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Mathematica |
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\[
{} 2 \sqrt {s t}-s+t s^{\prime } = 0
\]
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\[
{} t -s+t s^{\prime } = 0
\]
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\[
{} x y^{2} y^{\prime } = x^{3}+y^{3}
\]
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\[
{} x \cos \left (\frac {y}{x}\right ) \left (x y^{\prime }+y\right ) = y \sin \left (\frac {y}{x}\right ) \left (x y^{\prime }-y\right )
\]
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\[
{} 3 y-7 x +7-\left (3 x -7 y-3\right ) y^{\prime } = 0
\]
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\[
{} x +2 y+1-\left (4 y+2 x +3\right ) y^{\prime } = 0
\]
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\[
{} x +2 y+1-\left (2 x -3\right ) y^{\prime } = 0
\]
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\[
{} \frac {y-x y^{\prime }}{\sqrt {x^{2}+y^{2}}} = m
\]
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\[
{} \frac {x +y y^{\prime }}{\sqrt {x^{2}+y^{2}}} = m
\]
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\[
{} y+\frac {x}{y^{\prime }} = \sqrt {x^{2}+y^{2}}
\]
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\[
{} y y^{\prime } = -x +\sqrt {x^{2}+y^{2}}
\]
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\[
{} y^{\prime }-\frac {2 y}{1+x} = \left (1+x \right )^{3}
\]
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\[
{} y^{\prime }-\frac {a y}{x} = \frac {1+x}{x}
\]
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\[
{} \left (-x^{2}+x \right ) y^{\prime }+\left (2 x^{2}-1\right ) y-a \,x^{3} = 0
\]
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\[
{} s^{\prime } \cos \left (t \right )+s \sin \left (t \right ) = 1
\]
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\[
{} s^{\prime }+s \cos \left (t \right ) = \frac {\sin \left (2 t \right )}{2}
\]
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\[
{} y^{\prime }-\frac {n y}{x} = {\mathrm e}^{x} x^{n}
\]
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\[
{} y^{\prime }+\frac {n y}{x} = a \,x^{-n}
\]
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\[
{} y^{\prime }+y = {\mathrm e}^{-x}
\]
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\[
{} y^{\prime }+\frac {\left (1-2 x \right ) y}{x^{2}}-1 = 0
\]
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\[
{} y^{\prime }+x y = x^{3} y^{3}
\]
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\[
{} \left (-x^{2}+1\right ) y^{\prime }-x y+a x y^{2} = 0
\]
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\[
{} 3 y^{2} y^{\prime }-a y^{3}-x -1 = 0
\]
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\[
{} y^{\prime } \left (x^{2} y^{3}+x y\right ) = 1
\]
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\[
{} x y^{\prime } = \left (y \ln \left (x \right )-2\right ) y
\]
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\[
{} y-y^{\prime } \cos \left (x \right ) = y^{2} \cos \left (x \right ) \left (1-\sin \left (x \right )\right )
\]
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\[
{} x^{2}+y+\left (x -2 y\right ) y^{\prime } = 0
\]
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\[
{} y-3 x^{2}-\left (4 y-x \right ) y^{\prime } = 0
\]
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\[
{} \left (y^{3}-x \right ) y^{\prime } = y
\]
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\[
{} \frac {y^{2}}{\left (x -y\right )^{2}}-\frac {1}{x}+\left (\frac {1}{y}-\frac {x^{2}}{\left (x -y\right )^{2}}\right ) y^{\prime } = 0
\]
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\[
{} 6 x y^{2}+4 x^{3}+3 \left (2 x^{2} y+y^{2}\right ) y^{\prime } = 0
\]
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\[
{} \frac {x}{\left (x +y\right )^{2}}+\frac {\left (y+2 x \right ) y^{\prime }}{\left (x +y\right )^{2}} = 0
\]
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\[
{} \frac {1}{x^{2}}+\frac {3 y^{2}}{x^{4}} = \frac {2 y y^{\prime }}{x^{3}}
\]
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\[
{} \frac {x^{2} y^{\prime }}{\left (x -y\right )^{2}}-\frac {y^{2}}{\left (x -y\right )^{2}} = 0
\]
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\[
{} x +y y^{\prime } = \frac {y}{x^{2}+y^{2}}-\frac {x y^{\prime }}{x^{2}+y^{2}}
\]
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\[
{} y = 2 x y^{\prime }+{y^{\prime }}^{2}
\]
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\[
{} y = x {y^{\prime }}^{2}+{y^{\prime }}^{2}
\]
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\[
{} y = x \left (1+y^{\prime }\right )+{y^{\prime }}^{2}
\]
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\[
{} y = y {y^{\prime }}^{2}+2 x y^{\prime }
\]
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\[
{} y = y y^{\prime }+y^{\prime }-{y^{\prime }}^{2}
\]
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\[
{} y = x y^{\prime }+\sqrt {1-{y^{\prime }}^{2}}
\]
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\[
{} y = x y^{\prime }+y^{\prime }
\]
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\[
{} y = x y^{\prime }+\frac {1}{y^{\prime }}
\]
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\[
{} y = x y^{\prime }-\frac {1}{{y^{\prime }}^{2}}
\]
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\[
{} y^{\prime } = \frac {2 y}{x}-\sqrt {3}
\]
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\[
{} y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y = 0
\]
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\[
{} y^{\prime \prime } = \frac {1}{2 y^{\prime }}
\]
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\[
{} x y^{\prime \prime \prime } = 2
\]
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\[
{} y^{\prime \prime } = a^{2} y
\]
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\[
