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\[
{} y^{\prime \prime }+2 y^{\prime }+2 y = 2
\]
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\[
{} y^{\prime \prime }+y^{\prime } = 3 x^{2}
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+5 y = 3 \,{\mathrm e}^{-x} \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }+a^{2} y = f \left (x \right )
\]
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\[
{} y^{\prime \prime }+5 y^{\prime }+6 y = 4 \,{\mathrm e}^{3 t}
\]
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\[
{} y^{\prime \prime }+y^{\prime }-6 y = t
\]
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\[
{} y^{\prime \prime }-y^{\prime } = t^{2}
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = f \left (t \right )
\]
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\[
{} x^{\prime \prime }-x = t^{2}
\]
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\[
{} x^{\prime \prime }-x = {\mathrm e}^{t}
\]
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\[
{} x^{\prime \prime }+2 x^{\prime }+4 x = {\mathrm e}^{t} \cos \left (2 t \right )
\]
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\[
{} x^{\prime \prime }-x^{\prime }+x = \sin \left (2 t \right )
\]
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\[
{} x^{\prime \prime }+4 x^{\prime }+3 x = t \sin \left (t \right )
\]
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\[
{} x^{\prime \prime }+x = \cos \left (t \right )
\]
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\[
{} v^{\prime \prime }-6 v^{\prime }+13 v = {\mathrm e}^{-2 u}
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }-y = \sin \left (t \right )
\]
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\[
{} y^{\prime \prime }+3 y = \sin \left (x \right )+\frac {\sin \left (3 x \right )}{3}
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+3 y = 2 \,{\mathrm e}^{2 x}
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+3 y = 2 \,{\mathrm e}^{2 x}
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+2 y = x
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }-y = {\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = x
\]
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\[
{} y^{\prime \prime }+y = \cos \left (x \right )
\]
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\[
{} y^{\prime \prime }+y = \sin \left (x \right )
\]
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\[
{} e y^{\prime \prime } = \frac {P \left (\frac {L}{2}-x \right )}{2}
\]
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\[
{} e y^{\prime \prime } = \frac {w \left (\frac {L^{2}}{4}-x^{2}\right )}{2}
\]
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\[
{} e y^{\prime \prime } = -\frac {\left (w L +P \right ) x}{2}-\frac {w \,x^{2}}{2}
\]
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\[
{} e y^{\prime \prime } = -P \left (L -x \right )
\]
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\[
{} e y^{\prime \prime } = -P L +\left (w L +P \right ) x -\frac {w \left (L^{2}+x^{2}\right )}{2}
\]
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\[
{} y^{\prime \prime } = \cos \left (x \right )
\]
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\[
{} x = y^{\prime \prime }+y^{\prime }
\]
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\[
{} y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{4 x}
\]
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\[
{} y^{\prime \prime }-y = 2+5 x
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+y = 2 \,{\mathrm e}^{2 x}
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = 3 \,{\mathrm e}^{\frac {5 x}{2}}
\]
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\[
{} y^{\prime \prime }+a^{2} y = \cos \left (a x \right )
\]
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\[
{} y^{\prime \prime }-4 y = 2 \sin \left (\frac {x}{2}\right )
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{2 x} \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }+2 y = x^{2} {\mathrm e}^{3 x}+{\mathrm e}^{x} \cos \left (2 x \right )
\]
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\[
{} y^{\prime \prime }+4 y = x \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }-y = x^{2} \cos \left (x \right )
\]
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\[
{} y^{\prime \prime }+4 y = \sin \left (3 x \right )+{\mathrm e}^{x}+x^{2}
\]
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\[
{} y^{\prime \prime }-5 y^{\prime }+6 y = x +{\mathrm e}^{m x}
\]
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\[
{} y^{\prime \prime }-a^{2} y = {\mathrm e}^{a x}+{\mathrm e}^{n x}
\]
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\[
{} y^{\prime \prime }+a^{2} y = \sec \left (a x \right )
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = x^{2} {\mathrm e}^{3 x}
\]
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\[
{} y^{\prime \prime }+n^{2} y = {\mathrm e}^{x} x^{4}
\]
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\[
