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\[
{} y^{\prime \prime }-y = \frac {1}{\left (1+{\mathrm e}^{-x}\right )^{2}}
\]
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\[
{} y^{\prime \prime }+y = \csc \left (x \right )
\]
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\[
{} y^{\prime \prime }-3 y^{\prime }+2 y = \sin \left ({\mathrm e}^{-x}\right )
\]
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\[
{} y^{\prime \prime }+y = \csc \left (x \right )
\]
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\[
{} y^{\prime \prime }+4 y = 4 \sec \left (x \right )^{2}
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+3 y = \frac {1}{1+{\mathrm e}^{-x}}
\]
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\[
{} y^{\prime \prime }-y = {\mathrm e}^{-x} \sin \left ({\mathrm e}^{-x}\right )+\cos \left ({\mathrm e}^{-x}\right )
\]
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\[
{} y^{\prime \prime }-y = \frac {1}{\left (1+{\mathrm e}^{-x}\right )^{2}}
\]
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\[
{} y^{\prime \prime }+2 y = {\mathrm e}^{x}+2
\]
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\[
{} y^{\prime \prime }-y = {\mathrm e}^{x} \sin \left (2 x \right )
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+2 y = x^{2}+\sin \left (x \right )
\]
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\[
{} y^{\prime \prime }-9 y = x +{\mathrm e}^{2 x}-\sin \left (2 x \right )
\]
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\[
{} y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime } = x^{2}+4 x +8
\]
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\[
{} y^{\prime \prime }+y = -2 \sin \left (x \right )+4 x \cos \left (x \right )
\]
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\[
{} y^{\prime \prime \prime }-y^{\prime \prime }-4 y^{\prime }+4 y = 2 x^{2}-4 x -1+2 x^{2} {\mathrm e}^{2 x}+5 x \,{\mathrm e}^{2 x}+{\mathrm e}^{2 x}
\]
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\[
{} y^{\prime \prime }+y^{\prime }+y = {\mathrm e}^{3 x}+6 \,{\mathrm e}^{x}-3 \,{\mathrm e}^{-2 x}+5
\]
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\[
{} y^{\prime \prime }-y = {\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{x}+x \,{\mathrm e}^{2 x}
\]
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\[
{} y^{\prime \prime \prime \prime }-y = \sin \left (2 x \right )
\]
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\[
{} y^{\prime \prime \prime }+y = \cos \left (x \right )
\]
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\[
{} y^{\prime \prime }+4 y = \sin \left (2 x \right )
\]
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\[
{} y^{\prime \prime }+5 y = \cos \left (\sqrt {5}\, x \right )
\]
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\[
{} y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y = {\mathrm e}^{x}+{\mathrm e}^{-x}+\sin \left (x \right )
\]
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\[
{} y^{\prime \prime }-y = x^{2}
\]
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\[
{} y^{\prime \prime }+2 y = x^{3}+x^{2}+{\mathrm e}^{-2 x}+\cos \left (3 x \right )
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }-y = {\mathrm e}^{x} \cos \left (x \right )
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+4 y = \frac {{\mathrm e}^{2 x}}{x^{2}}
\]
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\[
{} y^{\prime \prime }-y = x \,{\mathrm e}^{3 x}
\]
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\[
{} y^{\prime \prime }+5 y^{\prime }+6 y = {\mathrm e}^{-2 x} \sec \left (x \right )^{2} \left (1+2 \tan \left (x \right )\right )
\]
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\[
{} y^{\prime \prime \prime }+y^{\prime \prime } = x^{2}
\]
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\[
{} y^{\prime \prime }-6 y^{\prime }+13 y = 0
\]
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\[
{} y^{\prime \prime }+y = \tan \left (x \right )
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+4 y = 0
\]
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\[
{} y^{\prime \prime }-5 y^{\prime }+6 y = 0
\]
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\[
{} 2 y^{\prime \prime }+7 y^{\prime }-4 y = 0
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+6 y = 10
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+4 y = 5 \sin \left (t \right )
\]
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\[
{} y^{\prime \prime } = f \left (x \right )
\]
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\[
{} y^{\prime \prime \prime \prime }-20 y^{\prime \prime \prime }+158 y^{\prime \prime }-580 y^{\prime }+841 y = 0
\]
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\[
{} x^{\prime \prime }+x = 0
\]
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\[
{} x^{\prime \prime }+x = 0
\]
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\[
{} x^{\prime \prime }+x = 0
\]
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\[
{} x^{\prime \prime }+x = 0
\]
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\[
{} y^{\prime \prime }-y = 0
\]
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\[
{} y^{\prime \prime }-y = 0
\]
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\[
{} y^{\prime \prime }-y = 0
\]
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\[
{} y^{\prime \prime }-y = 0
\]
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\[
