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\[
{} a^{2}+y^{2}+2 x \sqrt {a x -x^{2}}\, y^{\prime } = 0
\]
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\[
{} y^{\prime } = \frac {y}{x}
\]
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\[
{} x^{2} \cos \left (y\right ) y^{\prime }+1 = 0
\]
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\[
{} y^{\prime } x^{2}+\cos \left (2 y\right ) = 1
\]
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\[
{} x^{3} y^{\prime }-\sin \left (y\right ) = 1
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime }-\frac {\cos \left (2 y\right )^{2}}{2} = 0
\]
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\[
{} x y^{\prime } = y+x \cos \left (\frac {y}{x}\right )^{2}
\]
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\[
{} 2 x y^{\prime }-y = 1-\frac {2}{\sqrt {x}}
\]
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\[
{} y^{\prime }-2 y \,{\mathrm e}^{x} = 2 \sqrt {y \,{\mathrm e}^{x}}
\]
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\[
{} y y^{\prime }+1 = \left (x -1\right ) {\mathrm e}^{-\frac {y^{2}}{2}}
\]
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\[
{} y^{\prime }+x \sin \left (2 y\right ) = 2 x \,{\mathrm e}^{-x^{2}} \cos \left (y\right )^{2}
\]
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\[
{} 3 x^{2}+6 x y^{2}+\left (6 x^{2} y+4 y^{3}\right ) y^{\prime } = 0
\]
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\[
{} \frac {x}{\sqrt {x^{2}+y^{2}}}+\frac {1}{x}+\frac {1}{y}+\left (\frac {y}{\sqrt {x^{2}+y^{2}}}+\frac {1}{y}-\frac {x}{y^{2}}\right ) y^{\prime } = 0
\]
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\[
{} 3 x^{2} \tan \left (y\right )-\frac {2 y^{3}}{x^{3}}+\left (x^{3} \sec \left (y\right )^{2}+4 y^{3}+\frac {3 y^{2}}{x^{2}}\right ) y^{\prime } = 0
\]
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\[
{} 2 x +\frac {x^{2}+y^{2}}{x^{2} y} = \frac {\left (x^{2}+y^{2}\right ) y^{\prime }}{x y^{2}}
\]
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\[
{} \frac {\sin \left (2 x \right )}{y}+x +\left (y-\frac {\sin \left (x \right )^{2}}{y^{2}}\right ) y^{\prime } = 0
\]
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\[
{} 3 x^{2}-2 x -y+\left (2 y-x +3 y^{2}\right ) y^{\prime } = 0
\]
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\[
{} \sin \left (y\right )+y \sin \left (x \right )+\frac {1}{x}+\left (x \cos \left (y\right )-\cos \left (x \right )+\frac {1}{y}\right ) y^{\prime } = 0
\]
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\[
{} \frac {y+\sin \left (x \right ) \cos \left (x y\right )^{2}}{\cos \left (x y\right )^{2}}+\left (\frac {x}{\cos \left (x y\right )^{2}}+\sin \left (y\right )\right ) y^{\prime } = 0
\]
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\[
{} \frac {2 x}{y^{3}}+\frac {\left (y^{2}-3 x^{2}\right ) y^{\prime }}{y^{4}} = 0
\]
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\[
{} y \left (a^{2}+x^{2}+y^{2}\right ) y^{\prime }+x \left (x^{2}+y^{2}-a^{2}\right ) = 0
\]
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\[
{} 3 x^{2} y+y^{3}+\left (x^{3}+3 x y^{2}\right ) y^{\prime } = 0
\]
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\[
{} {y^{\prime }}^{3}+\left (x +2\right ) {\mathrm e}^{y} = 0
\]
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\[
{} {y^{\prime }}^{2}-y y^{\prime }+{\mathrm e}^{x} = 0
\]
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\[
{} y^{\prime } = {\mathrm e}^{\frac {y^{\prime }}{y}}
\]
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\[
{} x = \ln \left (y^{\prime }\right )+\sin \left (y^{\prime }\right )
\]
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\[
{} {y^{\prime }}^{2} x = {\mathrm e}^{\frac {1}{y^{\prime }}}
\]
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\[
{} x = \sin \left (y^{\prime }\right )+y^{\prime }
\]
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\[
{} y = y^{\prime } \left (1+y^{\prime } \cos \left (y^{\prime }\right )\right )
\]
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\[
{} y = \arcsin \left (y^{\prime }\right )+\ln \left (1+{y^{\prime }}^{2}\right )
\]
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\[
{} y = 2 x y^{\prime }+\sin \left (y^{\prime }\right )
\]
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\[
{} y = {y^{\prime }}^{2} x -\frac {1}{y^{\prime }}
\]
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\[
{} y = \frac {3 x y^{\prime }}{2}+{\mathrm e}^{y^{\prime }}
\]
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\[
{} y = x y^{\prime }+\frac {a}{{y^{\prime }}^{2}}
\]
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\[
{} {y^{\prime }}^{2} x -y y^{\prime }-y^{\prime }+1 = 0
\]
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\[
{} y = x y^{\prime }+a \sqrt {1+{y^{\prime }}^{2}}
\]
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\[
{} x = \frac {y}{y^{\prime }}+\frac {1}{{y^{\prime }}^{2}}
\]
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\[
{} y^{2} \left (1+{y^{\prime }}^{2}\right )-4 y y^{\prime }-4 x = 0
\]
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\[
{} {y^{\prime }}^{3}-4 x y y^{\prime }+8 y^{2} = 0
\]
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\[
{} \left (x y^{\prime }+y\right )^{2}+3 x^{5} \left (x y^{\prime }-2 y\right ) = 0
\]
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\[
{} 8 {y^{\prime }}^{3}-12 {y^{\prime }}^{2} = 27 y-27 x
\]
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\[
{} y = {y^{\prime }}^{2}-x y^{\prime }+x
\]
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\[
{} {y^{\prime }}^{2}-y y^{\prime }+{\mathrm e}^{x} = 0
\]
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\[
{} y = x y^{\prime }+\sqrt {a^{2} {y^{\prime }}^{2}+b^{2}}
\]
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\[
{} 5 x y-4 y^{2}-6 x^{2}+\left (y^{2}-8 x y+\frac {5 x^{2}}{2}\right ) y^{\prime } = 0
\]
