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\[
{}y^{\prime } = \frac {2 x -y}{x +4 y}
\] |
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\[
{}y^{\prime }+\frac {2 y}{x} = 6 y^{2} x^{4}
\] |
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\[
{}y^{2}+\cos \left (x \right )+\left (2 x y+\sin \left (y\right )\right ) y^{\prime } = 0
\] |
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\[
{}x y-1+x^{2} y^{\prime } = 0
\] |
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\[
{}y^{\prime \prime }-y^{\prime }-2 y = 5 \,{\mathrm e}^{2 x}
\] |
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\[
{}y^{\prime \prime }+16 y = 4 \cos \left (x \right )
\] |
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\[
{}y^{\prime \prime }-4 y^{\prime }+3 y = 9 x^{2}+4
\] |
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\[
{}y^{\prime \prime }+y = \tan \left (x \right )^{2}
\] |
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\[
{}[x^{\prime }\left (t \right ) = -2 x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+5 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-3 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+2 y \left (t \right )+4 \,{\mathrm e}^{t}]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 6 x \left (t \right )-7 y \left (t \right )+10, y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right )-2 \,{\mathrm e}^{t}]
\] |
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\[
{}y^{\prime } = \frac {\cos \left (y\right ) \sec \left (x \right )}{x}
\] |
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\[
{}y^{\prime } = x \left (\cos \left (y\right )+y\right )
\] |
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\[
{}y^{\prime } = \frac {\sec \left (x \right ) \left (\sin \left (y\right )+y\right )}{x}
\] |
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\[
{}y^{\prime } = \left (5+\frac {\sec \left (x \right )}{x}\right ) \left (\sin \left (y\right )+y\right )
\] |
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\[
{}y^{\prime } = 1+y
\] |
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\[
{}y^{\prime } = 1+x
\] |
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\[
{}y^{\prime } = x
\] |
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\[
{}y^{\prime } = y
\] |
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\[
{}y^{\prime } = 0
\] |
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\[
{}y^{\prime } = 1+\frac {\sec \left (x \right )}{x}
\] |
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\[
{}y^{\prime } = x +\frac {\sec \left (x \right ) y}{x}
\] |
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\[
{}y^{\prime } = \frac {2 y}{x}
\] |
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\[
{}y^{\prime } = \frac {2 y}{x}
\] |
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\[
{}y^{\prime } = \frac {\ln \left (1+y^{2}\right )}{\ln \left (x^{2}+1\right )}
\] |
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\[
{}y^{\prime } = \frac {1}{x}
\] |
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\[
{}y^{\prime } = \frac {-x y-1}{4 x^{3} y-2 x^{2}}
\] |
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\[
{}\frac {{y^{\prime }}^{2}}{4}-x y^{\prime }+y = 0
\] |
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\[
{}y^{\prime } = \sqrt {\frac {1+y}{y^{2}}}
\] |
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\[
{}y^{\prime } = \sqrt {1-x^{2}-y^{2}}
\] |
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\[
{}y^{\prime }+\frac {y}{3} = \frac {\left (1-2 x \right ) y^{4}}{3}
\] |
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\[
{}y^{\prime } = \sqrt {y}+x
\] |
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\[
{}x^{2} y^{\prime }+y^{2} = x y y^{\prime }
\] |
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\[
{}y = x y^{\prime }+x^{2} {y^{\prime }}^{2}
\] |
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\[
{}\left (x +y\right ) y^{\prime } = 0
\] |
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\[
{}x y^{\prime } = 0
\] |
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\[
{}\frac {y^{\prime }}{x +y} = 0
\] |
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\[
{}\frac {y^{\prime }}{x} = 0
\] |
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\[
{}y^{\prime } = 0
\] |
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\[
{}y = x {y^{\prime }}^{2}+{y^{\prime }}^{2}
\] |
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\[
{}y^{\prime } = \frac {5 x^{2}-x y+y^{2}}{x^{2}}
\] |
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\[
{}2 t +3 x+\left (x+2\right ) x^{\prime } = 0
\] |
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\[
{}y^{\prime } = \frac {1}{1-y}
\] |
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\[
{}p^{\prime } = a p-b p^{2}
\] |
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\[
{}y^{2}+\frac {2}{x}+2 x y y^{\prime } = 0
\] |
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\[
{}x f^{\prime }-f = \frac {{f^{\prime }}^{2} \left (1-{f^{\prime }}^{\lambda }\right )^{2}}{\lambda ^{2}}
\] |
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\[
{}x y^{\prime }-2 y+b y^{2} = c \,x^{4}
\] |
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\[
{}x y^{\prime }-y+y^{2} = x^{{2}/{3}}
\] |
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\[
{}u^{\prime }+u^{2} = \frac {1}{x^{{4}/{5}}}
\] |
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\[
{}y y^{\prime }-y = x
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
