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Mathematica |
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\[
{} x y^{\prime }-y = x \sqrt {x^{2}+y^{2}}
\]
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\[
{} y^{\prime }+\frac {y}{\sqrt {-x^{2}+1}} = \frac {x +\sqrt {-x^{2}+1}}{\left (-x^{2}+1\right )^{2}}
\]
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\[
{} x \left (x^{2}+y^{2}-a^{2}\right )+y \left (x^{2}-y^{2}-b^{2}\right ) y^{\prime } = 0
\]
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\[
{} y y^{\prime }+x = m \left (x y^{\prime }-y\right )
\]
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\[
{} y+\left (a \,x^{2} y^{n}-2 x \right ) y^{\prime } = 0
\]
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\[
{} \left (1-3 x^{2} y+6 y^{2}\right ) y^{\prime } = 3 x y^{2}-x^{2}
\]
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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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\[
{} y^{\prime }+\frac {n y}{x} = a \,x^{-n}
\]
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\[
{} x -y y^{\prime } = a {y^{\prime }}^{2}
\]
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\[
{} y = -a y^{\prime }+\frac {c +a \arcsin \left (y^{\prime }\right )}{\sqrt {1-{y^{\prime }}^{2}}}
\]
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\[
{} 4 y = {y^{\prime }}^{2}+x^{2}
\]
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\[
{} y = y {y^{\prime }}^{2}+2 x y^{\prime }
\]
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\[
{} x^{2} \left (y-x y^{\prime }\right ) = y {y^{\prime }}^{2}
\]
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\[
{} y = x y^{\prime }+\arcsin \left (y^{\prime }\right )
\]
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\[
{} {\mathrm e}^{4 x} \left (y^{\prime }-1\right )+{\mathrm e}^{2 y} {y^{\prime }}^{2} = 0
\]
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\[
{} y = y^{\prime } \left (x -b \right )+\frac {a}{y^{\prime }}
\]
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\[
{} a y {y^{\prime }}^{2}+\left (2 x -b \right ) y^{\prime }-y = 0
\]
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\[
{} \left (x y^{\prime }-y\right )^{2} = a \left (1+{y^{\prime }}^{2}\right ) \left (x^{2}+y^{2}\right )^{{3}/{2}}
\]
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\[
{} \left (x y^{\prime }-y\right )^{2} = {y^{\prime }}^{2}-\frac {2 y y^{\prime }}{x}+1
\]
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\[
{} 3 y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }-x^{2}+4 y^{2} = 0
\]
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\[
{} \left (x^{2}+y^{2}\right ) \left (y^{\prime }+1\right )^{2}-2 \left (x +y\right ) \left (y^{\prime }+1\right ) \left (y y^{\prime }+x \right )+\left (y y^{\prime }+x \right )^{2} = 0
\]
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\[
{} \left (x y^{\prime }-y\right ) \left (y y^{\prime }+x \right ) = h^{2} y^{\prime }
\]
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\[
{} {y^{\prime }}^{3}-4 x y y^{\prime }+8 y^{2} = 0
\]
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\[
{} {y^{\prime }}^{3}+m {y^{\prime }}^{2} = a \left (y+m x \right )
\]
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\[
{} {\mathrm e}^{3 x} \left (y^{\prime }-1\right )+{\mathrm e}^{2 y} {y^{\prime }}^{3} = 0
\]
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\[
{} \left (1-y^{2}+\frac {y^{4}}{x^{2}}\right ) {y^{\prime }}^{2}-\frac {2 y y^{\prime }}{x}+\frac {y^{2}}{x^{2}} = 0
\]
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\[
{} y = x y^{\prime }+\frac {m}{y^{\prime }}
\]
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\[
{} y = 2 x y^{\prime }+y^{2} {y^{\prime }}^{3}
\]
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\[
{} y = x y^{\prime }+a \sqrt {1+{y^{\prime }}^{2}}
\]
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\[
{} x^{2} {y^{\prime }}^{2}-3 x y y^{\prime }+x^{3}+2 y^{2} = 0
\]
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\[
{} \left (y^{\prime }+1\right )^{3} = \frac {7 \left (x +y\right ) \left (1-y^{\prime }\right )^{3}}{4 a}
\]
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\[
{} {y^{\prime }}^{2}+2 x y^{\prime }-y = 0
\]
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\[
{} x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+a^{3} = 0
\]
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\[
{} y^{2}-2 x y y^{\prime }+{y^{\prime }}^{2} \left (x^{2}-1\right ) = m^{2}
\]
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\[
{} y = x y^{\prime }+\sqrt {b^{2}+a^{2} y^{\prime }}
