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\[
{}y^{\prime \prime } = \frac {1}{y^{2}}
\] |
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\[
{}y y^{\prime \prime }-{y^{\prime }}^{2} = 0
\] |
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\[
{}y y^{\prime \prime }-{y^{\prime }}^{2} = 1
\] |
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\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-1-{y^{\prime }}^{2} = 0
\] |
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\[
{}x y^{\prime \prime }+3 y^{\prime } = 3 x
\] |
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\[
{}x = y^{\prime \prime }+y^{\prime }
\] |
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\[
{}x = y+{y^{\prime }}^{2}
\] |
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\[
{}y = x y^{\prime }-{y^{\prime }}^{2}
\] |
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\[
{}V^{\prime \prime }+\frac {2 V^{\prime }}{r} = 0
\] |
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\[
{}V^{\prime \prime }+\frac {V^{\prime }}{r} = 0
\] |
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\[
{}[z^{\prime }\left (x \right )+7 y \left (x \right )-3 z \left (x \right ) = 0, 7 y^{\prime }\left (x \right )+63 y \left (x \right )-36 z \left (x \right ) = 0]
\] |
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\[
{}[z^{\prime }\left (x \right )+2 y^{\prime }\left (x \right )+3 y \left (x \right ) = 0, y^{\prime }\left (x \right )+3 y \left (x \right )-2 z \left (x \right ) = 0]
\] |
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\[
{}[y^{\prime }\left (x \right )+3 y \left (x \right )+z \left (x \right ) = 0, z^{\prime }\left (x \right )+3 y \left (x \right )+5 z \left (x \right ) = 0]
\] |
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\[
{}[y^{\prime }\left (x \right )+3 y \left (x \right )+2 z \left (x \right ) = 0, z^{\prime }\left (x \right )+2 y \left (x \right )-4 z \left (x \right ) = 0]
\] |
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\[
{}[y^{\prime }\left (x \right )-3 y \left (x \right )-2 z \left (x \right ) = 0, z^{\prime }\left (x \right )+y \left (x \right )-2 z \left (x \right ) = 0]
\] |
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\[
{}[y^{\prime }\left (x \right )+z^{\prime }\left (x \right )+6 y \left (x \right ) = 0, z^{\prime }\left (x \right )+5 y \left (x \right )+z \left (x \right ) = 0]
\] |
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\[
{}[z^{\prime }\left (x \right )+y^{\prime }\left (x \right )+5 y \left (x \right )-3 z \left (x \right ) = x +{\mathrm e}^{x}, y^{\prime }\left (x \right )+2 y \left (x \right )-z \left (x \right ) = {\mathrm e}^{x}]
\] |
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\[
{}[z^{\prime }\left (x \right )+y \left (x \right )+3 z \left (x \right ) = {\mathrm e}^{x}, y^{\prime }\left (x \right )+3 y \left (x \right )+4 z \left (x \right ) = {\mathrm e}^{2 x}]
\] |
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\[
{}[z^{\prime }\left (x \right )-3 y \left (x \right )+2 z \left (x \right ) = {\mathrm e}^{x}, y^{\prime }\left (x \right )+2 y \left (x \right )-z \left (x \right ) = {\mathrm e}^{3 x}]
\] |
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\[
{}[z^{\prime }\left (x \right )+5 y \left (x \right )-2 z \left (x \right ) = x, y^{\prime }\left (x \right )+4 y \left (x \right )+z \left (x \right ) = x]
\] |
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\[
{}[z^{\prime }\left (x \right )+7 y \left (x \right )-9 z \left (x \right ) = {\mathrm e}^{x}, y^{\prime }\left (x \right )-y \left (x \right )-3 z \left (x \right ) = {\mathrm e}^{2 x}]
\] |
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\[
{}[y^{\prime }\left (x \right )-2 y \left (x \right )-2 z \left (x \right ) = {\mathrm e}^{3 x}, z^{\prime }\left (x \right )+5 y \left (x \right )-2 z \left (x \right ) = {\mathrm e}^{4 x}]
\] |
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\[
{}{y^{\prime }}^{2}+x y^{\prime }-y = 0
\] |
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\[
{}y^{\prime \prime }-\frac {2 y^{\prime }}{x}+\frac {2 y}{x^{2}} = 0
\] |
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\[
{}v^{\prime \prime }+\frac {2 v^{\prime }}{r} = 0
\] |
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\[
{}y^{\prime \prime }-k^{2} y = 0
\] |
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\[
{}\left (1-x \right ) y^{\prime }-1-y = 0
\] |
