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Mathematica |
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\[
{}y^{\prime } = y^{2}+x^{2}-1
\] |
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\[
{}y y^{\prime \prime } = 6 x^{4}
\] |
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\[
{}x^{2} y^{\prime }+y = 0
\] |
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\[
{}x^{3} y^{\prime } = 2 y
\] |
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\[
{}x^{2} y^{\prime \prime }+\cos \left (x \right ) y^{\prime }+x y = 0
\] |
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\[
{}3 x^{3} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (-x^{2}+1\right ) y = 0
\] |
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\[
{}x^{3} \left (1-x \right ) y^{\prime \prime }+\left (3 x +2\right ) y^{\prime }+x y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y = 0
\] |
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\[
{}x^{3} y^{\prime \prime }-x y^{\prime }+y = 0
\] |
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\[
{}[x^{\prime }\left (t \right ) = t x \left (t \right )-y \left (t \right )+{\mathrm e}^{t} z \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+t^{2} y \left (t \right )-z \left (t \right ), z^{\prime }\left (t \right ) = {\mathrm e}^{-t} x \left (t \right )+3 t y \left (t \right )+t^{3} z \left (t \right )]
\] |
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\[
{}y^{\prime } = 1+x^{2}+y^{2}+x^{2} y^{4}
\] |
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\[
{}x^{2} y^{\prime }+y = 0
\] |
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\[
{}x^{3} y^{\prime } = 2 y
\] |
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\[
{}y^{\prime } = \frac {-{\mathrm e}^{-x}+x}{{\mathrm e}^{y}+x}
\] |
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\[
{}{\mathrm e}^{x} \sin \left (y\right )+3 y-\left (3 x -{\mathrm e}^{x} \sin \left (y\right )\right ) y^{\prime } = 0
\] |
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\[
{}x \ln \left (x \right )+x y+\left (\ln \left (x \right ) y+x y\right ) y^{\prime } = 0
\] |
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\[
{}u^{\prime \prime }+u^{\prime }+\frac {u^{3}}{5} = \cos \left (t \right )
\] |
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\[
{}t \left (t -1\right ) y^{\prime \prime \prime \prime }+{\mathrm e}^{t} y^{\prime \prime }+4 t^{2} y = 0
\] |
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\[
{}y^{\prime } = \frac {x^{2}+y^{2}}{\sin \left (x \right )}
\] |
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\[
{}y^{\prime } = \frac {{\mathrm e}^{x}+y}{x^{2}+y^{2}}
\] |
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\[
{}y^{\prime } = \frac {x^{2}+y^{2}}{\ln \left (x y\right )}
\] |
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\[
{}y^{\prime } = \left (x^{2}+y^{2}\right ) y^{{1}/{3}}
\] |
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\[
{}y^{\prime } = \ln \left (1+x^{2}+y^{2}\right )
\] |
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\[
{}y^{\prime } = \sqrt {x^{2}+y^{2}}
\] |
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\[
{}y^{\prime } = \left (x^{2}+y^{2}\right )^{2}
\] |
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\[
{}2 x^{2}+8 x y+y^{2}+\left (2 x^{2}+\frac {x y^{3}}{3}\right ) y^{\prime } = 0
\] |
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\[
{}y \sin \left (x y\right )+x y^{2} \cos \left (x y\right )+\left (x \sin \left (x y\right )+x y^{2} \cos \left (x y\right )\right ) y^{\prime } = 0
\] |
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\[
{}3 x^{2} \cos \left (x \right ) y-x^{3} y \sin \left (x \right )+4 x +\left (8 y-x^{4} \sin \left (x \right ) y\right ) y^{\prime } = 0
\] |
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\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+2 y^{\prime }-2 y = {\mathrm e}^{2 x} \left (\left (-x^{2}+5 x +27\right ) \cos \left (x \right )+\left (9 x^{2}+13 x +2\right ) \sin \left (x \right )\right )