\]
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\[
{} \left (8 {y^{\prime }}^{3}-27\right ) x = 12 y {y^{\prime }}^{2}
\]
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\[
{} \left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2}-b^{2} = 0
\]
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\[
{} \left (x y^{\prime }-y\right ) \left (x -y y^{\prime }\right ) = 2 y^{\prime }
\]
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\[
{} \left (5+2 x \right )^{2} y^{\prime \prime }-6 \left (5-2 x \right ) y^{\prime }+8 y = 0
\]
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\[
{} \left (2 x -1\right )^{3} y^{\prime \prime }+\left (2 x -1\right ) y^{\prime }-2 y = 0
\]
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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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\[
{} 16 \left (1+x \right )^{4} y^{\prime \prime \prime \prime }+96 \left (1+x \right )^{3} y^{\prime \prime \prime }+104 \left (1+x \right )^{2} y^{\prime \prime }+8 \left (1+x \right ) y^{\prime }+y = x^{2}+4 x +3
\]
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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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\[
{} x y^{\prime \prime \prime }+\left (x^{2}-3\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0
\]
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\[
{} x^{5} y^{\prime \prime }+3 x^{3} y^{\prime }+\left (3-6 x \right ) x^{2} y = x^{4}+2 x -5
\]
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\[
{} x y^{\prime \prime }+2 x y^{\prime }+2 y = 0
\]
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\[
{} y^{\prime \prime }+2 \,{\mathrm e}^{x} y^{\prime }+2 y \,{\mathrm e}^{x} = x^{2}
\]
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\[
{} \sqrt {x}\, y^{\prime \prime }+2 x y^{\prime }+3 y = x
\]
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\[
{} y^{\prime \prime } y^{\prime }-x^{2} y y^{\prime } = x y^{2}
\]
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\[
{} x^{2} y y^{\prime \prime }+\left (x y^{\prime }-y\right )^{2}-3 y^{2} = 0
\]
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\[
{} y^{\prime \prime } = \frac {1}{\sqrt {a y}}
\]
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\[
{} y^{\prime \prime } = \sqrt {1+{y^{\prime }}^{2}}
\]
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\[
{} 2 x y^{\prime \prime \prime } y^{\prime \prime } = {y^{\prime \prime }}^{2}-a^{2}
\]
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\[
{} y y^{\prime \prime }+{y^{\prime }}^{2} = 1
\]
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\[
{} y y^{\prime \prime }-{y^{\prime }}^{2} = y^{2} \ln \left (y\right )
\]
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\[
{} x^{2} y^{\prime \prime \prime \prime }+a^{2} y^{\prime \prime } = 0
\]
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\[
{} a y^{\prime \prime } = \sqrt {1+{y^{\prime }}^{2}}
\]
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\[
{} y^{\prime \prime } y^{\prime \prime \prime } = 2
\]
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\[
{} x^{4} y^{\prime \prime }+x y^{\prime }+y = \frac {1}{x}
\]
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\[
{} 2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = x^{2}
\]
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\[
{} \left (y^{2}+2 y^{\prime } x^{2}\right ) y^{\prime \prime }+2 {y^{\prime }}^{2} \left (x +y\right )+x y^{\prime }+y = 0
\]
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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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\[
{} \left (x^{3}+x +1\right ) y^{\prime \prime \prime }+\left (6 x +3\right ) y^{\prime \prime }+6 y = 0
\]
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\[
{} x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }+x \left (x^{2}+2\right ) y^{\prime }+3 x^{2} y = 2 x
\]
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\[
{} {y^{\prime }}^{2}-y y^{\prime \prime } = n \sqrt {{y^{\prime }}^{2}+a^{2} {y^{\prime \prime }}^{2}}
\]
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\[
{} \left (x^{3}-x \right ) y^{\prime \prime \prime }+\left (8 x^{2}-3\right ) y^{\prime \prime }+14 x y^{\prime }+4 y = \frac {2}{x^{3}}
\]
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\[
{} \sin \left (x \right ) y^{\prime \prime }-\cos \left (x \right ) y^{\prime }+2 y \sin \left (x \right ) = 0
\]
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\[
{} x y^{\prime \prime \prime }-x y^{\prime \prime }-y^{\prime } = 0