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\[
{}y^{\prime }+\sqrt {\frac {1-y^{2}}{-x^{2}+1}} = 0
\] |
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\[
{}-x y^{\prime }+y = a \left (y^{2}+y^{\prime }\right )
\] |
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\[
{}3 \,{\mathrm e}^{x} \tan \left (y\right )+\left (1-{\mathrm e}^{x}\right ) \sec \left (y\right )^{2} y^{\prime } = 0
\] |
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\[
{}x^{2}+y^{2}-2 x y y^{\prime } = 0
\] |
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\[
{}y^{2}+\left (x y+x^{2}\right ) y^{\prime } = 0
\] |
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\[
{}x^{2} y-\left (y^{3}+x^{3}\right ) y^{\prime } = 0
\] |
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\[
{}\left (4 y+3 x \right ) y^{\prime }+y-2 x = 0
\] |
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\[
{}3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0
\] |
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\[
{}\left (y-3 x +3\right ) y^{\prime } = 2 y-x -4
\] |
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\[
{}x^{2}-4 x y-2 y^{2}+\left (y^{2}-4 x y-2 x^{2}\right ) y^{\prime } = 0
\] |
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\[
{}x +y y^{\prime }+\frac {x y^{\prime }-y}{x^{2}+y^{2}} = 0
\] |
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\[
{}a^{2}-2 x y-y^{2}-\left (x +y\right )^{2} y^{\prime } = 0
\] |
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\[
{}2 a x +b y+g +\left (2 c y+b x +e \right ) y^{\prime } = 0
\] |
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\[
{}\left (2 x^{2} y+4 x^{3}-12 x y^{2}+3 y^{2}-x \,{\mathrm e}^{y}+{\mathrm e}^{2 x}\right ) y^{\prime }+12 x^{2} y+2 x y^{2}+4 x^{3}-4 y^{3}+2 y \,{\mathrm e}^{2 x}-{\mathrm e}^{y} = 0
\] |
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\[
{}y-x y^{\prime }+\ln \left (x \right ) = 0
\] |
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\[
{}\left (x y+1\right ) y-\left (1-x y\right ) x y^{\prime } = 0
\] |
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\[
{}a \left (x y^{\prime }+2 y\right ) = x y y^{\prime }
\] |
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\[
{}x^{4} {\mathrm e}^{x}-2 m x y^{2}+2 m \,x^{2} y y^{\prime } = 0
\] |
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\[
{}y \left (2 x y+{\mathrm e}^{x}\right )-{\mathrm e}^{x} y^{\prime } = 0
\] |
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\[
{}x^{2} y-2 x y^{2}-\left (x^{3}-3 x^{2} y\right ) y^{\prime } = 0
\] |
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\[
{}y \left (x y+2 x^{2} y^{2}\right )+x \left (x y-x^{2} y^{2}\right ) y^{\prime } = 0
\] |
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\[
{}x^{2}+y^{2}+2 x +2 y y^{\prime } = 0
\] |
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\[
{}x^{2}+y^{2}-x^{2} y y^{\prime } = 0
\] |
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\[
{}3 x^{2} y^{4}+2 x y+\left (2 x^{3} y^{3}-x^{2}\right ) y^{\prime } = 0
\] |
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\[
{}y^{4}+2 y+\left (x y^{3}+2 y^{4}-4 x \right ) y^{\prime } = 0
\] |
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\[
{}y^{3}-2 x^{2} y+\left (2 x y^{2}-x^{3}\right ) y^{\prime } = 0
\] |
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\[
{}2 x^{2} y-3 y^{4}+\left (3 x^{3}+2 x y^{3}\right ) y^{\prime } = 0
\] |
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\[
{}y^{2}+2 x^{2} y+\left (2 x^{3}-x y\right ) y^{\prime } = 0
\] |
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\[
{}x y^{\prime }-a y = 1+x
\] |
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\[
{}y^{\prime }+y = {\mathrm e}^{-x}
\] |
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\[
{}\cos \left (x \right )^{2} y^{\prime }+y = \tan \left (x \right )
\] |
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\[
{}\left (1+x \right ) y^{\prime }-n y = {\mathrm e}^{x} \left (1+x \right )^{n +1}
\] |
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\[
{}\left (x^{2}+1\right ) y^{\prime }+2 x y = 4 x^{2}
\] |
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\[
{}y^{\prime }+\frac {y}{x} = y^{6} x^{2}
\] |
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\[
{}1+y^{2} = \left (\arctan \left (y\right )-x \right ) y^{\prime }
\] |
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\[
{}y^{\prime }+\frac {2 y}{x} = 3 x^{2} y^{{1}/{3}}
\] |
