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\[
{} y^{\prime \prime }-4 y^{\prime }+3 y = \frac {1}{1+{\mathrm e}^{-x}}
\]
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\[
{} \left (1+x \right )^{2} y^{\prime \prime }+\left (1+x \right ) y^{\prime }-y = \ln \left (1+x \right )^{2}+x -1
\]
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\[
{} \left (2 x +1\right )^{2} y^{\prime \prime }-2 \left (2 x +1\right ) y^{\prime }-12 y = 6 x
\]
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\[
{} x y^{\prime \prime }-\left (x +2\right ) y^{\prime }+2 y = 0
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 2
\]
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\[
{} \left (x^{2}+4\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 8
\]
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\[
{} \left (1+x \right ) y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+\left (x +2\right ) y = \left (x^{2}+2 x +1\right ) {\mathrm e}^{2 x}
\]
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\[
{} y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }-10 y = 0
\]
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\[
{} x^{2} y^{\prime \prime }-x \left (2 x +3\right ) y^{\prime }+\left (x^{2}+3 x +3\right ) y = \left (-x^{2}+6\right ) {\mathrm e}^{x}
\]
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\[
{} 4 x^{2} y^{\prime \prime }+4 x^{3} y^{\prime }+\left (x^{2}+1\right )^{2} y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+\left (-4 x^{2}+x \right ) y^{\prime }+\left (4 x^{2}-2 x +1\right ) y = \left (x^{2}-x +1\right ) {\mathrm e}^{x}
\]
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\[
{} x^{4} y^{\prime \prime }+2 x^{3} y^{\prime }+y = \frac {1+x}{x}
\]
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\[
{} x^{8} y^{\prime \prime }+4 x^{7} y^{\prime }+y = \frac {1}{x^{3}}
\]
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\[
{} \left (x \sin \left (x \right )+\cos \left (x \right )\right ) y^{\prime \prime }-x \cos \left (x \right ) y^{\prime }+\cos \left (x \right ) y = x
\]
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\[
{} \left (1+x \right ) y^{\prime \prime }-\left (3 x +4\right ) y^{\prime }+3 y = \left (3 x +2\right ) {\mathrm e}^{3 x}
\]
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\[
{} x y^{\prime \prime }+2 y^{\prime }+4 x y = 4
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = \frac {-x^{2}+1}{x}
\]
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\[
{} y y^{\prime \prime }+{y^{\prime }}^{3} = 0
\]
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\[
{} y y^{\prime \prime }+{y^{\prime }}^{2} = 0
\]
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\[
{} y y^{\prime \prime } = {y^{\prime }}^{2} \left (1-y^{\prime } \cos \left (y\right )+y y^{\prime } \sin \left (y\right )\right )
\]
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\[
{} \left (2 x -3\right ) y^{\prime \prime \prime }-\left (6 x -7\right ) y^{\prime \prime }+4 x y^{\prime }-4 y = 8
\]
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\[
{} \left (2 x^{3}-1\right ) y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+6 x y^{\prime } = 0
\]
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\[
{} y y^{\prime \prime }-{y^{\prime }}^{2} = y^{2} \ln \left (y\right )
\]
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\[
{} \left (x +2 y\right ) y^{\prime \prime }+2 {y^{\prime }}^{2}+2 y^{\prime } = 2
\]
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\[
{} \left (1+2 y+3 y^{2}\right ) y^{\prime \prime \prime }+6 y^{\prime } \left (y^{\prime \prime }+{y^{\prime }}^{2}+3 y y^{\prime \prime }\right ) = x
\]
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\[
{} 3 x \left (y^{2} y^{\prime \prime \prime }+6 y y^{\prime } y^{\prime \prime }+2 {y^{\prime }}^{3}\right )-3 y \left (y y^{\prime \prime }+2 {y^{\prime }}^{2}\right ) = -\frac {2}{x}
\]
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\[
{} y y^{\prime \prime \prime }+3 y^{\prime } y^{\prime \prime }-2 y y^{\prime \prime }-2 {y^{\prime }}^{2}+y y^{\prime } = {\mathrm e}^{2 x}
\]
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\[
{} 2 \left (y+1\right ) y^{\prime \prime }+2 {y^{\prime }}^{2}+y^{2}+2 y = 0
\]
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\[
{} [x^{\prime }\left (t \right )-x \left (t \right )+y^{\prime }\left (t \right )+3 y \left (t \right ) = {\mathrm e}^{-t}-1, x^{\prime }\left (t \right )+2 x \left (t \right )+y^{\prime }\left (t \right )+3 y \left (t \right ) = {\mathrm e}^{2 t}+1]
\]
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\[
{} x y^{\prime } = 1-x +2 y
\]
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\[
{} y^{\prime \prime }+x^{2} y = x^{2}+x +1
\]
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\[
{} 2 x y^{\prime \prime }+y^{\prime }-y = 1+x
\]
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\[
{} x^{3} \left (1+x \right ) y^{\prime \prime \prime }-\left (2+4 x \right ) x^{2} y^{\prime \prime }+\left (4+10 x \right ) x y^{\prime }-\left (4+12 x \right ) y = 0
\]
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\[
{} x^{3} \left (x^{2}+1\right ) y^{\prime \prime \prime }-\left (4 x^{2}+2\right ) x^{2} y^{\prime \prime }+\left (10 x^{2}+4\right ) x y^{\prime }-\left (12 x^{2}+4\right ) y = 0
\]
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\[
{} 2 x^{2} \left (2-x \right ) y^{\prime \prime }-\left (4-x \right ) x y^{\prime }+\left (3-x \right ) y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+4 \left (x +a \right ) y = 0
\]
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\[
{} \sin \left (x \right ) y^{\prime \prime }-2 \cos \left (x \right ) y^{\prime }-\sin \left (x \right ) y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}+\frac {1}{4}\right ) y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}+\frac {9}{4}\right ) y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}+\frac {25}{4}\right ) y = 0
\]
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\[
{} x^{3} y^{\prime \prime }+y = \frac {1}{x^{4}}
\]
