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Mathematica |
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\[
{} y^{\prime \prime \prime }-y^{\prime \prime }+4 y^{\prime }-4 y = 8 \,{\mathrm e}^{2 t}-5 \,{\mathrm e}^{t}
\]
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\[
{} y^{\prime \prime \prime }-5 y^{\prime \prime }+y^{\prime }-y = -t^{2}+2 t -10
\]
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\[
{} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = 12 \operatorname {Heaviside}\left (t \right )-12 \operatorname {Heaviside}\left (t -1\right )
\]
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\[
{} y^{\prime \prime \prime \prime }-16 y = 32 \operatorname {Heaviside}\left (t \right )-32 \operatorname {Heaviside}\left (t -\pi \right )
\]
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\[
{} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y = 5
\]
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\[
{} y^{\prime \prime \prime } = 2 y^{\prime \prime }-4 y^{\prime }+\sin \left (t \right )
\]
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\[
{} y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y = 2 x +3
\]
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\[
{} y^{\prime \prime \prime \prime }-a^{4} y = 5 a^{4} {\mathrm e}^{a x} \sin \left (a x \right )
\]
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\[
{} y^{\prime \prime \prime \prime }+2 a^{2} y^{\prime \prime }+a^{4} y = 8 \cos \left (a x \right )
\]
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\[
{} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+13 y^{\prime \prime }-12 y^{\prime }+4 y = 2 \,{\mathrm e}^{x}-4 \,{\mathrm e}^{2 x}
\]
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\[
{} y^{\prime \prime \prime \prime }+4 y^{\prime \prime } = 24 x^{2}-6 x +14+32 \cos \left (2 x \right )
\]
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\[
{} y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = 3+\cos \left (2 x \right )
\]
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\[
{} y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime } = 6 x -20-120 x^{2} {\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime \prime }-6 y^{\prime \prime }+21 y^{\prime }-26 y = 36 \,{\mathrm e}^{2 x} \sin \left (3 x \right )
\]
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\[
{} y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y = \left (2 x^{2}+4 x +8\right ) \cos \left (x \right )+\left (6 x^{2}+8 x +12\right ) \sin \left (x \right )
\]
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\[
{} y^{\left (6\right )}-12 y^{\left (5\right )}+63 y^{\prime \prime \prime \prime }-18 y^{\prime \prime \prime }+315 y^{\prime \prime }-300 y^{\prime }+125 y = {\mathrm e}^{x} \left (48 \cos \left (x \right )+96 \sin \left (x \right )\right )
\]
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\[
{} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 2 \,{\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = 3 x +4
\]
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\[
{} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime } = x \,{\mathrm e}^{x}-3 x^{2}
\]
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\[
{} y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime } = x +\cos \left (x \right )
\]
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\[
{} y^{\prime \prime \prime \prime } = 1
\]
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\[
{} y^{\prime \prime \prime \prime }+6 y^{\prime \prime }+3 y^{\prime }-83 y-25 = 0
\]
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\[
{} y^{\prime \prime \prime }-9 y^{\prime \prime }+27 y^{\prime }-27 y = {\mathrm e}^{3 x} \sin \left (x \right )
\]
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\[
{} y^{\prime \prime \prime \prime }+y^{\prime \prime } = 1
\]
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\[
{} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime } = 12 \,{\mathrm e}^{-2 x}
\]
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\[
{} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime } = 10 \sin \left (2 x \right )
\]
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\[
{} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime } = 32 \,{\mathrm e}^{4 x}
\]
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\[
{} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime } = 32 x
\]
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\[
{} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = x^{2}
\]
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\[
{} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 30 \cos \left (2 x \right )
\]
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\[
{} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 6 \,{\mathrm e}^{x}
