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\[
{} y^{\prime \prime }-3 y^{\prime }-4 y = 16 x -12 \,{\mathrm e}^{2 x}
\]
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\[
{} y^{\prime \prime }+6 y^{\prime }+5 y = 2 \,{\mathrm e}^{x}+10 \,{\mathrm e}^{5 x}
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+10 y = 5 x \,{\mathrm e}^{-2 x}
\]
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\[
{} y^{\prime \prime }+y^{\prime }-6 y = 10 \,{\mathrm e}^{2 x}-18 \,{\mathrm e}^{3 x}-6 x -11
\]
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\[
{} y^{\prime \prime }+y^{\prime }-2 y = 6 \,{\mathrm e}^{-2 x}+3 \,{\mathrm e}^{x}-4 x^{2}
\]
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\[
{} y^{\prime \prime }+y = x \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }+4 y = 12 x^{2}-16 x \cos \left (2 x \right )
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+3 y = 9 x^{2}+4
\]
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\[
{} y^{\prime \prime }+5 y^{\prime }+4 y = 16 x +20 \,{\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }-8 y^{\prime }+15 y = 9 x \,{\mathrm e}^{2 x}
\]
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\[
{} y^{\prime \prime }+7 y^{\prime }+10 y = 4 x \,{\mathrm e}^{-3 x}
\]
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\[
{} y^{\prime \prime }+8 y^{\prime }+16 y = 8 \,{\mathrm e}^{-2 x}
\]
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\[
{} y^{\prime \prime }+6 y^{\prime }+9 y = 27 \,{\mathrm e}^{-6 x}
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+13 y = 18 \,{\mathrm e}^{-2 x}
\]
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\[
{} y^{\prime \prime }-10 y^{\prime }+29 y = 8 \,{\mathrm e}^{5 x}
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+13 y = 8 \sin \left (3 x \right )
\]
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\[
{} y^{\prime \prime }-y^{\prime }-6 y = 8 \,{\mathrm e}^{2 x}-5 \,{\mathrm e}^{3 x}
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = 2 x \,{\mathrm e}^{2 x}+6 \,{\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }-y = 3 x^{2} {\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }+y = 3 x^{2}-4 \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }+4 y = 8 \sin \left (2 x \right )
\]
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\[
{} y^{\prime \prime }-6 y^{\prime }+8 y = x^{3}+x +{\mathrm e}^{-2 x}
\]
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\[
{} y^{\prime \prime }+9 y = {\mathrm e}^{3 x}+{\mathrm e}^{-3 x}+{\mathrm e}^{3 x} \sin \left (3 x \right )
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+5 y = {\mathrm e}^{-2 x} \left (\cos \left (x \right )+1\right )
\]
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\[
{} y^{\prime \prime }-6 y^{\prime }+9 y = x^{4} {\mathrm e}^{x}+x^{3} {\mathrm e}^{2 x}+x^{2} {\mathrm e}^{3 x}
\]
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\[
{} y^{\prime \prime }+6 y^{\prime }+13 y = x \,{\mathrm e}^{-3 x} \sin \left (2 x \right )+x^{2} {\mathrm e}^{-2 x} \sin \left (3 x \right )
\]
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\[
{} y^{\prime \prime }+y = \cot \left (x \right )
\]
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\[
{} y^{\prime \prime }+y = \tan \left (x \right )^{2}
\]
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\[
{} y^{\prime \prime }+y = \sec \left (x \right )
\]
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\[
{} y^{\prime \prime }+y = \sec \left (x \right )^{3}
\]
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\[
{} y^{\prime \prime }+4 y = \sec \left (x \right )^{2}
\]
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\[
{} y^{\prime \prime }+y = \tan \left (x \right ) \sec \left (x \right )
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+5 y = {\mathrm e}^{-2 x} \sec \left (x \right )
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+5 y = {\mathrm e}^{x} \tan \left (2 x \right )
\]
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\[
{} y^{\prime \prime }+6 y^{\prime }+9 y = \frac {{\mathrm e}^{-3 x}}{x^{3}}
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = x \,{\mathrm e}^{x} \ln \left (x \right )
\]
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\[
{} y^{\prime \prime }+y = \sec \left (x \right ) \csc \left (x \right )
\]
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\[
{} y^{\prime \prime }+y = \tan \left (x \right )^{3}
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = \frac {1}{1+{\mathrm e}^{x}}
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = \frac {1}{{\mathrm e}^{2 x}+1}
\]
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\[
{} y^{\prime \prime }+y = \frac {1}{\sin \left (x \right )+1}
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{x} \arcsin \left (x \right )
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = \frac {{\mathrm e}^{-x}}{x}
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = x \ln \left (x \right )
\]
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\[
{} x^{2} y^{\prime \prime }-6 x y^{\prime }+10 y = 3 x^{4}+6 x^{3}
\]
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\[
{} \left (1+x \right )^{2} y^{\prime \prime }-2 \left (1+x \right ) y^{\prime }+2 y = 1
\]
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\[
{} \left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (1+x \right ) y^{\prime }+2 y = \left (x +2\right )^{2}
\]
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\[
{} x^{2} y^{\prime \prime }-x \left (x +2\right ) y^{\prime }+\left (x +2\right ) y = x^{3}
\]
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\[
{} x \left (x -2\right ) y^{\prime \prime }-\left (x^{2}-2\right ) y^{\prime }+2 \left (x -1\right ) y = 3 x^{2} \left (x -2\right )^{2} {\mathrm e}^{x}
\]
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\[
{} \left (2 x +1\right ) \left (1+x \right ) y^{\prime \prime }+2 x y^{\prime }-2 y = \left (2 x +1\right )^{2}
\]
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\[
{} \sin \left (x \right )^{2} y^{\prime \prime }-2 \sin \left (x \right ) \cos \left (x \right ) y^{\prime }+\left (\cos \left (x \right )^{2}+1\right ) y = \sin \left (x \right )^{3}
