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\[
{} y^{\prime \prime }-4 y^{\prime }+5 y = 2 x^{2} {\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }-6 y^{\prime }+9 y = 16 \,{\mathrm e}^{-x}+9 x -6
\]
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\[
{} y^{\prime \prime }-y^{\prime } = -5 \,{\mathrm e}^{-x} \left (\cos \left (x \right )+\sin \left (x \right )\right )
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+2 y = 4 \,{\mathrm e}^{x} \cos \left (x \right )
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+5 y = \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+5 y = 4 \cos \left (2 x \right )+\sin \left (2 x \right )
\]
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\[
{} y^{\prime \prime }-y = 1
\]
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\[
{} y^{\prime \prime }-y = -2 \cos \left (x \right )
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = 4 \,{\mathrm e}^{-x}
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+3 y = 8 \,{\mathrm e}^{x}+9
\]
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\[
{} y^{\prime \prime }-y^{\prime }-5 y = 1
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+4 y = 2 \,{\mathrm e}^{x} \left (\sin \left (x \right )+7 \cos \left (x \right )\right )
\]
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\[
{} y^{\prime \prime }-5 y^{\prime }+6 y = 2 \,{\mathrm e}^{-2 x} \left (9 \sin \left (2 x \right )+4 \cos \left (2 x \right )\right )
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{-x} \left (9 x^{2}+5 x -12\right )
\]
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\[
{} y^{\prime \prime }+y = \frac {1}{\sin \left (x \right )}
\]
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\[
{} y^{\prime \prime }+y^{\prime } = \frac {1}{1+{\mathrm e}^{x}}
\]
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\[
{} y^{\prime \prime }+y = \frac {1}{\cos \left (x \right )^{3}}
\]
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\[
{} y^{\prime \prime }+y = \frac {1}{\sqrt {\sin \left (x \right )^{5} \cos \left (x \right )}}
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{x^{2}+1}
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+2 y = \frac {{\mathrm e}^{-x}}{\sin \left (x \right )}
\]
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\[
{} y^{\prime \prime }+y = \frac {2}{\sin \left (x \right )^{3}}
\]
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\[
{} y^{\prime \prime }+y^{\prime } = {\mathrm e}^{2 x} \cos \left ({\mathrm e}^{x}\right )
\]
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\[
{} y^{\prime \prime }+\alpha ^{2} y = 1
\]
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\[
{} y^{\prime \prime }+y = 1
\]
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\[
{} y^{\prime \prime }+4 y = \cos \left (x \right )^{2}
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+4 y = \pi ^{2}-x^{2}
\]
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\[
{} y^{\prime \prime }-4 y = \cos \left (\pi x \right )
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+4 y = \arcsin \left (\sin \left (x \right )\right )
\]
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\[
{} y^{\prime \prime }+9 y = \sin \left (x \right )^{3}
\]
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\[
{} x^{\prime \prime } = 1
\]
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\[
{} x^{\prime \prime } = \cos \left (t \right )
\]
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\[
{} x^{\prime \prime }-x^{\prime } = 1
\]
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\[
{} x^{\prime \prime }+x = t
\]
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\[
{} x^{\prime \prime }+6 x^{\prime } = 12 t +2
\]
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\[
{} x^{\prime \prime }-2 x^{\prime }+2 x = 2
\]
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\[
{} x^{\prime \prime }+4 x^{\prime }+4 x = 4
\]
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\[
{} 2 x^{\prime \prime }-2 x^{\prime } = \left (t +1\right ) {\mathrm e}^{t}
\]
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\[
{} x^{\prime \prime }+x = 2 \cos \left (t \right )
\]
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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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\[
{} y^{\prime \prime }+4 y = g \left (t \right )
\]
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\[
{} y^{\prime \prime }+y = g \left (t \right )
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+2 y = t^{2} {\mathrm e}^{t}+7
\]
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\[
{} y^{\prime \prime }-5 y^{\prime }-6 y = t^{2}+7
\]
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\[
{} y^{\prime \prime }+4 y = 3 \,{\mathrm e}^{-2 t} \sin \left (2 t \right )
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+5 y = t \cos \left (2 t \right )
\]
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\[
{} y^{\prime \prime }+16 y = \left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+4 y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 1 & 1\le t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = t
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+29 y = {\mathrm e}^{-2 t} \sin \left (5 t \right )
\]
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\[
{} y^{\prime \prime }+w^{2} y = \cos \left (2 t \right )
\]
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