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\[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x^{2}
\]
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\[
{} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = \ln \left (x \right )
\]
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\[
{} x^{2} y^{\prime \prime }-2 y = \frac {1}{x -2}
\]
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\[
{} x y^{\prime \prime }-y^{\prime }-4 x^{3} y = x^{3} {\mathrm e}^{x^{2}}
\]
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\[
{} x y^{\prime \prime }+\left (2 x +2\right ) y^{\prime }+2 y = 8 \,{\mathrm e}^{2 x}
\]
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\[
{} \left (1+x \right ) y^{\prime \prime }+x y^{\prime }-y = \left (1+x \right )^{2}
\]
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\[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }-4 y = \frac {10}{x}
\]
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\[
{} 2 x y^{\prime \prime }+y^{\prime } = \sqrt {x}
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 3 \sqrt {x}
\]
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\[
{} x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 18 \ln \left (x \right )
\]
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\[
{} 2 x^{2} y^{\prime \prime }-x y^{\prime }-2 y = 10 x^{2}
\]
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\[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }+2 y = 6
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }-y = \frac {1}{x^{2}+1}
\]
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\[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {1}{\left (1+x \right )^{2}}
\]
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\[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {1}{x}
\]
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\[
{} y^{\prime \prime }-\frac {y^{\prime }}{t}+\frac {y}{t^{2}} = \frac {1}{t}
\]
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\[
{} t^{2} y^{\prime \prime }+3 t y^{\prime }+y = \ln \left (t \right )
\]
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\[
{} t^{2} y^{\prime \prime }+t y^{\prime }+4 y = t
\]
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\[
{} t^{2} y^{\prime \prime }-4 t y^{\prime }-6 y = 2 \ln \left (t \right )
\]
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\[
{} t^{2} y^{\prime \prime }-4 t y^{\prime }+\left (t^{2}+6\right ) y = t^{3}+2 t
\]
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\[
{} t y^{\prime \prime }+2 y^{\prime }+t y = -t
\]
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\[
{} 4 t^{2} y^{\prime \prime }+4 t y^{\prime }+\left (16 t^{2}-1\right ) y = 16 t^{{3}/{2}}
\]
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\[
{} t^{2} \left (\ln \left (t \right )-1\right ) y^{\prime \prime }-t y^{\prime }+y = -\frac {3 \left (1+\ln \left (t \right )\right )}{4 \sqrt {t}}
\]
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\[
{} \left (\sin \left (t \right )-t \cos \left (t \right )\right ) y^{\prime \prime }-t \sin \left (t \right ) y^{\prime }+\sin \left (t \right ) y = t
\]
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\[
{} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = \frac {1}{x^{5}}
\]
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\[
{} x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = x^{3}
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+y = \frac {1}{x^{2}}
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+4 y = \frac {1}{x^{2}}
\]
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\[
{} x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 2 x
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }-16 y = \ln \left (x \right )
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 8
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+36 y = x^{2}
\]
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\[
{} 2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y = \frac {1}{x^{2}}
\]
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\[
{} x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = \ln \left (x \right )
\]
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\[
{} 4 x^{2} y^{\prime \prime }+y = x^{3}
\]
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\[
{} 9 x^{2} y^{\prime \prime }+27 x y^{\prime }+10 y = \frac {1}{x}
\]
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\[
{} \left (x^{2}+1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}+1\right ) y^{\prime }+4 y = \arctan \left (x \right )
\]
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\[
{} \left (x^{2}+1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}+1\right ) y^{\prime }+4 y = \arctan \left (x \right )
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+y = x^{2}
\]
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\[
{} x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = 8 x
\]
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\[
{} \left (x -1\right ) y^{\prime \prime } = 1
\]
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\[
{} y^{\prime \prime } \left (x +2\right )^{5} = 1
\]
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\[
{} x y^{\prime \prime } = y^{\prime }+x^{2}
\]
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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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\[
{} y^{\prime \prime }+y^{\prime }+y \,{\mathrm e}^{-2 x} = {\mathrm e}^{-3 x}
\]
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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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\[
