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\[
{} y^{\prime \prime }-4 y^{\prime }+4 y = x^{2}
\]
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\[
{} y^{\prime \prime }+8 y^{\prime } = 8 x
\]
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\[
{} y^{\prime \prime }-2 k y^{\prime }+k^{2} y = {\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+4 y = 8 \,{\mathrm e}^{-2 x}
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+3 y = 9 \,{\mathrm e}^{-3 x}
\]
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\[
{} 7 y^{\prime \prime }-y^{\prime } = 14 x
\]
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\[
{} y^{\prime \prime }+3 y^{\prime } = 3 x \,{\mathrm e}^{-3 x}
\]
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\[
{} y^{\prime \prime }+5 y^{\prime }+6 y = 10 \left (1-x \right ) {\mathrm e}^{-2 x}
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+2 y = 1+x
\]
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\[
{} y^{\prime \prime }+y^{\prime }+y = \left (x^{2}+x \right ) {\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }-2 y = 8 \sin \left (2 x \right )
\]
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\[
{} y^{\prime \prime }+y = 4 x \cos \left (x \right )
\]
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\[
{} y^{\prime \prime }-2 m y^{\prime }+m^{2} y = \sin \left (n x \right )
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+5 y = {\mathrm e}^{-x} \sin \left (2 x \right )
\]
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\[
{} y^{\prime \prime }+a^{2} y = 2 \cos \left (m x \right )+3 \sin \left (m x \right )
\]
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\[
{} y^{\prime \prime }-y^{\prime } = {\mathrm e}^{x} \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }+2 y^{\prime } = 4 \left (\cos \left (x \right )+\sin \left (x \right )\right ) {\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+5 y = 10 \,{\mathrm e}^{-2 x} \cos \left (x \right )
\]
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\[
{} 4 y^{\prime \prime }+8 y^{\prime } = x \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }-3 y^{\prime }+2 y = x \,{\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }+y^{\prime }-2 y = x^{2} {\mathrm e}^{4 x}
\]
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\[
{} y^{\prime \prime }-3 y^{\prime }+2 y = \left (x^{2}+x \right ) {\mathrm e}^{3 x}
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = x^{3}
\]
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\[
{} y^{\prime \prime }+y = x^{2} \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+y = x^{2} {\mathrm e}^{-x} \cos \left (x \right )
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+5 y = {\mathrm e}^{2 x} \left (\sin \left (x \right )+2 \cos \left (x \right )\right )
\]
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\[
{} y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{x}+{\mathrm e}^{-2 x}
\]
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\[
{} y^{\prime \prime }+4 y^{\prime } = x +{\mathrm e}^{-4 x}
\]
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\[
{} y^{\prime \prime }-y = x +\sin \left (x \right )
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+2 y = \left (\sin \left (x \right )+1\right ) {\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }+4 y = \sin \left (x \right ) \sin \left (2 x \right )
\]
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\[
{} y^{\prime \prime }-4 y^{\prime } = 2 \cos \left (4 x \right )^{2}
\]
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\[
{} y^{\prime \prime }-y^{\prime }-2 y = 4 x -2 \,{\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }-3 y^{\prime } = 18 x -10 \cos \left (x \right )
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = 2+{\mathrm e}^{x} \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+2 y = \left (5 x +4\right ) {\mathrm e}^{x}+{\mathrm e}^{-x}
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+5 y = 4 \,{\mathrm e}^{-x}+17 \sin \left (2 x \right )
\]
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\[
{} 2 y^{\prime \prime }-3 y^{\prime }-2 y = 5 \,{\mathrm e}^{x} \cosh \left (x \right )
\]
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\[
{} y^{\prime \prime }+4 y = x \sin \left (x \right )^{2}
\]
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\[
{} y^{\prime \prime }+y^{\prime } = \cos \left (x \right )^{2}+{\mathrm e}^{x}+x^{2}
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+5 y = 10 \sin \left (x \right )+17 \sin \left (2 x \right )
\]
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\[
{} y^{\prime \prime }+y^{\prime } = x^{2}-{\mathrm e}^{-x}+{\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }-3 y = 2 x +{\mathrm e}^{-x}-2 \,{\mathrm e}^{3 x}
\]
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\[
{} y^{\prime \prime }+4 y = {\mathrm e}^{x}+4 \sin \left (2 x \right )+2 \cos \left (x \right )^{2}-1
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }+2 y = 6 x \,{\mathrm e}^{-x} \left (1-{\mathrm e}^{-x}\right )
\]
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\[
{} y^{\prime \prime }+y = \cos \left (2 x \right )^{2}+\sin \left (\frac {x}{2}\right )^{2}
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+5 y = 1+8 \cos \left (x \right )+{\mathrm e}^{2 x}
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+2 y = {\mathrm e}^{x} \sin \left (\frac {x}{2}\right )^{2}
\]
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\[
{} y^{\prime \prime }-3 y^{\prime } = 1+{\mathrm e}^{x}+\cos \left (x \right )+\sin \left (x \right )
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+5 y = {\mathrm e}^{x} \left (1-2 \sin \left (x \right )^{2}\right )+10 x +1
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+4 y = 4 x +\sin \left (x \right )+\sin \left (2 x \right )