{} y^{\prime \prime } = \frac {a}{y^{3}}
\]
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\[
{} x y^{\prime \prime }-y^{\prime } = x^{2} {\mathrm e}^{x}
\]
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\[
{} y y^{\prime \prime }-{y^{\prime }}^{2}+{y^{\prime }}^{3} = 0
\]
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\[
{} y^{\prime \prime }+\tan \left (x \right ) y^{\prime } = \sin \left (2 x \right )
\]
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\[
{} {y^{\prime \prime }}^{2}+{y^{\prime }}^{2} = a^{2}
\]
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\[
{} y^{\prime \prime } = \frac {1}{2 y^{\prime }}
\]
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\[
{} y^{\prime \prime \prime } = {y^{\prime \prime }}^{2}
\]
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\[
{} y^{\prime } y^{\prime \prime \prime }-3 {y^{\prime \prime }}^{2} = 0
\]
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\[
{} y^{\prime \prime } = 9 y
\]
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\[
{} y^{\prime \prime }+y = 0
\]
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\[
{} y^{\prime \prime }-y = 0
\]
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\[
{} y^{\prime \prime }+12 y = 7 y^{\prime }
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+4 y = 0
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+10 y = 0
\]
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\[
{} y^{\prime \prime }+3 y^{\prime }-2 y = 0
\]
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\[
{} 4 y^{\prime \prime }-12 y^{\prime }+9 y = 0
\]
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\[
{} y^{\prime \prime }+y^{\prime }+y = 0
\]
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\[
{} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = 0
\]
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\[
{} y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y = 0
\]
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\[
{} y^{\prime \prime \prime }-3 a y^{\prime \prime }+3 a^{2} y^{\prime }-a^{3} y = 0
\]
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\[
{} y^{\left (5\right )}-4 y^{\prime \prime \prime } = 0
\]
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\[
{} y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+9 y = 0
\]
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\[
{} y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+16 y = 0
\]
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\[
{} y^{\prime \prime \prime \prime }+y = 0
\]
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\[
{} y^{\prime \prime \prime \prime }-a^{4} y = 0
\]
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\[
{} y^{\prime \prime }-7 y^{\prime }+12 y = x
\]
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\[
{} s^{\prime \prime }-a^{2} s = t +1
\]
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\[
{} y^{\prime \prime }+y^{\prime }-2 y = 8 \sin \left (2 x \right )
\]
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\[
{} y^{\prime \prime }-y = 5 x +2
\]
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\[
{} y^{\prime \prime }-2 a y^{\prime }+a^{2} y = {\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }+6 y^{\prime }+5 y = {\mathrm e}^{2 x}
\]
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\[
{} y^{\prime \prime }+9 y = 6 \,{\mathrm e}^{3 x}
\]
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\[
{} y^{\prime \prime }-3 y^{\prime } = 2-6 x
\]
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\[
{} y^{\prime \prime }-2 y^{\prime }+3 y = {\mathrm e}^{-x} \cos \left (x \right )
\]
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\[
{} y^{\prime \prime }+4 y = 2 \sin \left (2 x \right )
\]
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\[
{} y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y = 2 x +3
\]
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\[
{} y^{\prime \prime \prime \prime }-a^{4} y = 5 a^{4} {\mathrm e}^{a x} \sin \left (a x \right )
\]
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\[
{} y^{\prime \prime \prime \prime }+2 a^{2} y^{\prime \prime }+a^{4} y = 8 \cos \left (a x \right )
\]
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\[
{} y^{\prime \prime }+2 h y^{\prime }+n^{2} y = 0
\]
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\[
{} y^{\prime \prime }+n^{2} y = h \sin \left (r x \right )
\]
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\[
{} y^{\prime \prime }-7 y^{\prime }+6 y = \sin \left (x \right )
\]
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\[
{} y^{\prime \prime }+y = \sec \left (x \right )
\]
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\[
{} y^{\prime \prime }+y = \frac {1}{\cos \left (2 x \right )^{{3}/{2}}}
\]
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\[
{} [x^{\prime }\left (t \right ) = 1+y \left (t \right ), y^{\prime }\left (t \right ) = 1+x \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )]
\]
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\[
{} [4 x^{\prime }\left (t \right )-y^{\prime }\left (t \right )+3 x \left (t \right ) = \sin \left (t \right ), x^{\prime }\left (t \right )+y \left (t \right ) = \cos \left (t \right )]
\]
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\[
{} y y^{\prime \prime } = 1+{y^{\prime }}^{2}
\]
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\[
{} \frac {x^{2} y^{\prime }}{\left (x -y\right )^{2}}-\frac {y^{2}}{\left (x -y\right )^{2}} = 0
\]
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\[
{} y = x {y^{\prime }}^{2}+{y^{\prime }}^{2}
\]
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\[
{} y^{\prime \prime }+y = \sec \left (x \right )
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime }-x y-\alpha = 0
\]
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