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\[
{}5 y^{\prime \prime }+2 y^{\prime }+4 y = 0
\] |
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\[
{}y^{\prime \prime }+y^{\prime }+4 y = 1
\] |
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\[
{}y^{\prime \prime }+y^{\prime }+4 y = \sin \left (x \right )
\] |
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\[
{}y = x {y^{\prime }}^{2}
\] |
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\[
{}y y^{\prime } = 1-x {y^{\prime }}^{3}
\] |
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\[
{}f^{\prime } = \frac {1}{f}
\] |
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\[
{}t y^{\prime \prime }+4 y^{\prime } = t^{2}
\] |
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\[
{}\left (t^{2}+9\right ) y^{\prime \prime }+2 t y^{\prime } = 0
\] |
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\[
{}t^{2} y^{\prime \prime }-3 t y^{\prime }+5 y = 0
\] |
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\[
{}t y^{\prime \prime }+y^{\prime } = 0
\] |
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\[
{}t^{2} y^{\prime \prime }-2 y^{\prime } = 0
\] |
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\[
{}y^{\prime \prime }+\frac {\left (t^{2}-1\right ) y^{\prime }}{t}+\frac {t^{2} y}{\left (1+{\mathrm e}^{\frac {t^{2}}{2}}\right )^{2}} = 0
\] |
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\[
{}t y^{\prime \prime }-y^{\prime }+4 t^{3} y = 0
\] |
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\[
{}y^{\prime \prime } = 0
\] |
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\[
{}y^{\prime \prime } = 1
\] |
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\[
{}y^{\prime \prime } = f \left (t \right )
\] |
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\[
{}y^{\prime \prime } = k
\] |
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\[
{}y^{\prime } = -4 \sin \left (x -y\right )-4
\] |
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\[
{}y^{\prime }+\sin \left (x -y\right ) = 0
\] |
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\[
{}y^{\prime \prime } = 4 \sin \left (x \right )-4
\] |
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\[
{}y y^{\prime \prime } = 0
\] |
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\[
{}y y^{\prime \prime } = 1
\] |
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\[
{}y y^{\prime \prime } = x
\] |
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\[
{}y^{2} y^{\prime \prime } = x
\] |
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\[
{}y^{2} y^{\prime \prime } = 0
\] |
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\[
{}3 y y^{\prime \prime } = \sin \left (x \right )
\] |
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\[
{}3 y y^{\prime \prime }+y = 5
\] |
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\[
{}a y y^{\prime \prime }+b y = c
\] |
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\[
{}a y^{2} y^{\prime \prime }+b y^{2} = c
\] |
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\[
{}a y y^{\prime \prime }+b y = 0
\] |
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\[
{}[x^{\prime }\left (t \right ) = 9 x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = -6 x \left (t \right )-y \left (t \right ), z^{\prime }\left (t \right ) = 6 x \left (t \right )+4 y \left (t \right )+3 z \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-3 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+7 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+5 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 7 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -4 x \left (t \right )+3 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right ), z^{\prime }\left (t \right ) = z \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )-z \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+2 z \left (t \right ), z^{\prime }\left (t \right ) = -x \left (t \right )-2 y \left (t \right )+4 z \left (t \right )]
\] |
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\[
{}x^{\prime } = 4 A k \left (\frac {x}{A}\right )^{{3}/{4}}-3 k x
\] |
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\[
{}\frac {y^{\prime } y}{1+\frac {\sqrt {1+{y^{\prime }}^{2}}}{2}} = -x
\] |
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\[
{}\frac {y^{\prime } y}{1+\frac {\sqrt {1+{y^{\prime }}^{2}}}{2}} = -x
\] |
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\[
{}y^{\prime } = \frac {y \left (1+\frac {a^{2} x}{\sqrt {a^{2} \left (x^{2}+1\right )}}\right )}{\sqrt {a^{2} \left (x^{2}+1\right )}}
\] |
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\[
{}y^{\prime } = x^{2}+y^{2}
\] |
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\[
{}y^{\prime } = 2 \sqrt {y}
\] |
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\[
{}z^{\prime \prime }+3 z^{\prime }+2 z = 24 \,{\mathrm e}^{-3 t}-24 \,{\mathrm e}^{-4 t}
\] |
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\[
{}y^{\prime } = \sqrt {1-y^{2}}
\] |
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\[
{}y^{\prime } = y^{2}+x^{2}-1
\] |
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\[
{}y^{\prime } = 2 y \left (x \sqrt {y}-1\right )
\] |
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\[
{}y^{\prime \prime } = \frac {1}{y}-\frac {x y^{\prime }}{y^{2}}
\] |
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\[
{}y^{\prime \prime }+y^{\prime }+y = 0
\] |
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