{} y^{\prime \prime }-y^{\prime }+y \,{\mathrm e}^{2 x} = x \,{\mathrm e}^{2 x}-1
\]
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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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\[
{} x y^{\prime \prime }-\left (2 x^{2}+1\right ) y^{\prime } = 4 x^{3} {\mathrm e}^{x^{2}}
\]
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\[
{} y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime } = 1
\]
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\[
{} x \ln \left (x \right ) y^{\prime \prime }-y^{\prime } = \ln \left (x \right )^{2}
\]
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\[
{} x y^{\prime \prime }+\left (2 x -1\right ) y^{\prime } = -4 x^{2}
\]
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\[
{} y^{\prime \prime }+\tan \left (x \right ) y^{\prime } = \cos \left (x \right ) \cot \left (x \right )
\]
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\[
{} 4 x y^{\prime \prime }+2 y^{\prime }+y = 1
\]
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\[
{} 4 x y^{\prime \prime }+2 y^{\prime }+y = \frac {x +6}{x^{2}}
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime } = \frac {1}{x^{2}+1}
\]
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\[
{} \left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = \left (x -1\right )^{2} {\mathrm e}^{x}
\]
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\[
{} 2 x^{2} \left (2-\ln \left (x \right )\right ) y^{\prime \prime }+x \left (4-\ln \left (x \right )\right ) y^{\prime }-y = \frac {\left (2-\ln \left (x \right )\right )^{2}}{\sqrt {x}}
\]
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\[
{} y^{\prime \prime }+\frac {2 y^{\prime }}{x}-y = 4 \,{\mathrm e}^{x}
\]
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\[
{} x^{3} \left (\ln \left (x \right )-1\right ) y^{\prime \prime }-y^{\prime } x^{2}+x y = 2 \ln \left (x \right )
\]
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\[
{} \left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-2 \left (1-x \right ) y = 2 x -2
\]
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\[
{} y^{\prime \prime }-t y = \frac {1}{\pi }
\]
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\[
{} a \,x^{2} y^{\prime \prime }+b x y^{\prime }+c y = d
\]
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\[
{} t y^{\prime \prime }+3 y = t
\]
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\[
{} \left (t -1\right ) y^{\prime \prime }-3 t y^{\prime }+4 y = \sin \left (t \right )
\]
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\[
{} t \left (-4+t \right ) y^{\prime \prime }+3 t y^{\prime }+4 y = 2
\]
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\[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = \ln \left (x \right )
\]
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\[
{} x^{2} y^{\prime \prime }+7 x y^{\prime }+5 y = x
\]
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\[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 3 x^{2}+2 \ln \left (x \right )
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+4 y = \sin \left (\ln \left (x \right )\right )
\]
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\[
{} t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y = 2 t^{3}
\]
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\[
{} t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y = {\mathrm e}^{2 t} t^{2}
\]
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\[
{} \left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y = 2 \left (t -1\right )^{2} {\mathrm e}^{-t}
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 3 x^{{3}/{2}} \sin \left (x \right )
\]
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\[
{} \left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = g \left (x \right )
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = g \left (x \right )
\]
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\[
{} t^{2} y^{\prime \prime }-2 y = 3 t^{2}-1
\]
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\[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x^{2} \ln \left (x \right )
\]
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\[
{} t^{2} y^{\prime \prime }-2 t y^{\prime }+2 y = 4 t^{2}
\]
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\[
{} t^{2} y^{\prime \prime }+7 t y^{\prime }+5 y = t
\]
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\[
{} t y^{\prime \prime }-\left (t +1\right ) y^{\prime }-y = {\mathrm e}^{2 t} t^{2}
\]
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\[
{} \left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y = 2 \left (t -1\right )^{2} {\mathrm e}^{-t}
\]
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\[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 2 x^{3}
\]
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\[
{} y^{\prime \prime }+\frac {x y^{\prime }}{1-x}-\frac {y}{1-x} = x -1
\]
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\[
{} y^{\prime \prime }+\frac {y}{x^{2} \ln \left (x \right )} = {\mathrm e}^{x} \left (\frac {2}{x}+\ln \left (x \right )\right )
\]
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\[
{} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x
\]
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\[
{} x^{2} y^{\prime \prime }-x y^{\prime }+2 y = x \ln \left (x \right )
\]
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\[
{} x^{2} y^{\prime \prime }-2 y = x^{2}+\frac {1}{x}
\]
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\[
{} \left (1+x \right )^{2} y^{\prime \prime }+\left (1+x \right ) y^{\prime }+y = 4 \cos \left (\ln \left (1+x \right )\right )
\]
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