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\[
{}y^{\prime }+\frac {x y}{-x^{2}+1} = x \sqrt {y}
\] |
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\[
{}3 x \left (-x^{2}+1\right ) y^{2} y^{\prime }+\left (2 x^{2}-1\right ) y^{3} = a \,x^{3}
\] |
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\[
{}\left (x +y\right )^{2} y^{\prime } = a^{2}
\] |
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\[
{}x y^{\prime }-y = \sqrt {x^{2}+y^{2}}
\] |
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\[
{}x y^{\prime }-y = x \sqrt {x^{2}+y^{2}}
\] |
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\[
{}\sec \left (x \right )^{2} \tan \left (y\right )+\sec \left (y\right )^{2} \tan \left (x \right ) y^{\prime } = 0
\] |
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\[
{}\left (x^{2}-x^{2} y\right ) y^{\prime }+y^{2}+x y^{2} = 0
\] |
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\[
{}y^{\prime }+\frac {\left (1-2 x \right ) y}{x^{2}} = 1
\] |
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\[
{}3 y^{\prime }+\frac {2 y}{1+x} = \frac {x^{3}}{y^{2}}
\] |
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\[
{}2 x -y+1+\left (2 y-x -1\right ) y^{\prime } = 0
\] |
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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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\[
{}x y^{\prime }+\frac {y^{2}}{x} = y
\] |
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\[
{}x \left (-a^{2}+x^{2}+y^{2}\right )+y \left (x^{2}-y^{2}-b^{2}\right ) y^{\prime } = 0
\] |
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\[
{}y^{\prime }+\frac {4 x y}{x^{2}+1} = \frac {1}{\left (x^{2}+1\right )^{3}}
\] |
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\[
{}x^{2} y-\left (y^{3}+x^{3}\right ) y^{\prime } = 0
\] |
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\[
{}x \left (-x^{2}+1\right ) y^{\prime }+\left (2 x^{2}-1\right ) y = a \,x^{3}
\] |
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\[
{}x^{2}+y^{2}+1-2 x y y^{\prime } = 0
\] |
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\[
{}x +y y^{\prime } = m \left (x y^{\prime }-y\right )
\] |
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\[
{}y^{\prime }+y \cos \left (x \right ) = y^{n} \sin \left (2 x \right )
\] |
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\[
{}\left (1+x \right ) y^{\prime }+1 = 2 \,{\mathrm e}^{y}
\] |
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\[
{}y^{\prime } = x^{3} y^{3}-x y
\] |
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\[
{}y+\left (a \,x^{2} y^{n}-2 x \right ) y^{\prime } = 0
\] |
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\[
{}\left (1+6 y^{2}-3 x^{2} y\right ) y^{\prime } = 3 x y^{2}-x^{2}
\] |
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\[
{}y \left (x^{2}+y^{2}+a^{2}\right ) y^{\prime }+x \left (-a^{2}+x^{2}+y^{2}\right ) = 0
\] |
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\[
{}\left (x^{2} y^{3}+x y\right ) y^{\prime } = 1
\] |
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\[
{}y y^{\prime } = a x
\] |
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\[
{}\sqrt {a^{2}+x^{2}}\, y^{\prime }+y = \sqrt {a^{2}+x^{2}}-x
\] |
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\[
{}\left (x +y\right ) y^{\prime }+x -y = 0
\] |
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\[
{}y y^{\prime }+b y^{2} = a \cos \left (x \right )
\] |
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\[
{}2 x y+\left (y^{2}-x^{2}\right ) y^{\prime } = 0
\] |
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\[
{}-x y^{\prime }+y = b \left (1+x^{2} y^{\prime }\right )
\] |
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\[
{}3 y+2 x +4-\left (4 x +6 y+5\right ) y^{\prime } = 0
\] |
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\[
{}\left (x^{3} y^{3}+x^{2} y^{2}+x y+1\right ) y+\left (x^{3} y^{3}-x^{2} y^{2}-x y+1\right ) x y^{\prime } = 0
\] |
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\[
{}2 x^{2} y^{2}+y-\left (x^{3} y-3 x \right ) y^{\prime } = 0
\] |
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\[
{}y^{2}+x^{2} y^{\prime } = x y y^{\prime }
\] |
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\[
{}y^{\prime }+\frac {n y}{x} = a \,x^{-n}
\] |
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\[
{}\left (x -y\right )^{2} y^{\prime } = a^{2}
\] |
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