\]
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\[
{} y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime } = x^{2} {\mathrm e}^{3 x}
\]
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\[
{} y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime } = x^{2} \sin \left (3 x \right )
\]
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\[
{} y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime } = x^{2} {\mathrm e}^{3 x} \sin \left (3 x \right )
\]
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\[
{} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 30 x \cos \left (2 x \right )
\]
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\[
{} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 3 x \cos \left (x \right )
\]
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\[
{} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 3 x \,{\mathrm e}^{x} \cos \left (x \right )
\]
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\[
{} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 5 x^{5} {\mathrm e}^{2 x}
\]
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\[
{} y^{\prime \prime \prime }-4 y^{\prime } = 30 \,{\mathrm e}^{3 x}
\]
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\[
{} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = \tan \left (x \right )
\]
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\[
{} y^{\prime \prime \prime \prime }-81 y = \sinh \left (x \right )
\]
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\[
{} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime } = 8
\]
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\[
{} y^{\prime \prime \prime }+8 y = {\mathrm e}^{-2 x}
\]
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\[
{} y^{\left (6\right )}-64 y = {\mathrm e}^{-2 x}
\]
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\[
{} y^{\prime \prime \prime }-27 y = {\mathrm e}^{-3 t}
\]
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\[
{} y^{\prime \prime \prime }+9 y^{\prime } = \delta \left (t -1\right )
\]
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\[
{} y^{\prime \prime \prime \prime }-16 y = \delta \left (t \right )
\]
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\[
{} y^{\prime \prime \prime }-2 y^{\prime \prime }+5 y^{\prime }+y = {\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime \prime }+y^{\prime \prime } = {\mathrm e}^{t}
\]
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\[
{} y^{\prime \prime \prime \prime }-16 y = 1
\]
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\[
{} y^{\left (5\right )}-y^{\prime \prime \prime \prime } = 1
\]
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\[
{} y^{\prime \prime \prime \prime }+9 y^{\prime \prime } = 1
\]
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\[
{} y^{\prime \prime \prime \prime }+9 y^{\prime \prime } = 9 \,{\mathrm e}^{3 t}
\]
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\[
{} y^{\prime \prime \prime }+10 y^{\prime \prime }+34 y^{\prime }+40 y = t \,{\mathrm e}^{-4 t}+2 \,{\mathrm e}^{-3 t} \cos \left (t \right )
\]
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\[
{} y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y = 2 \,{\mathrm e}^{-3 t}-t \,{\mathrm e}^{-t}
\]
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\[
{} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+13 y^{\prime \prime }-24 y^{\prime }+36 y = 108 t
\]
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\[
{} y^{\prime \prime \prime }+6 y^{\prime \prime }-14 y^{\prime }-104 y = -111 \,{\mathrm e}^{t}
\]
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\[
{} y^{\prime \prime \prime \prime }-10 y^{\prime \prime \prime }+38 y^{\prime \prime }-64 y^{\prime }+40 y = 153 \,{\mathrm e}^{-t}
\]
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\[
{} y^{\prime \prime \prime }+4 y^{\prime } = \tan \left (2 t \right )
\]
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\[
{} y^{\prime \prime \prime }+4 y^{\prime } = \sec \left (2 t \right ) \tan \left (2 t \right )
\]
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\[
{} y^{\prime \prime \prime \prime }+4 y^{\prime \prime } = \sec \left (2 t \right )^{2}
\]
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\[
{} y^{\prime \prime \prime \prime }+4 y^{\prime \prime } = \tan \left (2 t \right )^{2}
\]
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\[
{} y^{\prime \prime \prime }+9 y^{\prime } = \sec \left (3 t \right )
\]
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\[
{} y^{\prime \prime \prime }+y^{\prime } = -\sec \left (t \right ) \tan \left (t \right )
\]
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\[
{} y^{\prime \prime \prime }+4 y^{\prime } = \sec \left (2 t \right )
\]
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\[
