y^{\prime \prime }+4 y = 3 \sin \left (2 t \right )
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+5 y = 4 \,{\mathrm e}^{-t} \cos \left (2 t \right )
\]
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\[
{} y^{\prime \prime }+3 y^{\prime } = 2 t^{4}+t^{2} {\mathrm e}^{-3 t}+\sin \left (3 t \right )
\]
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\[
{} y^{\prime \prime }+y = t \left (\sin \left (t \right )+1\right )
\]
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\[
{} y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{t} \cos \left (2 t \right )+{\mathrm e}^{2 t} \left (3 t +4\right ) \sin \left (t \right )
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+2 y = 3 \,{\mathrm e}^{-t}+2 \,{\mathrm e}^{-t} \cos \left (t \right )+4 \,{\mathrm e}^{-t} t^{2} \sin \left (t \right )
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+4 y = 2 t^{2}+4 t \,{\mathrm e}^{2 t}+t \sin \left (2 t \right )
\]
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\[
{} y^{\prime \prime }+4 y = t^{2} \sin \left (2 t \right )+\left (6 t +7\right ) \cos \left (2 t \right )
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{t} \left (t^{2}+1\right ) \sin \left (2 t \right )+3 \,{\mathrm e}^{-t} \cos \left (t \right )+4 \,{\mathrm e}^{t}
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+5 y = 3 t \,{\mathrm e}^{-t} \cos \left (2 t \right )-2 t \,{\mathrm e}^{-2 t} \cos \left (t \right )
\]
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\[
{} y^{\prime \prime }-3 y^{\prime }-4 y = 2 \,{\mathrm e}^{-t}
\]
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\[
{} y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0\le t \le \pi \\ \pi \,{\mathrm e}^{-t +\pi } & \pi <t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+5 y = \left \{\begin {array}{cc} 1 & 0\le t \le \frac {\pi }{2} \\ 0 & \frac {\pi }{2}<t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+y = \left \{\begin {array}{cc} A t & 0\le t \le \pi \\ A \left (2 \pi -t \right ) & \pi <t \le 2 \pi \\ 0 & 2 \pi <t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+\frac {y^{\prime }}{4}+2 y = 2 \cos \left (w t \right )
\]
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\[
{} y^{\prime \prime }+y = 2 \cos \left (w t \right )
\]
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\[
{} y^{\prime \prime }+y = 3 \cos \left (w t \right )
\]
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\[
{} y^{\prime \prime }+\frac {y^{\prime }}{8}+4 y = 3 \cos \left (\frac {t}{4}\right )
\]
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\[
{} y^{\prime \prime }+\frac {y^{\prime }}{8}+4 y = 3 \cos \left (2 t \right )
\]
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\[
{} y^{\prime \prime }+\frac {y^{\prime }}{8}+4 y = 3 \cos \left (6 t \right )
\]
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\[
{} y^{\prime \prime }-5 y^{\prime }+6 y = 2 \,{\mathrm e}^{t}
\]
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\[
{} y^{\prime \prime }-y^{\prime }-2 y = 2 \,{\mathrm e}^{-t}
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+y = 3 \,{\mathrm e}^{-t}
\]
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\[
{} 4 y^{\prime \prime }-4 y^{\prime }+y = 16 \,{\mathrm e}^{\frac {t}{2}}
\]
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\[
{} y^{\prime \prime }+y = \tan \left (t \right )
\]
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\[
{} y^{\prime \prime }+4 y = 3 \sec \left (2 t \right )^{2}
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+4 y = \frac {{\mathrm e}^{2 t}}{t^{2}}
\]
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\[
{} y^{\prime \prime }+4 y = 2 \csc \left (\frac {t}{2}\right )
\]
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\[
{} 4 y^{\prime \prime }+y = 2 \sec \left (2 t \right )
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{t}}{t^{2}+1}
\]
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\[
{} y^{\prime \prime }-5 y^{\prime }+6 y = g \left (t \right )
\]
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