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\[
{} y^{\prime \prime }+y^{\prime } = {\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }-\frac {a^{2} y^{\prime }}{x \left (a^{2}-x^{2}\right )} = \frac {x^{2}}{a \left (a^{2}-x^{2}\right )}
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+a x = 0
\]
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\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }+x y^{\prime } = a x
\]
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\[
{} y^{\prime }-x y^{\prime \prime }-\frac {a^{2} y^{\prime }}{x}+\frac {x^{2}}{a} = 0
\]
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\[
{} x y^{\prime \prime }+y^{\prime } = x
\]
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\[
{} \left (a^{2}-x^{2}\right ) y^{\prime \prime }-\frac {a^{2} y^{\prime }}{x}+\frac {x^{2}}{a} = 0
\]
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\[
{} {y^{\prime }}^{2}+y y^{\prime \prime } = 1
\]
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\[
{} y y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0
\]
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\[
{} a^{2} y^{\prime \prime } y^{\prime } = x
\]
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\[
{} y^{\prime \prime } = 1+{y^{\prime }}^{2}
\]
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\[
{} y^{\prime \prime } = a^{2}+k^{2} {y^{\prime }}^{2}
\]
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\[
{} a^{2} {y^{\prime \prime }}^{2} = 1+{y^{\prime }}^{2}
\]
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\[
{} y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0
\]
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\[
{} {\mathrm e}^{x} \left (x y^{\prime \prime }-y^{\prime }\right ) = x^{3}
\]
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\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime } = 2
\]
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\[
{} y^{\prime \prime }-x^{2} y^{\prime }+x y = x
\]
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\[
{} x y^{\prime \prime }+\left (1-x \right ) y^{\prime } = y+{\mathrm e}^{x}
\]
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\[
{} \left (1+x \right ) y^{\prime \prime }-2 \left (x +3\right ) y^{\prime }+\left (x +5\right ) y = {\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }+x y^{\prime }-y = X
\]
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\[
{} x^{2} y^{\prime \prime }-\left (x^{2}+2 x \right ) y^{\prime }+\left (x +2\right ) y = x^{3} {\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }-2 b x y^{\prime }+b^{2} x^{2} y = x
\]
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\[
{} y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }+5 y = \sec \left (x \right ) {\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-3\right ) y = {\mathrm e}^{x^{2}}
\]
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\[
{} x y^{\prime \prime }+\left (x -2\right ) y^{\prime }-2 y = x^{2}
\]
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\[
{} x^{2} y^{\prime \prime }+y^{\prime }-\left (x^{2}+1\right ) y = {\mathrm e}^{-x}
\]
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\[
{} \left (x +2\right ) y^{\prime \prime }-\left (5+2 x \right ) y^{\prime }+2 y = \left (1+x \right ) {\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }+y = x
\]
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\[
{} y^{\prime \prime }+y = \csc \left (x \right )
\]
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\[
{} y^{\prime \prime }+4 y = 4 \tan \left (2 x \right )
\]
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\[
{} \left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = \left (1-x \right )^{2}
\]
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\[
{} y^{\prime \prime }-y = \frac {2}{1+{\mathrm e}^{x}}
\]
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\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-4 x y^{\prime }-\left (x^{2}+1\right ) y = x
\]
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\[
{} x^{2} y^{\prime \prime }-2 x \left (1+x \right ) y^{\prime }+2 \left (1+x \right ) y = -4 x^{3}
\]
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\[
{} x^{2} y^{\prime \prime }-2 x \left (1+x \right ) y^{\prime }+2 \left (1+x \right ) y = x^{3}
\]
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\[
{} y^{\prime \prime }+2 x y^{\prime }+\left (x^{2}+1\right ) y = x^{3}+3 x
\]
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\[
{} \left (2 x -1\right ) y^{\prime \prime }-2 y^{\prime }+\left (3-2 x \right ) y = 2 \,{\mathrm e}^{x}
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }-y = 8 x^{3}
\]
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\[
{} y^{\prime \prime }+2 x y^{\prime }+\left (x^{2}+5\right ) y = x \,{\mathrm e}^{-\frac {x^{2}}{2}}
\]
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\[
{} y^{\prime \prime }+\left (1-\frac {2}{x^{2}}\right ) y = x^{2}
\]
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\[
{} x y^{\prime \prime }-2 \left (1+x \right ) y^{\prime }+\left (x +2\right ) y = \left (x -2\right ) {\mathrm e}^{2 x}
\]
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\[
{} x y^{\prime \prime }-y^{\prime }+4 x^{3} y = x^{5}
\]
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\[
{} \left (x^{2}-1\right ) y^{\prime \prime }-\left (4 x^{2}-3 x -5\right ) y^{\prime }+\left (4 x^{2}-6 x -5\right ) y = {\mathrm e}^{2 x}
