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\[
{}y^{\prime \prime }+3 y^{\prime }-4 y = 6 \,{\mathrm e}^{2 t -3}
\] |
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\[
{}y^{\prime \prime }+6 y^{\prime }+8 y = {\mathrm e}^{-3 t}-{\mathrm e}^{-5 t}
\] |
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\[
{}y^{\prime \prime }+10 y^{\prime }+24 y = 144 t^{2}
\] |
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\[
{}y^{\prime \prime }+9 y = \left \{\begin {array}{cc} 8 \sin \left (t \right ) & 0<t <\pi \\ 0 & \pi <t \end {array}\right .
\] |
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\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 4 t & 0<t <1 \\ 8 & 1<t \end {array}\right .
\] |
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\[
{}y^{\prime \prime }+y^{\prime }-2 y = \left \{\begin {array}{cc} 3 \sin \left (t \right )-\cos \left (t \right ) & 0<t <2 \pi \\ 3 \sin \left (2 t \right )-\cos \left (2 t \right ) & 2 \pi <t \end {array}\right .
\] |
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\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0<t <1 \\ 0 & 1<t \end {array}\right .
\] |
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\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0<t <1 \\ 0 & 1<t \end {array}\right .
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = \left \{\begin {array}{cc} 10 \sin \left (t \right ) & 0<t <2 \pi \\ 0 & 2 \pi <t \end {array}\right .
\] |
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\[
{}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 8 t^{2} & 0<t <5 \\ 0 & 5<t \end {array}\right .
\] |
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\[
{}y^{\prime \prime }+4 y = \delta \left (t -\pi \right )
\] |
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\[
{}y^{\prime \prime }+16 y = 4 \delta \left (t -3 \pi \right )
\] |
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\[
{}y^{\prime \prime }+y = \delta \left (t -\pi \right )-\delta \left (t -2 \pi \right )
\] |
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\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = \delta \left (t -1\right )
\] |
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\[
{}4 y^{\prime \prime }+24 y^{\prime }+37 y = 17 \,{\mathrm e}^{-t}+\delta \left (t -\frac {1}{2}\right )
\] |
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\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 10 \sin \left (t \right )+10 \delta \left (t -1\right )
\] |
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\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = \left (1-\operatorname {Heaviside}\left (t -10\right )\right ) {\mathrm e}^{t}-{\mathrm e}^{10} \delta \left (t -10\right )
\] |
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\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = \delta \left (t -\frac {\pi }{2}\right )+\operatorname {Heaviside}\left (t -\pi \right ) \cos \left (t \right )
\] |
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\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = \operatorname {Heaviside}\left (t -1\right )+\delta \left (t -2\right )
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 25 t -100 \delta \left (t -\pi \right )
\] |
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\[
{}y^{\prime \prime }-2 y^{\prime }-3 y = 1+3 x
\] |
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\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{2 x} x
\] |
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\[
{}y^{\prime \prime }+y = 4 \sin \left (x \right )
\] |
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\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 50 \,{\mathrm e}^{2 x}
\] |
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\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 50 \,{\mathrm e}^{2 x}
\] |
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\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \cos \left (2 x \right )
\] |
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\[
{}y^{\prime \prime }+4 y = x^{2}
\] |
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\[
{}y^{\prime \prime }-4 y^{\prime }+3 y = x^{3}
\] |
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\[
{}y^{\prime \prime } = x +2
\] |
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\[
{}y^{\prime \prime } = 1+3 x
\] |
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\[
{}y^{\prime \prime }+4 y = \cos \left (x \right )
\] |
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\[
{}y^{\prime \prime }+9 y = \sin \left (3 x \right )
\] |
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\[
{}y^{\prime \prime }+y = \tan \left (x \right )
\] |
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\[
{}y^{\prime \prime }+2 i y^{\prime }+y = x
\] |
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\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = 3 \,{\mathrm e}^{-x}+2 x^{2}
\] |
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\[
{}y^{\prime \prime }-7 y^{\prime }+6 y = \sin \left (x \right )
\] |
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\[
{}y^{\prime \prime }+y = 2 \sin \left (x \right ) \sin \left (2 x \right )
\] |
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\[
{}y^{\prime \prime }+y = \sec \left (x \right )
\] |
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\[
{}4 y^{\prime \prime }-y = {\mathrm e}^{x}
\] |
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\[
{}6 y^{\prime \prime }+5 y^{\prime }-6 y = x
\] |
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\[
{}y^{\prime \prime }+\omega ^{2} y = A \cos \left (\omega x \right )
\] |
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\[
{}y^{\prime \prime }-2 i y^{\prime }-y = {\mathrm e}^{i x}-2 \,{\mathrm e}^{-i x}
\] |
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\[
{}y^{\prime \prime }+4 y = \cos \left (x \right )
\] |
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\[
{}y^{\prime \prime }+4 y = \sin \left (2 x \right )
\] |
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\[
{}y^{\prime \prime }-4 y = 3 \,{\mathrm e}^{2 x}+4 \,{\mathrm e}^{-x}
\] |
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\[