{} y^{\prime \prime \prime }-2 y^{\prime \prime } = -\frac {1}{t^{2}}-\frac {2}{t}
\]
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\[
{} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = \frac {{\mathrm e}^{t}}{t}
\]
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\[
{} y^{\prime \prime \prime }-4 y^{\prime \prime }-11 y^{\prime }+30 y = {\mathrm e}^{4 t}
\]
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\[
{} y^{\prime \prime \prime }+3 y^{\prime \prime }-10 y^{\prime }-24 y = {\mathrm e}^{-3 t}
\]
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\[
{} y^{\prime \prime \prime }-13 y^{\prime }+12 y = \cos \left (t \right )
\]
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\[
{} y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime } = \cos \left (t \right )
\]
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\[
{} y^{\left (6\right )}+y^{\prime \prime \prime \prime } = -24
\]
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\[
{} y^{\prime \prime \prime \prime }+y^{\prime \prime } = \tan \left (t \right )^{2}
\]
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\[
{} y^{\prime \prime \prime }-y^{\prime \prime } = 3 t^{2}
\]
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\[
{} y^{\prime \prime \prime \prime }+y^{\prime \prime } = \sec \left (t \right )^{2}
\]
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\[
{} y^{\prime \prime \prime }+y^{\prime } = \sec \left (t \right )
\]
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\[
{} y^{\prime \prime \prime \prime }+y^{\prime \prime } = \cos \left (t \right )
\]
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\[
{} y^{\prime \prime \prime \prime }+y^{\prime \prime } = t
\]
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\[
{} y^{\prime \prime \prime }+3 y^{\prime \prime }-9 y^{\prime }+5 y = {\mathrm e}^{t}
\]
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\[
{} y^{\prime \prime \prime }-12 y^{\prime }-16 y = {\mathrm e}^{4 t}-{\mathrm e}^{-2 t}
\]
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\[
{} y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+18 y^{\prime \prime }+30 y^{\prime }+25 y = {\mathrm e}^{-t} \cos \left (2 t \right )+{\mathrm e}^{-2 t} \sin \left (t \right )
\]
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\[
{} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+14 y^{\prime \prime }+20 y^{\prime }+25 y = t^{2}
\]
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\[
{} y^{\prime \prime \prime \prime } = x
\]
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\[
{} y^{\prime \prime \prime } = x +\cos \left (x \right )
\]
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\[
{} y^{\prime \prime \prime }+y = x
\]
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\[
{} y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y = 1
\]
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\[
{} y^{\prime \prime \prime }+y^{\prime } = 2
\]
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\[
{} y^{\prime \prime \prime }+y^{\prime \prime } = 3
\]
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\[
{} y^{\prime \prime \prime \prime }-y = 1
\]
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\[
{} y^{\prime \prime \prime \prime }-y^{\prime } = 2
\]
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\[
{} y^{\prime \prime \prime \prime }-y^{\prime \prime } = 3
\]
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\[
{} y^{\prime \prime \prime \prime }-y^{\prime \prime \prime } = 4
\]
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\[
{} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+4 y^{\prime \prime } = 1
\]
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\[
{} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+y^{\prime \prime } = {\mathrm e}^{4 x}
\]
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\[
{} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+y^{\prime \prime } = {\mathrm e}^{-x}
\]
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\[
{} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+y^{\prime \prime } = x \,{\mathrm e}^{-x}
\]
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\[
{} y^{\prime \prime \prime \prime }+4 y^{\prime \prime }+4 y = \sin \left (2 x \right )
\]
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\[
{} y^{\prime \prime \prime \prime }+4 y^{\prime \prime }+4 y = \cos \left (x \right )
\]
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\[
{} y^{\prime \prime \prime \prime }+4 y^{\prime \prime }+4 y = \sin \left (2 x \right ) x
\]
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\[
{} y^{\prime \prime \prime \prime }+2 n^{2} y^{\prime \prime }+n^{4} y = a \sin \left (n x +\alpha \right )
\]
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