{} y^{\prime \prime }+4 y = 0
\]
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\[
{} y^{\prime \prime }+4 y = 0
\]
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\[
{} y^{\prime \prime }+4 y = 0
\]
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\[
{} y^{\prime \prime }+4 y = 0
\]
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\[
{} y^{\prime \prime }+4 y = 0
\]
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\[
{} y^{\prime \prime }+4 y = 0
\]
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\[
{} y^{\prime \prime }+9 y = 18
\]
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\[
{} y^{\prime \prime } = y^{\prime }
\]
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\[
{} y^{\prime \prime }+y = 2 \cos \left (x \right )-2 \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }+y = \sec \left (x \right )
\]
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\[
{} y^{\prime \prime }+y = {\mathrm e}^{x^{2}}
\]
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\[
{} y^{\prime \prime }+9 y = 5
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }-3 y = 6 x +4
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }-3 y = 6 x +4
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }-3 y = 6 x +4
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }-3 y = 6 x +4
\]
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\[
{} y^{\prime \prime }-y^{\prime }-6 y = 0
\]
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\[
{} y^{\prime \prime }+9 y = 10 \,{\mathrm e}^{-t}
\]
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\[
{} y^{\prime \prime }-\frac {y}{4} = 0
\]
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\[
{} y^{\prime \prime }-6 y^{\prime }+5 y = 29 \cos \left (2 t \right )
\]
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\[
{} y^{\prime \prime }+7 y^{\prime }+12 y = 21 \,{\mathrm e}^{3 t}
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+4 y = 0
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+3 y = 6 t -8
\]
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\[
{} y^{\prime \prime }+\frac {y}{25} = \frac {t^{2}}{50}
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+\frac {9 y}{4} = 9 t^{3}+64
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }-3 y = 0
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+5 y = 50 t -100
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }-4 y = 6 \,{\mathrm e}^{2 t -3}
\]
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\[
{} 9 y^{\prime \prime }-6 y^{\prime }+y = 0
\]
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\[
{} y^{\prime \prime }+6 y^{\prime }+8 y = {\mathrm e}^{-3 t}-{\mathrm e}^{-5 t}
\]
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\[
{} y^{\prime \prime }+10 y^{\prime }+24 y = 144 t^{2}
\]
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\[
{} y^{\prime \prime }+9 y = \left \{\begin {array}{cc} 8 \sin \left (t \right ) & 0<t <\pi \\ 0 & \pi <t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 4 t & 0<t <1 \\ 8 & 1<t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+y^{\prime }-2 y = \left \{\begin {array}{cc} 3 \sin \left (t \right )-\cos \left (t \right ) & 0<t <2 \pi \\ 3 \sin \left (2 t \right )-\cos \left (2 t \right ) & 2 \pi <t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0<t <1 \\ 0 & 1<t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0<t <1 \\ 0 & 1<t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+5 y = \left \{\begin {array}{cc} 10 \sin \left (t \right ) & 0<t <2 \pi \\ 0 & 2 \pi <t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 8 t^{2} & 0<t <5 \\ 0 & 5<t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+4 y = \delta \left (t -\pi \right )
\]
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\[
{} y^{\prime \prime }+16 y = 4 \delta \left (t -3 \pi \right )
\]
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\[
{} y^{\prime \prime }+y = \delta \left (t -\pi \right )-\delta \left (t -2 \pi \right )
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+5 y = \delta \left (t -1\right )
\]
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\[
{} 4 y^{\prime \prime }+24 y^{\prime }+37 y = 17 \,{\mathrm e}^{-t}+\delta \left (t -\frac {1}{2}\right )
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = 10 \sin \left (t \right )+10 \delta \left (t -1\right )
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+5 y = \left (1-\operatorname {Heaviside}\left (t -10\right )\right ) {\mathrm e}^{t}-{\mathrm e}^{10} \delta \left (t -10\right )
\]
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\[
{} y^{\prime \prime }+5 y^{\prime }+6 y = \delta \left (t -\frac {\pi }{2}\right )+\operatorname {Heaviside}\left (t -\pi \right ) \cos \left (t \right )
\]
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\[
{} y^{\prime \prime }+5 y^{\prime }+6 y = \operatorname {Heaviside}\left (t -1\right )+\delta \left (t -2\right )
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+5 y = 25 t -100 \delta \left (t -\pi \right )
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }-y = 0
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }-3 y = 0
\]
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\[
{} s^{\prime \prime }+2 s^{\prime }+s = 0
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+5 y = 0
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }-3 y = 3 x +1
\]
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