{}y^{\prime \prime }-y^{\prime }-2 y = x^{2}+\cos \left (x \right )
\] |
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\[
{}y^{\prime \prime }+9 y = x^{2} {\mathrm e}^{3 x}
\] |
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\[
{}y^{\prime \prime }+y = x \,{\mathrm e}^{x} \cos \left (2 x \right )
\] |
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\[
{}y^{\prime \prime }+i y^{\prime }+2 y = 2 \cosh \left (2 x \right )+{\mathrm e}^{-2 x}
\] |
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\[
{}y^{\prime \prime }+y^{\prime } = 1
\] |
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\[
{}\frac {y^{\prime \prime }}{y^{\prime }} = x^{2}
\] |
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\[
{}y^{\prime \prime }+3 y^{\prime }-10 y = 6 \,{\mathrm e}^{4 x}
\] |
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\[
{}y^{\prime \prime }+4 y = 3 \sin \left (x \right )
\] |
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\[
{}y^{\prime \prime }+10 y^{\prime }+25 y = 14 \,{\mathrm e}^{-5 x}
\] |
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\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = 25 x^{2}+12
\] |
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\[
{}y^{\prime \prime }-y^{\prime }-6 y = 20 \,{\mathrm e}^{-2 x}
\] |
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\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = 14 \sin \left (2 x \right )-18 \cos \left (2 x \right )
\] |
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\[
{}y^{\prime \prime }+y = 2 \cos \left (x \right )
\] |
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\[
{}y^{\prime \prime }-2 y^{\prime } = 12 x -10
\] |
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\[
{}y^{\prime \prime }-2 y^{\prime }+y = 6 \,{\mathrm e}^{x}
\] |
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\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = {\mathrm e}^{x} \sin \left (x \right )
\] |
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\[
{}y^{\prime \prime }+y^{\prime } = 10 x^{4}+2
\] |
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\[
{}y^{\prime \prime }+4 y = 4 \cos \left (2 x \right )+6 \cos \left (x \right )+8 x^{2}-4 x
\] |
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\[
{}y^{\prime \prime }+9 y = 2 \sin \left (3 x \right )+4 \sin \left (x \right )-26 \,{\mathrm e}^{-2 x}+27 x^{3}
\] |
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\[
{}y^{\prime \prime }-3 y = {\mathrm e}^{2 x}
\] |
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\[
{}y^{\prime \prime }+4 y = \tan \left (2 x \right )
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-x} \ln \left (x \right )
\] |
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\[
{}y^{\prime \prime }-2 y^{\prime }-3 y = 64 x \,{\mathrm e}^{-x}
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = {\mathrm e}^{-x} \sec \left (2 x \right )
\] |
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\[
{}2 y^{\prime \prime }+3 y^{\prime }+y = {\mathrm e}^{-3 x}
\] |
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\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = \frac {1}{1+{\mathrm e}^{-x}}
\] |
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\[
{}y^{\prime \prime }+y = \sec \left (x \right )
\] |
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\[
{}y^{\prime \prime }+y = \cot \left (x \right )^{2}
\] |
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\[
{}y^{\prime \prime }+y = \cot \left (2 x \right )
\] |
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\[
{}y^{\prime \prime }+y = x \cos \left (x \right )
\] |
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\[
{}y^{\prime \prime }+y = \tan \left (x \right )
\] |
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\[
{}y^{\prime \prime }+y = \sec \left (x \right ) \tan \left (x \right )
\] |
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\[
{}y^{\prime \prime }+y = \sec \left (x \right ) \csc \left (x \right )
\] |
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\[
{}y^{\prime \prime }-2 y^{\prime }+y = 2 x
\] |
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\[
{}y^{\prime \prime }-y^{\prime }-6 y = {\mathrm e}^{-x}
\] |
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\[
{}y^{\prime \prime }-2 y^{\prime }-5 y = x
\] |
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\[
{}y^{\prime \prime }+y = {\mathrm e}^{x}
\] |
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\[
{}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right )
\] |
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\[
{}y^{\prime \prime }-y = {\mathrm e}^{3 x}
\] |
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\[
{}y^{\prime \prime }-y^{\prime }+4 y = x
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = {\mathrm e}^{x}
\] |
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\[
{}y^{\prime \prime }+3 y^{\prime }+4 y = \sin \left (x \right )
\] |
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\[
{}y^{\prime \prime }+y = {\mathrm e}^{-x}
\] |
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\[
{}y^{\prime \prime }-y = \cos \left (x \right )
\] |
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\[
{}y^{\prime \prime } = \tan \left (x \right )
\] |
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\[
{}y^{\prime \prime }-2 y^{\prime } = \ln \left (x \right )
\] |
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\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 2 x -1
\] |
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\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{-x}
\] |
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\[
{}y^{\prime \prime }-y^{\prime }-2 y = \cos \left (x \right )
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }-y = x \,{\mathrm e}^{x} \sin \left (x \right )
\] |
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\[
{}y^{\prime \prime }+9 y = \sec \left (2 x \right )
\] |
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\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = x \ln \left (x \right )
\] |
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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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