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\[
{} y^{\prime \prime }+4 y = \tan \left (x \right )^{2}
\]
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\[
{} y^{\prime \prime }-y = 3 \,{\mathrm e}^{2 x}
\]
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\[
{} y^{\prime \prime }+y = -8 \sin \left (3 x \right )
\]
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\[
{} y^{\prime \prime }+y^{\prime }+y = x^{2}+2 x +2
\]
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\[
{} y^{\prime \prime }+y^{\prime } = \frac {x -1}{x}
\]
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\[
{} y^{\prime \prime }+9 y = -3 \cos \left (2 x \right )
\]
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\[
{} y^{\prime \prime }+5 y^{\prime }+6 y = 5 \,{\mathrm e}^{3 t}
\]
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\[
{} y^{\prime \prime }+y^{\prime }-6 y = t
\]
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\[
{} y^{\prime \prime }-y = t^{2}
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }-5 y = 1
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }-2 y = -6 \,{\mathrm e}^{-t +\pi }
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }-y = t \,{\mathrm e}^{-t}
\]
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\[
{} y^{\prime \prime }-y^{\prime }+y = 3 \,{\mathrm e}^{-t}
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+3 y = 2
\]
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\[
{} y^{\prime \prime }+y^{\prime }+2 y = t
\]
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\[
{} y^{\prime \prime }-7 y^{\prime }+12 y = t \,{\mathrm e}^{2 t}
\]
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\[
{} i^{\prime \prime }+2 i^{\prime }+3 i = \left \{\begin {array}{cc} 30 & 0<t <2 \pi \\ 0 & 2 \pi \le t \le 5 \pi \\ 10 & 5 \pi <t <\infty \end {array}\right .
\]
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\[
{} y^{\prime \prime }-4 y^{\prime } = 6 \,{\mathrm e}^{3 t}-3 \,{\mathrm e}^{-t}
\]
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\[
{} y^{\prime \prime }+y = \sqrt {2}\, \sin \left (\sqrt {2}\, t \right )
\]
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\[
{} y^{\prime \prime }+9 y = {\mathrm e}^{t}
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+4 y = t^{3} {\mathrm e}^{2 t}
\]
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\[
{} y^{\prime \prime }-6 y^{\prime }+9 y = t
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+4 y = t^{3}
\]
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\[
{} y^{\prime \prime }-y = {\mathrm e}^{t} \cos \left (t \right )
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+5 y = t +1
\]
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\[
{} y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+4 y = \sin \left (t \right ) \operatorname {Heaviside}\left (t -2 \pi \right )
\]
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\[
{} y^{\prime \prime }-5 y^{\prime }+6 y = \operatorname {Heaviside}\left (t -1\right )
\]
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\[
{} y^{\prime \prime }+y = \left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 1 & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+3 y = 1-\operatorname {Heaviside}\left (t -2\right )-\operatorname {Heaviside}\left (t -4\right )+\operatorname {Heaviside}\left (t -6\right )
\]
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\[
{} y^{\prime \prime }+9 y = \cos \left (3 t \right )
\]
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\[
{} y^{\prime \prime }+y = \sin \left (t \right )
\]
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\[
{} y^{\prime \prime }+16 y = \left \{\begin {array}{cc} \cos \left (4 t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+y = \left \{\begin {array}{cc} 1 & 0\le t <\frac {\pi }{2} \\ \sin \left (t \right ) & \frac {\pi }{2}\le t \end {array}\right .
