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\[
{} y^{\prime \prime }+6 y^{\prime }+9 y = 27 \,{\mathrm e}^{-6 x}
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+13 y = 18 \,{\mathrm e}^{-2 x}
\]
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\[
{} y^{\prime \prime }-10 y^{\prime }+29 y = 8 \,{\mathrm e}^{5 x}
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+13 y = 8 \sin \left (3 x \right )
\]
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\[
{} y^{\prime \prime }-y^{\prime }-6 y = 8 \,{\mathrm e}^{2 x}-5 \,{\mathrm e}^{3 x}
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = 2 \,{\mathrm e}^{2 x} x +6 \,{\mathrm e}^{x}
\]
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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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\[
{} y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }+6 y = 3 x \,{\mathrm e}^{x}+2 \,{\mathrm e}^{x}-\sin \left (x \right )
\]
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\[
{} y^{\prime \prime \prime }-6 y^{\prime \prime }+9 y^{\prime }-4 y = 8 x^{2}+3-6 \,{\mathrm e}^{2 x}
\]
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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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\[
{} y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = x^{2} {\mathrm e}^{x}+3 \,{\mathrm e}^{2 x} x +5 x^{2}
\]
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\[
{} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = {\mathrm e}^{2 x} x +x^{2} {\mathrm e}^{3 x}
\]
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\[
{} y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+4 y^{\prime \prime }+3 y^{\prime }+y = x^{2} {\mathrm e}^{-x}+3 \,{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right )
\]
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\[
{} y^{\prime \prime \prime \prime }-16 y = x^{2} \sin \left (2 x \right )+x^{4} {\mathrm e}^{2 x}
\]
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\[
{} y^{\left (6\right )}+2 y^{\left (5\right )}+5 y^{\prime \prime \prime \prime } = x^{3}+x^{2} {\mathrm e}^{-x}+{\mathrm e}^{-x} \sin \left (2 x \right )
\]
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\[
{} y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = x^{2} \cos \left (x \right )
\]
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\[
{} y^{\prime \prime \prime \prime }+16 y = x \,{\mathrm e}^{\sqrt {2}\, x} \sin \left (\sqrt {2}\, x \right )+{\mathrm e}^{-\sqrt {2}\, x} \cos \left (\sqrt {2}\, x \right )
\]
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\[
{} y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-4 y = \cos \left (x \right )^{2}-\cosh \left (x \right )
\]
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\[
{} y^{\prime \prime \prime \prime }+10 y^{\prime \prime }+9 y = \sin \left (x \right ) \sin \left (2 x \right )
\]
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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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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = \frac {1}{1+{\mathrm e}^{2 x}}
\]
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\[
{} y^{\prime \prime }+y = \frac {1}{1+\sin \left (x \right )}
\]
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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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\[
{} x^{2} y^{\prime \prime }-6 x y^{\prime }+10 y = 3 x^{4}+6 x^{3}
\]
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\[
{} \left (1+x \right )^{2} y^{\prime \prime }-2 \left (1+x \right ) y^{\prime }+2 y = 1
\]
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\[
{} \left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (1+x \right ) y^{\prime }+2 y = \left (x +2\right )^{2}
\]
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\[
{} x^{2} y^{\prime \prime }-x \left (x +2\right ) y^{\prime }+\left (x +2\right ) y = x^{3}
\]
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\[
{} x \left (x -2\right ) y^{\prime \prime }-\left (x^{2}-2\right ) y^{\prime }+2 \left (x -1\right ) y = 3 x^{2} \left (x -2\right )^{2} {\mathrm e}^{x}
\]
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\[
{} \left (2 x +1\right ) \left (1+x \right ) y^{\prime \prime }+2 x y^{\prime }-2 y = \left (2 x +1\right )^{2}
\]
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\[
{} \sin \left (x \right )^{2} y^{\prime \prime }-2 \sin \left (x \right ) \cos \left (x \right ) y^{\prime }+\left (\cos \left (x \right )^{2}+1\right ) y = \sin \left (x \right )^{3}
\]
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\[
{} y^{\prime \prime \prime }-3 y^{\prime \prime }-y^{\prime }+3 y = x^{2} {\mathrm e}^{x}
\]
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\[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }+3 y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }-4 y = 0
\]
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\[
{} 4 x^{2} y^{\prime \prime }-4 x y^{\prime }+3 y = 0
\]
