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\[
{} a y^{\prime \prime }+b y^{\prime }+c y = 0
\]
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\[
{} t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y = 0
\]
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\[
{} t^{2} y^{\prime \prime }+2 t y^{\prime }-2 y = 0
\]
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\[
{} t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0
\]
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\[
{} t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y = 0
\]
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\[
{} x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0
\]
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\[
{} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\]
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\[
{} x^{2} y^{\prime \prime }-\left (x -\frac {3}{16}\right ) y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
\]
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\[
{} x y^{\prime \prime }-\left (x +n \right ) y^{\prime }+n y = 0
\]
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\[
{} y^{\prime \prime }+a \left (x y^{\prime }+y\right ) = 0
\]
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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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\[
{} a \,x^{2} y^{\prime \prime }+b x y^{\prime }+c y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }+\frac {5 y}{4} = 0
\]
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\[
{} x^{2} y^{\prime \prime }-4 x y^{\prime }-6 y = 0
\]
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\[
{} x^{2} y^{\prime \prime }-2 y = 0
\]
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\[
{} x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+2 x y^{\prime }+4 y = 0
\]
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\[
{} 2 x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0
\]
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\[
{} 2 x^{2} y^{\prime \prime }+x y^{\prime }-3 y = 0
\]
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\[
{} 4 x^{2} y^{\prime \prime }+8 x y^{\prime }+17 y = 0
\]
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\[
{} x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }+5 y = 0
\]
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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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\[
{} y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{t} t +4
\]
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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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\[
{} y^{\prime \prime }+y = t \left (1+\sin \left (t \right )\right )
\]
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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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