\]
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\[
{} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 4 x -6
\]
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\[
{} x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = 2 x^{3}
\]
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\[
{} x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 4 \ln \left (x \right )
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 2 x \ln \left (x \right )
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 4 \sin \left (\ln \left (x \right )\right )
\]
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\[
{} x^{2} y^{\prime \prime }-2 y = 4 x -8
\]
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\[
{} x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y = -6 x^{3}+4 x^{2}
\]
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\[
{} x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 10 x^{2}
\]
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\[
{} x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = 2 x^{3}
\]
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\[
{} x^{2} y^{\prime \prime }-6 y = \ln \left (x \right )
\]
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\[
{} y^{\prime \prime }+4 y = 8
\]
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\[
{} y^{\prime \prime }-y^{\prime }-2 y = 18 \,{\mathrm e}^{-t} \sin \left (3 t \right )
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+y = t \,{\mathrm e}^{-2 t}
\]
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\[
{} y^{\prime \prime }+7 y^{\prime }+10 y = 4 t \,{\mathrm e}^{-3 t}
\]
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\[
{} y^{\prime \prime }-8 y^{\prime }+15 y = 9 t \,{\mathrm e}^{2 t}
\]
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\[
{} y^{\prime \prime }-3 y^{\prime }+2 y = \left \{\begin {array}{cc} 2 & 0<t <4 \\ 0 & 4<t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+5 y^{\prime }+6 y = \left \{\begin {array}{cc} 6 & 0<t <2 \\ 0 & 2<t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+5 y = \left \{\begin {array}{cc} 1 & 0<t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}<t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+6 y^{\prime }+8 y = \left \{\begin {array}{cc} 3 & 0<t <2 \pi \\ 0 & 2 \pi <t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+4 y = \left \{\begin {array}{cc} -4 t +8 \pi & 0<t <2 \pi \\ 0 & 2<t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0<t <\pi \\ \pi & \pi <t \end {array}\right .
\]
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\[
{} x^{\prime \prime }-4 x = t^{2}
\]
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\[
{} x^{\prime \prime }-4 x^{\prime } = t^{2}
\]
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\[
{} x^{\prime \prime }+x^{\prime }-2 x = 3 \,{\mathrm e}^{-t}
\]
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\[
{} x^{\prime \prime }+x^{\prime }-2 x = {\mathrm e}^{t}
\]
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\[
{} x^{\prime \prime }+2 x^{\prime }+x = {\mathrm e}^{-t}
\]
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\[
{} x^{\prime \prime }+\omega ^{2} x = \sin \left (\alpha t \right )
\]
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\[
{} x^{\prime \prime }+\omega ^{2} x = \sin \left (\omega t \right )
\]
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\[
{} x^{\prime \prime }+2 x^{\prime }+10 x = {\mathrm e}^{-t}
\]
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\[
{} x^{\prime \prime }+2 x^{\prime }+10 x = {\mathrm e}^{-t} \cos \left (3 t \right )
\]
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\[
{} x^{\prime \prime }+6 x^{\prime }+10 x = {\mathrm e}^{-2 t} \cos \left (t \right )
\]
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\[
{} x^{\prime \prime }+4 x^{\prime }+4 x = {\mathrm e}^{2 t}
\]
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\[
{} x^{\prime \prime }+x^{\prime }-2 x = 12 \,{\mathrm e}^{-t}-6 \,{\mathrm e}^{t}
\]
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\[
{} x^{\prime \prime }+4 x = 289 t \,{\mathrm e}^{t} \sin \left (2 t \right )
\]
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\[
{} x^{\prime \prime }+\omega ^{2} x = \cos \left (\alpha t \right )
\]
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\[
{} x^{\prime \prime }+\omega ^{2} x = \cos \left (\omega t \right )
\]
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\[
{} y^{\prime \prime }-y^{\prime }-6 y = {\mathrm e}^{x}
\]
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\[
{} x^{\prime \prime }-x = \frac {1}{t}
\]
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\[
{} y^{\prime \prime }+4 y = \cot \left (2 x \right )
\]
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\[
{} t^{2} x^{\prime \prime }-2 x = t^{3}
\]
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\[
{} x^{\prime \prime }-4 x^{\prime } = \tan \left (t \right )
\]
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\[
{} \left (\tan \left (x \right )^{2}-1\right ) y^{\prime \prime }-4 \tan \left (x \right )^{3} y^{\prime }+2 y \sec \left (x \right )^{4} = \left (\tan \left (x \right )^{2}-1\right ) \left (1-2 \sin \left (x \right )^{2}\right )
\]
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\[
{} y^{\prime \prime }-6 y^{\prime }+10 y = 100
\]
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\[
{} x^{\prime \prime }+x = \sin \left (t \right )-\cos \left (2 t \right )
\]
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\[
{} y^{\prime \prime }+y = \frac {1}{\sin \left (x \right )^{3}}
\]
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\[
{} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 2
\]
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\[
{} y^{\prime \prime }+y = \cosh \left (x \right )
\]
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\[
{} x^{\prime \prime }-4 x^{\prime }+4 x = {\mathrm e}^{t}+{\mathrm e}^{2 t}+1
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0
\]
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