\]
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\[
{} y \left (1-\ln \left (y\right )\right ) y^{\prime \prime }+\left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2} = 0
\]
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\[
{} y^{\prime \prime \prime }+y^{\prime \prime } \cos \left (x \right )-2 \sin \left (x \right ) y^{\prime }-\cos \left (x \right ) y = \sin \left (2 x \right )
\]
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\[
{} \sin \left (x \right )^{2} y^{\prime \prime } = 2 y
\]
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\[
{} x y^{\prime \prime }+\left (1-x \right ) y^{\prime }-y = {\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }-y^{\prime } x^{2}+x y = x
\]
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\[
{} \left (3-x \right ) y^{\prime \prime }-\left (9-4 x \right ) y^{\prime }+\left (6-3 x \right ) y = 0
\]
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\[
{} 3 x^{2} y^{\prime \prime }+\left (-6 x^{2}+2\right ) y^{\prime }-4 y = 0
\]
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\[
{} a^{2} {y^{\prime \prime }}^{2} = 1+{y^{\prime }}^{2}
\]
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\[
{} y^{\prime \prime }+\frac {y^{\prime }}{x^{{1}/{3}}}+\left (\frac {1}{4 x^{{2}/{3}}}-\frac {1}{6 x^{{1}/{3}}}-\frac {6}{x^{2}}\right ) y = 0
\]
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\[
{} 4 x^{2} y^{\prime \prime }+4 x^{5} y^{\prime }+\left (x^{8}+6 x^{4}+4\right ) y = 0
\]
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\[
{} y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }+5 y = 0
\]
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\[
{} x^{2} y^{\prime \prime }-2 \left (x^{2}+x \right ) y^{\prime }+\left (x^{2}+2 x +2\right ) y = 0
\]
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\[
{} y^{\prime \prime }+\cot \left (x \right ) y^{\prime }+4 y \csc \left (x \right )^{2} = 0
\]
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\[
{} x y^{\prime \prime }-y^{\prime }+4 x^{3} y = x^{5}
\]
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\[
{} x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+y a^{2} = \frac {1}{x^{2}}
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime \prime }+3 x y^{\prime }+y = 0
\]
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\[
{} \left (x -3\right ) y^{\prime \prime }-\left (4 x -9\right ) y^{\prime }+3 \left (x -2\right ) y = 0
\]
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\[
{} y^{\prime \prime }-2 b y^{\prime }+y b^{2} x^{2} = 0
\]
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\[
{} y^{\prime \prime }+4 x y^{\prime }+4 x^{2} y = 0
\]
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\[
{} x y^{\prime \prime }-\left (2 x -1\right ) y^{\prime }+\left (x -1\right ) y = 0
\]
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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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\[
{} \left (x \sin \left (x \right )+\cos \left (x \right )\right ) y^{\prime \prime }-x \cos \left (x \right ) y^{\prime }+\cos \left (x \right ) y = 0
\]
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\[
{} x^{2} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\]
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\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }-y a^{2} = 0
\]
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\[
{} y^{\prime \prime }+x y^{\prime }-y = f \left (x \right )
\]
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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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\[
{} \left (a^{2}-x^{2}\right ) y^{\prime \prime }-\frac {a^{2} y^{\prime }}{x}+\frac {x^{2} y}{a} = 0
\]
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\[
{} \left (x^{3}-x \right ) y^{\prime \prime }+y^{\prime }+n^{2} x^{3} y = 0
\]
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\[
{} x^{2} y y^{\prime \prime }+\left (x y^{\prime }-y\right )^{2} = 0
\]
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\[
{} y y^{\prime \prime }+1+{y^{\prime }}^{2} = 0
\]
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\[
{} [x^{\prime }\left (t \right ) = n y \left (t \right )-m z \left (t \right ), y^{\prime }\left (t \right ) = L z \left (t \right )-m x \left (t \right ), z^{\prime }\left (t \right ) = m x \left (t \right )-L y \left (t \right )]
\]
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\[
{} x +y y^{\prime }+\frac {x y^{\prime }-y}{x^{2}+y^{2}} = 0
\]
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