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\[
{}t^{2} y^{\prime \prime }-t y^{\prime }+2 y = 0
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\[
{}t^{2} y^{\prime \prime }-3 t y^{\prime }+4 y = 0
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\[
{}2 t^{2} y^{\prime \prime }+3 t y^{\prime }-y = 0
\] |
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\[
{}y^{\prime \prime }+t y^{\prime }+y = 0
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\[
{}y^{\prime \prime }-y = 0
\] |
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\[
{}6 y^{\prime \prime }-7 y^{\prime }+y = 0
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\[
{}y^{\prime \prime }-3 y^{\prime }+y = 0
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\[
{}3 y^{\prime \prime }+6 y^{\prime }+2 y = 0
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\[
{}y^{\prime \prime }-3 y^{\prime }-4 y = 0
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\[
{}2 y^{\prime \prime }+y^{\prime }-10 y = 0
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\[
{}5 y^{\prime \prime }+5 y^{\prime }-y = 0
\] |
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\[
{}y^{\prime \prime }-6 y^{\prime }+y = 0
\] |
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\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }+\alpha t y^{\prime }+\beta y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }+5 t y^{\prime }-2 y = 0
\] |
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\[
{}y^{\prime \prime }+y^{\prime }+y = 0
\] |
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\[
{}2 y^{\prime \prime }+3 y^{\prime }+4 y = 0
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }+3 y = 0
\] |
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\[
{}4 y^{\prime \prime }-y^{\prime }+y = 0
\] |
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\[
{}y^{\prime \prime }+y^{\prime }+2 y = 0
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 0
\] |
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\[
{}2 y^{\prime \prime }-y^{\prime }+3 y = 0
\] |
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\[
{}3 y^{\prime \prime }-2 y^{\prime }+4 y = 0
\] |
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\[
{}y^{\prime \prime }+w^{2} y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }+t y^{\prime }+y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }+2 t y^{\prime }+2 y = 0
\] |
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\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 0
\] |
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\[
{}4 y^{\prime \prime }-12 y^{\prime }+9 y = 0
\] |
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\[
{}9 y^{\prime \prime }+6 y^{\prime }+y = 0
\] |
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\[
{}4 y^{\prime \prime }-4 y^{\prime }+y = 0
\] |
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\[
{}6 y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
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\[
{}9 y^{\prime \prime }-12 y^{\prime }+4 y = 0
\] |
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\[
{}y^{\prime \prime }-\frac {2 \left (t +1\right ) y^{\prime }}{t^{2}+2 t -1}+\frac {2 y}{t^{2}+2 t -1} = 0
\] |
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\[
{}y^{\prime \prime }-4 t y^{\prime }+\left (4 t^{2}-2\right ) y = 0
\] |
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\[
{}\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y = 0
\] |
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\[
{}\left (t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y = 0
\] |
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\[
{}\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+6 y = 0
\] |
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\[
{}\left (2 t +1\right ) y^{\prime \prime }-4 \left (t +1\right ) y^{\prime }+4 y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-\frac {1}{4}\right ) y = 0
\] |
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\[
{}t y^{\prime \prime }-\left (1+3 t \right ) y^{\prime }+3 y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }-t y^{\prime }+y = 0
\] |
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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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\[
{}t^{2} y^{\prime \prime }-2 y = t^{2}
\] |
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\[
{}y^{\prime \prime }+p \left (t \right ) y^{\prime }+q \left (t \right ) y = t +1
\] |
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\[
{}y^{\prime \prime }-\frac {2 t y^{\prime }}{t^{2}+1}+\frac {2 y}{t^{2}+1} = t^{2}+1
\] |
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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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\[
{}t^{2} y^{\prime \prime }+5 t y^{\prime }-5 y = 0
\] |
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\[
{}2 t^{2} y^{\prime \prime }+3 t y^{\prime }-y = 0
\] |
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\[
{}\left (t -1\right )^{2} y^{\prime \prime }-2 \left (t -1\right ) y^{\prime }+2 y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }-t y^{\prime }+y = 0
\] |
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\[
{}\left (t -2\right )^{2} y^{\prime \prime }+5 \left (t -2\right ) y^{\prime }+4 y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }+t y^{\prime }+y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }+3 t y^{\prime }+2 y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }-t y^{\prime }-2 y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }-3 t y^{\prime }+4 y = 0
\] |
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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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