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\[
{} 3 x y^{2}-x^{2}+\left (3 x^{2} y-6 y^{2}-1\right ) y^{\prime } = 0
\]
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\[
{} y^{\prime } = \frac {1}{2 x -y^{2}}
\]
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\[
{} \frac {1}{x^{2}-x y+y^{2}} = \frac {y^{\prime }}{2 y^{2}-x y}
\]
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\[
{} x^{2} y^{n} y^{\prime } = 2 x y^{\prime }-y
\]
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\[
{} \sin \left (\ln \left (x \right )\right )-\cos \left (\ln \left (y\right )\right ) y^{\prime } = 0
\]
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\[
{} \left (5 x -7 y+1\right ) y^{\prime }+x +y-1 = 0
\]
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\[
{} y^{\prime } = \frac {2 \left (y+2\right )^{2}}{\left (x +y-1\right )^{2}}
\]
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\[
{} y^{\prime }+{y^{\prime }}^{2} x -y = 0
\]
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\[
{} y^{\prime \prime } = \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}
\]
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\[
{} y y^{\prime \prime }+{y^{\prime }}^{2} = 1
\]
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\[
{} y^{\prime \prime } = \sqrt {1+{y^{\prime }}^{2}}
\]
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\[
{} y^{\prime \prime } = \sqrt {1-{y^{\prime }}^{2}}
\]
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\[
{} y^{\prime \prime } = y^{\prime } \ln \left (y^{\prime }\right )
\]
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\[
{} 3 y^{\prime \prime } = \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}
\]
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\[
{} y y^{\prime \prime } = {y^{\prime }}^{2}
\]
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\[
{} y^{\prime \prime } = 2 y y^{\prime }
\]
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\[
{} 3 y^{\prime \prime } y^{\prime } = 2 y
\]
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\[
{} 2 y^{\prime \prime } = 3 y^{2}
\]
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\[
{} y y^{\prime \prime }+{y^{\prime }}^{2} = 0
\]
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\[
{} y y^{\prime \prime } = {y^{\prime }}^{2}+y^{\prime }
\]
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\[
{} y y^{\prime \prime } = 1+{y^{\prime }}^{2}
\]
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\[
{} 2 y y^{\prime \prime } = 1+{y^{\prime }}^{2}
\]
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\[
{} y^{3} y^{\prime \prime } = -1
\]
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\[
{} y y^{\prime \prime }-{y^{\prime }}^{2} = y^{2} y^{\prime }
\]
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\[
{} y^{\prime \prime } = {\mathrm e}^{2 y}
\]
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\[
{} 2 y y^{\prime \prime }-3 {y^{\prime }}^{2} = 4 y^{2}
\]
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\[
{} y^{\prime \prime \prime } = 3 y y^{\prime }
\]
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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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\[
{} y^{\prime \prime }+y^{\prime } = x^{2}-{\mathrm e}^{-x}+{\mathrm e}^{x}
\]
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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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\[
{} \left (2 x +1\right )^{2} y^{\prime \prime }-2 \left (2 x +1\right ) y^{\prime }+4 y = 0
\]
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\[
{} \left (2 x +1\right )^{2} y^{\prime \prime \prime }+2 \left (2 x +1\right ) y^{\prime \prime }+y^{\prime } = 0
\]
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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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\[
{} \left (2 x +1\right ) y^{\prime \prime }+\left (4 x -2\right ) y^{\prime }-8 y = 0
\]
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\[
{} \left (x^{2}-x \right ) y^{\prime \prime }+\left (2 x -3\right ) y^{\prime }-2 y = 0
\]
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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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\[
{} x^{2} \left (\ln \left (x \right )-1\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\]
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\[
{} y^{\prime \prime }+\left (\tan \left (x \right )-2 \cot \left (x \right )\right ) y^{\prime }+2 \cot \left (x \right )^{2} y = 0
\]
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\[
{} y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+y \cos \left (x \right )^{2} = 0
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }-y = 1
\]
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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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\[
{} y^{\prime \prime }+y^{\prime } = \frac {1}{{\mathrm e}^{x}+1}
\]
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\[
{} y^{\prime \prime }+y = \frac {1}{\sqrt {\sin \left (x \right )^{5} \cos \left (x \right )}}
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{x^{2}+1}
\]
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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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\[
{} 4 x y^{\prime \prime }+2 y^{\prime }+y = 1
\]
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\[
{} 4 x y^{\prime \prime }+2 y^{\prime }+y = \frac {x +6}{x^{2}}
\]
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\[
{} \left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = \left (x -1\right )^{2} {\mathrm e}^{x}
\]
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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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