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\[
{}y^{\prime \prime }+y = \sec \left (t \right )
\] |
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\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = t \,{\mathrm e}^{2 t}
\] |
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\[
{}2 y^{\prime \prime }-3 y^{\prime }+y = \left (t^{2}+1\right ) {\mathrm e}^{t}
\] |
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\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = t \,{\mathrm e}^{3 t}+1
\] |
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\[
{}3 y^{\prime \prime }+4 y^{\prime }+y = \sin \left (t \right ) {\mathrm e}^{-t}
\] |
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\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = t^{{5}/{2}} {\mathrm e}^{-2 t}
\] |
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\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = \sqrt {t +1}
\] |
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\[
{}y^{\prime \prime }-y = f \left (t \right )
\] |
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\[
{}m y^{\prime \prime }+c y^{\prime }+k y = F_{0} \cos \left (\omega t \right )
\] |
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\[
{}y^{\prime \prime }+y = \sec \left (t \right )
\] |
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\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = t \,{\mathrm e}^{2 t}
\] |
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\[
{}2 y^{\prime \prime }-3 y^{\prime }+y = \left (t^{2}+1\right ) {\mathrm e}^{t}
\] |
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\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = t \,{\mathrm e}^{3 t}+1
\] |
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\[
{}3 y^{\prime \prime }+4 y^{\prime }+y = \sin \left (t \right ) {\mathrm e}^{-t}
\] |
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\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = t^{{5}/{2}} {\mathrm e}^{-2 t}
\] |
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\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = \sqrt {t +1}
\] |
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\[
{}y^{\prime \prime }-y = f \left (t \right )
\] |
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\[
{}y^{\prime \prime }+3 y = t^{3}-1
\] |
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\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = t \,{\mathrm e}^{\alpha t}
\] |
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\[
{}y^{\prime \prime }-y = t^{2} {\mathrm e}^{t}
\] |
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\[
{}y^{\prime \prime }+y^{\prime }+y = t^{2}+t +1
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-t}
\] |
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\[
{}y^{\prime \prime }+5 y^{\prime }+4 y = t^{2} {\mathrm e}^{7 t}
\] |
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\[
{}y^{\prime \prime }+4 y = t \sin \left (2 t \right )
\] |
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\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = \left (3 t^{7}-5 t^{4}\right ) {\mathrm e}^{3 t}
\] |
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\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = 2 \cos \left (t \right )^{2}
\] |
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\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = 2 \cos \left (t \right )^{2} {\mathrm e}^{t}
\] |
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\[
{}y^{\prime \prime }+y^{\prime }-6 y = \sin \left (t \right )+t \,{\mathrm e}^{2 t}
\] |
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\[
{}y^{\prime \prime }+y^{\prime }+4 y = t^{2}+\left (2 t +3\right ) \left (1+\cos \left (t \right )\right )
\] |
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\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{t}+{\mathrm e}^{2 t}
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime } = 1+t^{2}+{\mathrm e}^{-2 t}
\] |
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\[
{}y^{\prime \prime }+y = \cos \left (t \right ) \cos \left (2 t \right )
\] |
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\[
{}y^{\prime \prime }+y = \cos \left (t \right ) \cos \left (2 t \right ) \cos \left (3 t \right )
\] |
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\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = t^{{3}/{2}} {\mathrm e}^{3 t}
\] |
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\[
{}y^{\prime \prime }-5 y^{\prime }+4 y = {\mathrm e}^{2 t}
\] |
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\[
{}2 y^{\prime \prime }+y^{\prime }-y = {\mathrm e}^{3 t}
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-t}
\] |
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\[
{}y^{\prime \prime }+y = t^{2} \sin \left (t \right )
\] |
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\[
{}y^{\prime \prime }+3 y^{\prime }+7 y = \cos \left (t \right )
\] |
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\[
{}y^{\prime \prime }+y^{\prime }+y = t^{3}
\] |
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\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{-t}
\] |
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\[
{}y^{\prime \prime }+y = \sin \left (t \right )
\] |
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\[
{}y^{\prime \prime }+y = t \sin \left (t \right )
\] |
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\[
{}y^{\prime \prime }-2 y^{\prime }+y = t \,{\mathrm e}^{t}
\] |
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\[
{}y^{\prime \prime }-2 y^{\prime }+7 y = \sin \left (t \right )
\] |
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\[
{}y^{\prime \prime }+y^{\prime }+y = 1+{\mathrm e}^{-t}
\] |
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\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} 2 & 0\le t \le 3 \\ 3 t -7 & 3<t \end {array}\right .
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }+y = 2 \left (t -3\right ) \operatorname {Heaviside}\left (t -3\right )
\] |
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\[
{}y^{\prime \prime }+y^{\prime }+y = \operatorname {Heaviside}\left (t -\pi \right )-\operatorname {Heaviside}\left (t -2 \pi \right )
\] |
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\[
{}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 1 & 0\le t <4 \\ 0 & 4<t \end {array}\right .
\] |
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\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\pi \\ \cos \left (t \right ) & \pi \le t \end {array}\right .
