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\[
{} x^{3} x^{\prime \prime }+1 = 0
\]
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\[
{} y^{\prime \prime }+{y^{\prime }}^{2} = 1
\]
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\[
{} y^{\prime \prime }+y y^{\prime } = 1
\]
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\[
{} y^{\prime \prime } y = 1
\]
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\[
{} x y^{\prime \prime }+\left (6 x y^{2}+1\right ) y^{\prime }+2 y^{3}+1 = 0
\]
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\[
{} \frac {x y^{\prime \prime }}{y+1}+\frac {y y^{\prime }-x {y^{\prime }}^{2}+y^{\prime }}{\left (y+1\right )^{2}} = x \sin \left (x \right )
\]
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\[
{} y y^{\prime \prime } \sin \left (x \right )+\left (\sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y\right ) y^{\prime } = \cos \left (x \right )
\]
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\[
{} \left (\cos \left (y\right )-y \sin \left (y\right )\right ) y^{\prime \prime }-{y^{\prime }}^{2} \left (2 \sin \left (y\right )+y \cos \left (y\right )\right ) = \sin \left (x \right )
\]
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\[
{} {y^{\prime \prime }}^{2}+{y^{\prime }}^{2} = a^{2}
\]
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\[
{} y^{\prime \prime } y = 1+{y^{\prime }}^{2}
\]
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\[
{} y^{2} y^{\prime \prime } = 8 x^{2}
\]
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\[
{} y^{\prime } y^{\prime \prime } = 1
\]
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\[
{} x y^{\prime \prime }-{y^{\prime }}^{2} = 6 x^{5}
\]
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\[
{} y^{\prime } y^{\prime \prime } = 1
\]
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\[
{} 2 x y^{\prime } y^{\prime \prime } = {y^{\prime }}^{2}-1
\]
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\[
{} x {y^{\prime \prime }}^{2}+2 y = 2 x
\]
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\[
{} x^{\prime \prime }+2 \sin \left (x\right ) = \sin \left (2 t \right )
\]
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\[
{} t \left (y y^{\prime \prime }+{y^{\prime }}^{2}\right )+y^{\prime } y = 1
\]
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\[
{} y^{\prime \prime } y+{y^{\prime }}^{2} = 1
\]
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\[
{} y^{\prime \prime } = 1+{y^{\prime }}^{2}
\]
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\[
{} y^{\prime \prime } y = 1+{y^{\prime }}^{2}
\]
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\[
{} 2 y^{\prime \prime } y = 1+{y^{\prime }}^{2}
\]
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\[
{} y^{3} y^{\prime \prime } = -1
\]
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\[
{} y^{\prime \prime } y+1+{y^{\prime }}^{2} = 0
\]
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\[
{} y^{\prime \prime }-\frac {t}{y} = \frac {1}{\pi }
\]
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\[
{} y^{\prime \prime }+y+\frac {y^{3}}{5} = \cos \left (w t \right )
\]
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\[
{} y^{\prime \prime }+\frac {y^{\prime }}{5}+y+\frac {y^{3}}{5} = \cos \left (w t \right )
\]
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\[
{} 2 \left (2 a -y\right ) y^{\prime \prime } = 1+{y^{\prime }}^{2}
\]
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\[
{} y^{2} \left (x^{2} y^{\prime \prime }-x y^{\prime }+y\right ) = x^{3}
\]
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\[
{} x^{2} y^{2} y^{\prime \prime }-3 x y^{2} y^{\prime }+4 y^{3}+x^{6} = 0
\]
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\[
{} x \left (x^{2} y^{\prime }+2 x y\right ) y^{\prime \prime }+4 x {y^{\prime }}^{2}+8 x y y^{\prime }+4 y^{2}-1 = 0
\]
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\[
{} x \left (1+x y\right ) y^{\prime \prime }+x^{2} {y^{\prime }}^{2}+\left (4 x y+2\right ) y^{\prime }+y^{2}+1 = 0
\]
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\[
{} y^{\prime \prime } = x +y^{2}
\]
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\[
{} 2 y^{\prime \prime } y = 1+{y^{\prime }}^{2}
\]
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\[
{} y^{\prime \prime } = 1+{y^{\prime }}^{2}
\]
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\[
{} y^{\prime \prime }+{y^{\prime }}^{2} = 1
\]
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\[
{} \left (x \,{\mathrm e}^{y}+y-x^{2}\right ) y^{\prime \prime } = 2 x y-{\mathrm e}^{y}-x
\]
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\[
{} 1+{y^{\prime }}^{2}+\frac {m y^{\prime \prime }}{\sqrt {1+{y^{\prime }}^{2}}} = 0
\]
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\[
{} y^{\prime \prime } y-{y^{\prime }}^{2} = 1
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime \prime }-1-{y^{\prime }}^{2} = 0
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0
\]
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\[
{} y^{\prime \prime } y+{y^{\prime }}^{2} = 1
\]
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\[
{} a^{2} y^{\prime \prime } y^{\prime } = x
\]
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\[
{} y^{3} y^{\prime \prime } = a
\]
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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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\[
{} y^{\prime \prime } y+1+{y^{\prime }}^{2} = 0
\]
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\[
{} y^{3} y^{\prime \prime } = a
\]
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\[
{} y^{\prime \prime } y+{y^{\prime }}^{2} = 1
\]
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\[
{} y^{\prime \prime } y+1+{y^{\prime }}^{2} = 0
\]
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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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\[
{} 2 x^{2} \cos \left (y\right ) y^{\prime \prime }-2 x^{2} \sin \left (y\right ) {y^{\prime }}^{2}+x \cos \left (y\right ) y^{\prime }-\sin \left (y\right ) = \ln \left (x \right )
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0
\]
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