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\[
{} x y^{\prime \prime }-2 y^{\prime }+y = \cos \left (x \right )
\]
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\[
{} y^{\prime }-\frac {y}{x} = \cos \left (x \right )
\]
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\[
{} y^{\prime \prime }-x y = \frac {1}{1-x}
\]
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\[
{} x^{2} y^{\prime \prime }-y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (1+x \right ) y = 0
\]
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\[
{} x^{2} y^{\prime \prime }-y = 0
\]
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\[
{} x^{2} y^{\prime \prime }-x y^{\prime }-y = 0
\]
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\[
{} x^{2} y^{\prime \prime }+y^{\prime }+y = 0
\]
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\[
{} x^{3} y^{\prime \prime }+\left (1+x \right ) y = 0
\]
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\[
{} \sin \left (x \right ) y^{\prime \prime }-y = 0
\]
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\[
{} x^{2} y^{\prime \prime }-y = 0
\]
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\[
{} \left (1-x \right ) y^{\prime \prime }-4 x y^{\prime }+5 y = \cos \left (x \right )
\]
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\[
{} x y^{\prime \prime \prime }-{y^{\prime }}^{4}+y = 0
\]
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\[
{} t^{5} y^{\prime \prime \prime \prime }-t^{3} y^{\prime \prime }+6 y = 0
\]
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\[
{} u^{\prime \prime }+u^{\prime }+u = \cos \left (r +u\right )
\]
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\[
{} y^{\prime \prime } = \sqrt {1+{y^{\prime }}^{2}}
\]
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\[
{} x^{\prime \prime }-\left (1-\frac {{x^{\prime }}^{2}}{3}\right ) x^{\prime }+x = 0
\]
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\[
{} \sin \left (x^{\prime }\right )+y^{3} x = \sin \left (y \right )
\]
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\[
{} {y^{\prime }}^{2} = 9-y^{2}
\]
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\[
{} {y^{\prime }}^{2}-2 y^{\prime }+4 y = 4 x -1
\]
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\[
{} x y^{\prime } = 2 y
\]
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\[
{} y^{\prime } = \sqrt {y^{2}-9}
\]
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\[
{} y^{\prime } = \sqrt {y^{2}-9}
\]
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\[
{} x y^{\prime } = y
\]
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\[
{} y^{\prime } = y^{2}
\]
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\[
{} y^{\prime \prime }+4 y = 0
\]
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\[
{} y^{\prime \prime }+4 y = 0
\]
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\[
{} y^{\prime } = x^{2}+y^{2}
\]
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\[
{} 2 y^{\prime \prime }-3 y^{2} = 0
\]
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\[
{} y^{\prime } = x \sqrt {y}
\]
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\[
{} y^{\prime } = x^{2}+y^{2}
\]
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\[
{} y^{\prime } = 6 \sqrt {y}+5 x^{3}
\]
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\[
{} x^{2} y^{\prime \prime }+\left (x^{2}-x \right ) y^{\prime }+\left (1-x \right ) y = 0
\]
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\[
{} y^{\prime \prime } = 2 y {y^{\prime }}^{3}
\]
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\[
{} y^{\prime } = x^{2}-y^{2}
\]
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\[
{} y^{\prime } = x^{2}-y^{2}
\]
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\[
{} y^{\prime } = x^{2}-y^{2}
\]
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\[
{} y^{\prime } = x^{2}-y^{2}
\]
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\[
{} y^{\prime } = {\mathrm e}^{-\frac {x y^{2}}{100}}
\]
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\[
{} y^{\prime } = {\mathrm e}^{-\frac {x y^{2}}{100}}
\]
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\[
{} y^{\prime } = {\mathrm e}^{-\frac {x y^{2}}{100}}
\]
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\[
{} y^{\prime } = {\mathrm e}^{-\frac {x y^{2}}{100}}
\]
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\[
{} y^{\prime } = x^{2}+y^{2}
\]
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\[
{} y^{\prime } = x \left (y-4\right )^{2}-2
\]
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\[
{} \sqrt {1-y^{2}}-\sqrt {-x^{2}+1}\, y^{\prime } = 0
\]
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\[
{} y^{\prime } = y^{2}-4
\]
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\[
{} y^{\prime } = y^{2}-4
\]
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\[
{} y^{\prime } = y^{2}-4
\]
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\[
{} x y^{\prime } = y^{2}-y
\]
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\[
{} x y^{\prime } = y^{2}-y
\]
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\[
{} y^{\prime } = \left (-1+y\right )^{2}
\]
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\[
{} y^{\prime } = \sqrt {\frac {1-y^{2}}{-x^{2}+1}}
\]
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\[
{} y^{\prime } = -\frac {8 x +5}{3 y^{2}+1}
\]
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\[
{} y^{\prime } = -\frac {8 x +5}{3 y^{2}+1}
\]
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\[
{} y^{\prime } = -\frac {8 x +5}{3 y^{2}+1}
\]
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\[
{} y^{\prime } = -\frac {8 x +5}{3 y^{2}+1}
\]
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\[
{} y^{\prime } = \frac {x \left (1-x \right )}{y \left (y-2\right )}
\]
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\[
{} y^{\prime } = \frac {x \left (1-x \right )}{y \left (y-2\right )}
\]
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\[
{} y-4 \left (x +y^{6}\right ) y^{\prime } = 0
\]
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