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+y = 1+2 \cos \left (x \right )+\cos \left (2 x \right )-\sin \left (2 x \right )
\]
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\[
{} y^{\prime \prime }+y^{\prime }+y+1 = \sin \left (x \right )+x +x^{2}
\]
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\[
{} y^{\prime \prime }+6 y^{\prime }+9 y = 18 \,{\mathrm e}^{-3 x}+8 \sin \left (x \right )+6 \cos \left (x \right )
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+1 = 3 \sin \left (2 x \right )+\cos \left (x \right )
\]
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\[
{} y^{\prime \prime }+y = 2 \sin \left (x \right ) \sin \left (2 x \right )
\]
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\[
{} y^{\prime \prime }+y = -2 x +2
\]
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\[
{} y^{\prime \prime }-6 y^{\prime }+9 y = 9 x^{2}-12 x +2
\]
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\[
{} y^{\prime \prime }+9 y = 36 \,{\mathrm e}^{3 x}
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+4 y = 2 \,{\mathrm e}^{2 x}
\]
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\[
{} y^{\prime \prime }-5 y^{\prime }+6 y = \left (12 x -7\right ) {\mathrm e}^{-x}
\]
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\[
{} y^{\prime \prime }+y^{\prime } = {\mathrm e}^{-x}
\]
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\[
{} y^{\prime \prime }+6 y^{\prime }+9 y = 10 \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }+y = 2 \cos \left (x \right )
\]
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\[
{} y^{\prime \prime }+4 y = \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }+y = 4 x \cos \left (x \right )
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+5 y = 2 x^{2} {\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }-6 y^{\prime }+9 y = 16 \,{\mathrm e}^{-x}+9 x -6
\]
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\[
{} y^{\prime \prime }-y^{\prime } = -5 \,{\mathrm e}^{-x} \left (\cos \left (x \right )+\sin \left (x \right )\right )
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+2 y = 4 \,{\mathrm e}^{x} \cos \left (x \right )
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+5 y = \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+5 y = 4 \cos \left (2 x \right )+\sin \left (2 x \right )
\]
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\[
{} y^{\prime \prime }-y = 1
\]
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\[
{} y^{\prime \prime }-y = -2 \cos \left (x \right )
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = 4 \,{\mathrm e}^{-x}
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+3 y = 8 \,{\mathrm e}^{x}+9
\]
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\[
{} y^{\prime \prime }-y^{\prime }-5 y = 1
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+4 y = 2 \,{\mathrm e}^{x} \left (\sin \left (x \right )+7 \cos \left (x \right )\right )
\]
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\[
{} y^{\prime \prime }-5 y^{\prime }+6 y = 2 \,{\mathrm e}^{-2 x} \left (9 \sin \left (2 x \right )+4 \cos \left (2 x \right )\right )
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{-x} \left (9 x^{2}+5 x -12\right )
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+y = x \left (6-\ln \left (x \right )\right )
\]
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\[
{} x^{2} y^{\prime \prime }-2 y = \sin \left (\ln \left (x \right )\right )
\]
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\[
{} x^{2} y^{\prime \prime }-x y^{\prime }-3 y = -\frac {16 \ln \left (x \right )}{x}
\]
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\[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }-2 y = x^{2}-2 x +2
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{m}
\]
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\[
{} x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 2 \ln \left (x \right )^{2}+12 x
\]
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\[
{} \left (1+x \right )^{3} y^{\prime \prime }+3 \left (1+x \right )^{2} y^{\prime }+\left (1+x \right ) y = 6 \ln \left (1+x \right )
\]
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\[
{} \left (x -2\right )^{2} y^{\prime \prime }-3 \left (x -2\right ) y^{\prime }+4 y = x
\]
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\[
{} \left (2 x^{2}+3 x \right ) y^{\prime \prime }-6 \left (1+x \right ) y^{\prime }+6 y = 6
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }-y = 1
\]
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\[
{} x^{2} y^{\prime \prime }-x y^{\prime }-3 y = 5 x^{4}
\]
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\[
{} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = \left (x -1\right )^{2} {\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }+y^{\prime }+{\mathrm e}^{-2 x} y = {\mathrm e}^{-3 x}
\]
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\[
{} \left (x^{4}-x^{3}\right ) y^{\prime \prime }+\left (2 x^{3}-2 x^{2}-x \right ) y^{\prime }-y = \frac {\left (x -1\right )^{2}}{x}
\]
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\[
{} y^{\prime \prime }-y^{\prime }+{\mathrm e}^{2 x} y = x \,{\mathrm e}^{2 x}-1
\]
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\[
{} x \left (x -1\right ) y^{\prime \prime }-\left (2 x -1\right ) y^{\prime }+2 y = x^{2} \left (2 x -3\right )
\]
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\[
{} y^{\prime \prime }+y = \frac {1}{\sin \left (x \right )}
\]
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\[
{} y^{\prime \prime }+y^{\prime } = \frac {1}{1+{\mathrm e}^{x}}
\]
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\[
{} y^{\prime \prime }+y = \frac {1}{\cos \left (x \right )^{3}}
\]
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\[
{} y^{\prime \prime }+y = \frac {1}{\sqrt {\sin \left (x \right )^{5} \cos \left (x \right )}}
\]
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