\]
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\[
{} t y^{\prime \prime }-y^{\prime } = 2 t^{2}
\]
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\[
{} 2 y^{\prime \prime }+t y^{\prime }-2 y = 10
\]
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\[
{} y^{\prime \prime }+y = \sin \left (t \right )+t \sin \left (t \right )
\]
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\[
{} y^{\prime \prime }+y = \delta \left (t -2 \pi \right )
\]
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\[
{} y^{\prime \prime }+16 y = \delta \left (t -2 \pi \right )
\]
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\[
{} y^{\prime \prime }+y = \delta \left (t -\frac {\pi }{2}\right )+\delta \left (t -\frac {3 \pi }{2}\right )
\]
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\[
{} y^{\prime \prime }+y = \delta \left (t -2 \pi \right )+\delta \left (t -4 \pi \right )
\]
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\[
{} y^{\prime \prime }+2 y^{\prime } = \delta \left (t -1\right )
\]
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\[
{} y^{\prime \prime }-2 y^{\prime } = 1+\delta \left (t -2\right )
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+5 y = \delta \left (t -2 \pi \right )
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+y = \delta \left (t -1\right )
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+13 y = \delta \left (t -\pi \right )+\delta \left (t -3 \pi \right )
\]
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\[
{} y^{\prime \prime }-7 y^{\prime }+6 y = {\mathrm e}^{t}+\delta \left (t -2\right )+\delta \left (t -4\right )
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+10 y = \delta \left (t \right )
\]
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\[
{} x y^{\prime \prime } = y^{\prime }+x^{5}
\]
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\[
{} x y^{\prime \prime }+y^{\prime }+x = 0
\]
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\[
{} x^{3} y^{\prime \prime }-x^{2} y^{\prime } = -x^{2}+3
\]
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\[
{} y^{\prime \prime } = 1+{y^{\prime }}^{2}
\]
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\[
{} y^{\prime \prime } = 2 x +\left (x^{2}-y^{\prime }\right )^{2}
\]
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\[
{} {y^{\prime \prime }}^{2}-2 y^{\prime \prime }+{y^{\prime }}^{2}-2 x y^{\prime }+x^{2} = 0
\]
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\[
{} 3 y y^{\prime } y^{\prime \prime } = {y^{\prime }}^{3}-1
\]
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\[
{} 4 y {y^{\prime }}^{2} y^{\prime \prime } = {y^{\prime }}^{4}+3
\]
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\[
{} y^{\prime \prime }+y = -\cos \left (x \right )
\]
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\[
{} y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = 12 x^{2}
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = x^{2}+2 x +1
\]
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\[
{} y^{\prime \prime }-y^{\prime }-2 y = 5 \,{\mathrm e}^{2 x}
\]
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\[
{} y^{\prime \prime }+16 y = 4 \cos \left (x \right )
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+3 y = 9 x^{2}+4
\]
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\[
{} y^{\prime \prime }+y = \tan \left (x \right )^{2}
\]
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\[
{} y^{\prime \prime }+y^{\prime }+4 y = 1
\]
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\[
{} y^{\prime \prime }+y^{\prime }+4 y = \sin \left (x \right )
\]
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\[
{} t y^{\prime \prime }+4 y^{\prime } = t^{2}
\]
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\[
{} y^{\prime \prime } = 1
\]
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\[
{} y^{\prime \prime } = f \left (t \right )
\]
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\[
{} y^{\prime \prime } = k
\]
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\[
{} y^{\prime \prime } = 4 \sin \left (x \right )-4
\]
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\[
{} y y^{\prime \prime } = 1
\]
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\[
{} y y^{\prime \prime } = x
\]
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\[
{} y^{2} y^{\prime \prime } = x
\]
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\[
{} 3 y y^{\prime \prime } = \sin \left (x \right )
\]
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\[
{} 3 y y^{\prime \prime }+y = 5
\]
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\[
{} a y y^{\prime \prime }+b y = c
\]
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\[
{} a y^{2} y^{\prime \prime }+b y^{2} = c
\]
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\[
{} z^{\prime \prime }+3 z^{\prime }+2 z = 24 \,{\mathrm e}^{-3 t}-24 \,{\mathrm e}^{-4 t}
\]
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\[
{} y^{\prime \prime }-y y^{\prime } = 2 x
\]
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\[
{} y^{\prime \prime }-x y^{\prime }-x y-x = 0
\]
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\[
{} y^{\prime \prime }-x y^{\prime }-x y-2 x = 0
\]
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\[
{} y^{\prime \prime }-x y^{\prime }-x y-3 x = 0
\]
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\[
{} y^{\prime \prime }-x y^{\prime }-x y-x^{2}-x = 0
\]
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\[
{} y^{\prime \prime }-x y^{\prime }-x y-x^{3}+2 = 0
\]
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\[
{} y^{\prime \prime }-x y^{\prime }-x y-x^{4}-6 = 0
\]
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\[
{} y^{\prime \prime }-x y^{\prime }-x y-x^{5}+24 = 0
\]
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\[
{} y^{\prime \prime }-x y^{\prime }-x y-x = 0
\]
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\[
{} y^{\prime \prime }-x y^{\prime }-x y-x^{2} = 0
\]
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\[
{} y^{\prime \prime }-x y^{\prime }-x y-x^{3} = 0
\]
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\[
{} y^{\prime \prime }-a x y^{\prime }-b x y-c x = 0
\]
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\[
{} y^{\prime \prime }-a x y^{\prime }-b x y-c \,x^{2} = 0
\]
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\[
{} y^{\prime \prime }-a x y^{\prime }-b x y-c \,x^{3} = 0
\]
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\[
{} y^{\prime \prime }-y^{\prime }-x y-x = 0
\]
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\[
{} y^{\prime \prime }-y^{\prime }-x y-x^{2} = 0
\]
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\[
{} y^{\prime \prime }-y^{\prime }-x y-x^{2}-1 = 0
\]
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\[
{} y^{\prime \prime }-y^{\prime }-x y-x^{2}-1 = 0
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }-x y-x^{2}-2 = 0
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }-x y-x^{2}-4 = 0
\]
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\[
{} y^{\prime \prime }-y^{\prime }-x y-x^{3}+1 = 0
\]
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