\]
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\[
{} y^{\prime \prime }+\left (1-\frac {1}{x}\right ) y^{\prime }+4 x^{2} y \,{\mathrm e}^{-2 x} = 4 \left (x^{3}+x^{2}\right ) {\mathrm e}^{-3 x}
\]
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\[
{} x y^{\prime \prime }+\left (x^{2}+1\right ) y^{\prime }+2 x y = 2 x
\]
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\[
{} \left (x +2\right ) y^{\prime \prime }-\left (5+2 x \right ) y^{\prime }+2 y = \left (1+x \right ) {\mathrm e}^{x}
\]
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\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }-y = x \left (-x^{2}+1\right )^{{3}/{2}}
\]
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\[
{} y^{\prime \prime }+n^{2} y = \sec \left (n x \right )
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+y = a \cos \left (2 x \right )
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = x \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = x^{2} {\mathrm e}^{3 x}
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+4 y = 2 \sinh \left (2 x \right )
\]
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\[
{} y^{\prime \prime }+a^{2} y = \cos \left (a x \right )
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = x \sin \left (x \right )
\]
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\[
{} x^{2} y^{\prime \prime }-2 y = x^{2}+\frac {1}{x}
\]
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\[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 2 x^{2}
\]
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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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\[
{} \left (x +a \right )^{2} y^{\prime \prime }-4 \left (x +a \right ) y^{\prime }+6 y = x
\]
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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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\[
{} x^{2} y^{\prime \prime }-\left (2 m -1\right ) x y^{\prime }+\left (m^{2}+n^{2}\right ) y = n^{2} x^{m} \ln \left (x \right )
\]
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\[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }+y = \frac {\ln \left (x \right ) \sin \left (\ln \left (x \right )\right )+1}{x}
\]
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\[
{} \sqrt {x}\, y^{\prime \prime }+2 x y^{\prime }+3 y = x
\]
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\[
{} 2 x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (7 x +3\right ) y^{\prime }-3 y = x^{2}
\]
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\[
{} 2 x^{2} \cos \left (y\right ) y^{\prime \prime }-2 x^{2} \sin \left (y\right ) {y^{\prime }}^{2}+x \cos \left (y\right ) y^{\prime }-\sin \left (y\right ) = \ln \left (x \right )
\]
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\[
{} y^{\prime \prime } = x^{2} \sin \left (x \right )
\]
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\[
{} y^{\prime \prime } = \sec \left (x \right )^{2}
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0
\]
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\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }-y = x \left (-x^{2}+1\right )^{{3}/{2}}
\]
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\[
{} \left (x +2\right ) y^{\prime \prime }-\left (5+2 x \right ) y^{\prime }+2 y = \left (1+x \right ) {\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }-\cot \left (x \right ) y^{\prime }-\left (1-\cot \left (x \right )\right ) y = {\mathrm e}^{x} \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }+\left (1+\frac {2 \cot \left (x \right )}{x}-\frac {2}{x^{2}}\right ) y = x \cos \left (x \right )
\]
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\[
{} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-1\right ) y = -3 \,{\mathrm e}^{x^{2}} \sin \left (2 x \right )
\]
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\[
{} y^{\prime \prime }-\left (8 \,{\mathrm e}^{2 x}+2\right ) y^{\prime }+4 \,{\mathrm e}^{4 x} y = {\mathrm e}^{6 x}
\]
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\[
{} x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+a^{2} y = \frac {1}{x^{2}}
\]
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\[
{} x y^{\prime \prime }-y^{\prime }-4 x^{3} y = 8 x^{3} \sin \left (x^{2}\right )
\]
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\[
{} y^{\prime \prime } \cos \left (x \right )+\sin \left (x \right ) y^{\prime }-2 y \cos \left (x \right )^{3} = 2 \cos \left (x \right )^{5}
\]
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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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\[
{} x y^{\prime \prime }+\left (x -1\right ) y^{\prime }-y = x^{2}
\]
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\[
{} y^{\prime \prime }+a^{2} y = \sec \left (a x \right )
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{2} {\mathrm e}^{x}
\]
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\[
{} x^{2} y^{\prime \prime }-2 x \left (1+x \right ) y^{\prime }+2 \left (1+x \right ) y = x^{3}
\]
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\[
{} y^{\prime \prime }+\left (1-\cot \left (x \right )\right ) y^{\prime }-\cot \left (x \right ) y = \sin \left (x \right )^{2}
\]
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