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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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\[
{} y^{\prime \prime }+y = \sec \left (x \right ) \tan \left (x \right )
\]
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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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\[
{} y^{\prime \prime }+4 y = 8
\]
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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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\[
{} x^{\prime \prime }-4 x^{\prime } = \tan \left (t \right )
\]
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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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\[
{} y^{\prime \prime }+y = \cosh \left (x \right )
\]
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\[
{} x^{\prime \prime }-4 x^{\prime }+4 x = {\mathrm e}^{t}+{\mathrm e}^{2 t}+1
\]
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\[
{} y^{\prime \prime }+y = 1-\frac {1}{\sin \left (x \right )}
\]
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\[
{} x^{\prime \prime }+9 x = t \sin \left (3 t \right )
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+y = \sinh \left (x \right )
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+2 y = x \,{\mathrm e}^{x} \cos \left (x \right )
\]
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\[
{} {y^{\prime \prime }}^{3}+y^{\prime \prime }+1 = x
\]
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\[
{} x^{\prime \prime }+10 x^{\prime }+25 x = 2^{t}+t \,{\mathrm e}^{-5 t}
\]
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\[
{} y^{\prime \prime }+y = \sin \left (3 x \right ) \cos \left (x \right )
\]
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\[
{} y^{\prime \prime } = y+x^{2}
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+3 y = 9 t
\]
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\[
{} 4 y^{\prime \prime }+16 y^{\prime }+17 y = 17 t -1
\]
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\[
{} 4 y^{\prime \prime }+5 y^{\prime }+4 y = 3 \,{\mathrm e}^{-t}
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+4 y = t^{2} {\mathrm e}^{2 t}
\]
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\[
{} y^{\prime \prime }+9 y = {\mathrm e}^{-2 t}
\]
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\[
{} 2 y^{\prime \prime }-3 y^{\prime }+17 y = 17 t -1
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-t}
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+5 y = t +2
\]
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\[
{} y^{\prime \prime }+8 y^{\prime }+20 y = \sin \left (2 t \right )
\]
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\[
{} 4 y^{\prime \prime }-4 y^{\prime }+y = t^{2}
\]
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\[
{} 2 y^{\prime \prime }+y^{\prime }-y = 4 \sin \left (t \right )
\]
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\[
{} 3 y^{\prime \prime }+5 y^{\prime }-2 y = 7 \,{\mathrm e}^{-2 t}
\]
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\[
{} y^{\prime \prime }+9 y = 24 \sin \left (t \right ) \left (\operatorname {Heaviside}\left (t \right )+\operatorname {Heaviside}\left (t -\pi \right )\right )
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+y = \operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -1\right )
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+2 y = 5 \cos \left (t \right ) \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )\right )
\]
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\[
{} y^{\prime \prime }+5 y^{\prime }+6 y = 36 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -1\right )\right )
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+13 y = 39 \operatorname {Heaviside}\left (t \right )-507 \left (t -2\right ) \operatorname {Heaviside}\left (t -2\right )
\]
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\[
{} y^{\prime \prime }+4 y = 3 \operatorname {Heaviside}\left (t \right )-3 \operatorname {Heaviside}\left (t -4\right )+\left (2 t -5\right ) \operatorname {Heaviside}\left (t -4\right )
\]
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\[
{} 4 y^{\prime \prime }+4 y^{\prime }+5 y = 25 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )\right )
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+3 y = \operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -1\right )+\operatorname {Heaviside}\left (t -2\right )-\operatorname {Heaviside}\left (t -3\right )
\]
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\[
{} y^{\prime \prime }-2 y^{\prime } = \left \{\begin {array}{cc} 4 & 0\le t <1 \\ 6 & 1\le t \end {array}\right .
\]
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\[
{} y^{\prime \prime }-3 y^{\prime }+2 y = \left \{\begin {array}{cc} 0 & 0\le t <1 \\ 1 & 1\le t <2 \\ -1 & 2\le t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0\le t <2 \\ -1 & 2\le t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0\le t <\pi \\ -t & \pi \le t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 8 t & 0\le t <\frac {\pi }{2} \\ 8 \pi & \frac {\pi }{2}\le t \end {array}\right .
\]
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\[
{} y^{\prime \prime }+4 \pi ^{2} y = 3 \delta \left (t -\frac {1}{3}\right )-\delta \left (t -1\right )
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+2 y = 3 \delta \left (t -1\right )
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+29 y = 5 \delta \left (t -\pi \right )-5 \delta \left (t -2 \pi \right )
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = 1-\delta \left (t -1\right )
\]
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\[
{} 4 y^{\prime \prime }+4 y^{\prime }+y = {\mathrm e}^{-\frac {t}{2}} \delta \left (t -1\right )
\]
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\[
{} y^{\prime \prime }-7 y^{\prime }+6 y = \delta \left (t -1\right )
\]
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