{} y^{\prime \prime }+y^{\prime }+y = \sin \left (2 x \right )
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+4 y = {\mathrm e}^{x} \cos \left (x \right )
\]
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\[
{} y^{\prime \prime }-y = x \sin \left (x \right )+\left (x^{2}+1\right ) {\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+3 y = {\mathrm e}^{x} \cos \left (2 x \right )+\cos \left (3 x \right )
\]
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\[
{} y^{\prime \prime }-9 y^{\prime }+20 y = 20 x
\]
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\[
{} y^{\prime \prime } = x^{2} \sin \left (x \right )
\]
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\[
{} y^{\prime \prime } = \frac {a}{x}
\]
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\[
{} y^{\prime \prime }+y^{\prime } = {\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{4 x}
\]
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\[
{} y^{\prime \prime }-y = 2+5 x
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }-15 y = 15 x^{2}
\]
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\[
{} y^{\prime \prime }+y = \sec \left (x \right )^{2}
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = 2 \,{\mathrm e}^{\frac {5 x}{2}}
\]
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\[
{} y^{\prime \prime }+y^{\prime }+y = {\mathrm e}^{-x}
\]
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\[
{} y^{\prime \prime }+2 p y^{\prime }+\left (p^{2}+q^{2}\right ) y = {\mathrm e}^{k x}
\]
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\[
{} y^{\prime \prime }+9 y = \sin \left (2 x \right )+\cos \left (2 x \right )
\]
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\[
{} y^{\prime \prime }+a^{2} y = \cos \left (a x \right )+\cos \left (b x \right )
\]
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\[
{} y^{\prime \prime }+4 y = {\mathrm e}^{x}+\sin \left (2 x \right )
\]
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\[
{} y^{\prime \prime }-4 y = 2 \sin \left (\frac {x}{2}\right )
\]
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\[
{} y^{\prime \prime }+y = \sin \left (3 x \right )-\cos \left (\frac {x}{2}\right )^{2}
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+5 y = {\mathrm e}^{2 x} \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+4 y = {\mathrm e}^{x} \cos \left (x \right )
\]
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\[
{} y^{\prime \prime }-y = \cosh \left (x \right ) \cos \left (x \right )
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }-12 y = \left (x -1\right ) {\mathrm e}^{2 x}
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+y = x \cos \left (x \right )
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = x \,{\mathrm e}^{x} \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+4 y = 8 x^{2} {\mathrm e}^{2 x} \sin \left (2 x \right )
\]
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\[
{} y^{\prime \prime }+y = {\mathrm e}^{-x}+\cos \left (x \right )+x^{3}+{\mathrm e}^{x} \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }+y = 3 \cos \left (x \right )^{2}+2 \sin \left (x \right )^{3}
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+10 y+37 \sin \left (3 x \right ) = 0
\]
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\[
{} y^{\prime \prime } = x +\sin \left (x \right )
\]
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\[
{} y^{\prime \prime } = x \,{\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime } = \frac {a}{x}
\]
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\[
{} y^{\prime \prime }+y^{\prime } = {\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }+y = x
\]
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\[
{} y^{\prime \prime }+y = \csc \left (x \right )
\]
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\[
{} y^{\prime \prime }+4 y = 4 \tan \left (2 x \right )
\]
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\[
{} y^{\prime \prime }-y = \frac {2}{1+{\mathrm e}^{x}}
\]
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\[
{} y^{\prime \prime }+n^{2} y = \sec \left (n x \right )
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+y = a \cos \left (2 x \right )
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = x \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = x^{2} {\mathrm e}^{3 x}
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+4 y = 2 \sinh \left (2 x \right )
\]
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\[
{} y^{\prime \prime }+a^{2} y = \cos \left (a x \right )
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = x \sin \left (x \right )
\]
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\[
{} y^{\prime \prime } = x^{2} \sin \left (x \right )
\]
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\[
{} y^{\prime \prime } = \sec \left (x \right )^{2}
\]
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\[
{} y^{\prime \prime }+a^{2} y = \sec \left (a x \right )
\]
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