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\[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 0
\]
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\[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }+13 y = 0
\]
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\[
{} 3 x^{2} y^{\prime \prime }-4 x y^{\prime }+2 y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+9 y = 0
\]
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\[
{} 9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 0
\]
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\[
{} x^{2} y^{\prime \prime }-5 x y^{\prime }+10 y = 0
\]
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\[
{} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = 0
\]
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\[
{} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-10 x y^{\prime }-8 y = 0
\]
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\[
{} x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-6 x y^{\prime }+18 y = 0
\]
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\[
{} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 4 x -6
\]
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\[
{} x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = 2 x^{3}
\]
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\[
{} x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 4 \ln \left (x \right )
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 2 x \ln \left (x \right )
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 4 \sin \left (\ln \left (x \right )\right )
\]
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\[
{} x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y = x^{3}
\]
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\[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }-10 y = 0
\]
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\[
{} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+5 x y^{\prime }+3 y = 0
\]
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\[
{} x^{2} y^{\prime \prime }-2 y = 4 x -8
\]
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\[
{} x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y = -6 x^{3}+4 x^{2}
\]
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\[
{} x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 10 x^{2}
\]
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\[
{} x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = 2 x^{3}
\]
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\[
{} x^{2} y^{\prime \prime }-6 y = \ln \left (x \right )
\]
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\[
{} \left (x +2\right )^{2} y^{\prime \prime }-\left (x +2\right ) y^{\prime }-3 y = 0
\]
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\[
{} \left (2 x -3\right )^{2} y^{\prime \prime }-6 \left (2 x -3\right ) y^{\prime }+12 y = 0
\]
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\[
{} y^{\prime \prime }+x y^{\prime }+y = 0
\]
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\[
{} y^{\prime \prime }+8 x y^{\prime }-4 y = 0
\]
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\[
{} y^{\prime \prime }+x y^{\prime }+\left (2 x^{2}+1\right ) y = 0
\]
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\[
{} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-4\right ) y = 0
\]
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\[
{} y^{\prime \prime }+x y^{\prime }+\left (3 x +2\right ) y = 0
\]
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\[
{} y^{\prime \prime }-x y^{\prime }+\left (3 x -2\right ) y = 0
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+x y = 0
\]
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\[
{} \left (x -1\right ) y^{\prime \prime }-\left (3 x -2\right ) y^{\prime }+2 x y = 0
\]
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\[
{} \left (x^{3}-1\right ) y^{\prime \prime }+x^{2} y^{\prime }+x y = 0
\]
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\[
{} \left (x +3\right ) y^{\prime \prime }+\left (x +2\right ) y^{\prime }+y = 0
\]
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\[
{} y^{\prime \prime }-x y^{\prime }-y = 0
\]
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\[
{} y^{\prime \prime }+x y^{\prime }-2 y = 0
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+2 x y = 0
\]
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\[
{} \left (2 x^{2}-3\right ) y^{\prime \prime }-2 x y^{\prime }+y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }-y = 0
\]
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\[
{} x y^{\prime \prime }+y^{\prime }+2 y = 0
\]
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\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+n \left (n +1\right ) y = 0
\]
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\[
{} \left (x^{2}-3 x \right ) y^{\prime \prime }+\left (x +2\right ) y^{\prime }+y = 0
\]
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\[
{} \left (x^{3}+x^{2}\right ) y^{\prime \prime }+\left (x^{2}-2 x \right ) y^{\prime }+4 y = 0
\]
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