\] |
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\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} \cos \left (t \right ) & 0\le t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}\le t \end {array}\right .
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }+y = \left \{\begin {array}{cc} \sin \left (2 t \right ) & 0\le t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}\le t \end {array}\right .
\] |
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\[
{}y^{\prime \prime }+y^{\prime }+7 y = \left \{\begin {array}{cc} t & 0\le t <2 \\ 0 & 2\le t \end {array}\right .
\] |
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\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} t^{2} & 0\le t <1 \\ 0 & 1\le t \end {array}\right .
\] |
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\[
{}y^{\prime \prime }-2 y^{\prime }+y = \left \{\begin {array}{cc} 0 & 0\le t <1 \\ t & 1\le t <2 \\ 0 & 2\le t \end {array}\right .
\] |
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\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = \delta \left (t -1\right )
\] |
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\[
{}y^{\prime \prime }+4 y = \sin \left (t \right )+\delta \left (t -\pi \right )
\] |
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\[
{}y^{\prime \prime }+y^{\prime }+y = 2 \delta \left (t -1\right )-\delta \left (t -2\right )
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-t}+3 \delta \left (t -3\right )
\] |
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\[
{}y^{\prime \prime }-4 y = 3 \cos \left (x \right )
\] |
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\[
{}y^{\prime \prime }+y = \sin \left (2 x \right )
\] |
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\[
{}y^{\prime \prime }+y^{\prime }-2 y = {\mathrm e}^{x}
\] |
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\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{-2 x}
\] |
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\[
{}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right )
\] |
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\[
{}y^{\prime \prime }+y^{\prime }+y = x^{2}
\] |
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\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = x \,{\mathrm e}^{-x}
\] |
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\[
{}y^{\prime \prime }-4 y = x +{\mathrm e}^{2 x}
\] |
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\[
{}y^{\prime \prime }-9 y = {\mathrm e}^{3 x}+\sin \left (3 x \right )
\] |
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\[
{}y^{\prime \prime }-y^{\prime }-6 y = x^{3}
\] |
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\[
{}-2 y^{\prime \prime }+3 y = x \,{\mathrm e}^{x}
\] |
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\[
{}y^{\prime \prime }+4 y = x \sin \left (x \right )
\] |
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\[
{}y^{\prime \prime }+y^{\prime }+y = {\mathrm e}^{x} \sin \left (3 x \right )
\] |
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\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = x^{3} {\mathrm e}^{2 x}
\] |
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\[
{}y^{\prime \prime }+2 n y^{\prime }+n^{2} y = 5 \cos \left (6 x \right )
\] |
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\[
{}y^{\prime \prime }+9 y = \left (1+\sin \left (3 x \right )\right ) \cos \left (2 x \right )
\] |
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\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = 2 x -{\mathrm e}^{-4 x}+\sin \left (2 x \right )
\] |
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\[
{}y^{\prime \prime }+4 y = 8 \sin \left (x \right )^{2}
\] |
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\[
{}y^{\prime \prime }-5 y^{\prime }-6 y = {\mathrm e}^{3 x}
\] |
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\[
{}y^{\prime \prime }+4 y = 12 \cos \left (x \right )^{2}
\] |
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\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = x \,{\mathrm e}^{-x}
\] |
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\[
{}y^{\prime \prime }+y = {\mathrm e}^{x} \sin \left (x \right )
\] |
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\[
{}2 y^{\prime \prime }+y^{\prime } = 8 \sin \left (2 x \right )+{\mathrm e}^{-x}
\] |
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\[
{}y^{\prime \prime }+y = 3 x \sin \left (x \right )
\] |
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\[
{}2 y^{\prime \prime }+5 y^{\prime }-3 y = \sin \left (x \right )-8 x
\] |
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\[
{}8 y^{\prime \prime }-y = x \,{\mathrm e}^{-\frac {x}{2}}
\] |
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\[
{}y^{\prime \prime }+y = \sec \left (x \right )
\] |
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\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = {\mathrm e}^{x}
\] |
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\[
{}y^{\prime \prime }+4 y = x^{2}
\] |
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\[
{}y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{2 x}
\] |
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\[
{}y^{\prime \prime }+y = 4 \sin \left (2 x \right )
\] |
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\[
{}y^{\prime \prime }+4 y = 2 x -2 \sin \left (2 x \right )
\] |
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\[
{}y^{\prime \prime }-y = 3 x +5 \,{\mathrm e}^{x}
\] |
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\[
{}y^{\prime \prime }+9 y = {\mathrm e}^{x}+\sin \left (4 x \right )
\] |
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\[
{}y^{\prime \prime }+y = \tan \left (x \right )
\] |
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\[
{}y^{\prime \prime }+a^{2} y = \sec \left (a x \right )
\] |
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\[
{}y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{\left (1-x \right )^{2}}
\] |
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\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = \sin \left ({\mathrm e}^{-x}\right )
\] |
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\[
{}y^{\prime \prime }+4 y = \sec \left (x \right ) \tan \left (x \right )
\] |
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\[
{}y^{\prime \prime }-2 y = {\mathrm e}^{-x} \sin \left (2 x \right )
\] |
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