\] |
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\[
{}y^{\prime } = y^{2}+\cos \left (t^{2}\right )
\] |
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\[
{}y^{\prime } = {\mathrm e}^{-t^{2}}+y^{2}
\] |
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\[
{}y^{\prime } = {\mathrm e}^{-t^{2}}+y^{2}
\] |
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\[
{}y^{\prime } = {\mathrm e}^{-t^{2}}+y^{2}
\] |
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\[
{}y^{\prime } = y+{\mathrm e}^{-y}+{\mathrm e}^{-t}
\] |
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\[
{}y^{\prime } = y^{3}+{\mathrm e}^{-5 t}
\] |
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\[
{}y^{\prime } = \left (4 y+{\mathrm e}^{-t^{2}}\right ) {\mathrm e}^{2 y}
\] |
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\[
{}y^{\prime } = {\mathrm e}^{-t}+\ln \left (1+y^{2}\right )
\] |
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\[
{}t \left (t -2\right )^{2} y^{\prime \prime }+t y^{\prime }+y = 0
\] |
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\[
{}\left (-t^{2}+1\right ) y^{\prime \prime }+\frac {y^{\prime }}{\sin \left (t +1\right )}+y = 0
\] |
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\[
{}t^{3} y^{\prime \prime }-t y^{\prime }-\left (t^{2}+\frac {5}{4}\right ) y = 0
\] |
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\[
{}2 t \cos \left (y\right )+3 t^{2} y+\left (2 y+2 t^{2}\right ) y^{\prime } = 0
\] |
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\[
{}y^{\prime } = {\mathrm e}^{-t^{2}}+y^{2}
\] |
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\[
{}y^{\prime } = {\mathrm e}^{-t^{2}}+y^{2}
\] |
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\[
{}y^{\prime } = {\mathrm e}^{-t^{2}}+y^{2}
\] |
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\[
{}y^{\prime } = y+{\mathrm e}^{-y}+{\mathrm e}^{-t}
\] |
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\[
{}y^{\prime } = y^{3}+{\mathrm e}^{-5 t}
\] |
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\[
{}y^{\prime } = \left (4 y+{\mathrm e}^{-t^{2}}\right ) {\mathrm e}^{2 y}
\] |
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\[
{}y^{\prime } = {\mathrm e}^{-t}+\ln \left (1+y^{2}\right )
\] |
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\[
{}y^{\prime } = y+{\mathrm e}^{-y}+2 t
\] |
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\[
{}y^{\prime } = \frac {t^{2}+y^{2}}{1+t +y^{2}}
\] |
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\[
{}y^{\prime \prime }+p \left (t \right ) y^{\prime }+q \left (t \right ) y = t +1
\] |
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\[
{}t \left (t -2\right )^{2} y^{\prime \prime }+t y^{\prime }+y = 0
\] |
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\[
{}\left (-t^{2}+1\right ) y^{\prime \prime }+\frac {y^{\prime }}{\sin \left (t +1\right )}+y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }+\left (-t^{2}+1\right ) y^{\prime }+4 t y = 0
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-x \left (t \right )^{2}-2 x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = 2 y \left (t \right )-2 y \left (t \right )^{2}-3 x \left (t \right ) y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -b x \left (t \right ) y \left (t \right )+m, y^{\prime }\left (t \right ) = b x \left (t \right ) y \left (t \right )-g y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -1-y \left (t \right )-{\mathrm e}^{x \left (t \right )}, y^{\prime }\left (t \right ) = x \left (t \right )^{2}+y \left (t \right ) \left ({\mathrm e}^{x \left (t \right )}-1\right ), z^{\prime }\left (t \right ) = x \left (t \right )+\sin \left (z \left (t \right )\right )]
\] |
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\[
{}\left [x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -\frac {\left (x_{1} \left (t \right )^{2}+\sqrt {x_{1} \left (t \right )^{2}+4 x_{2} \left (t \right )^{2}}\right ) x_{1} \left (t \right )}{2}\right ]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-x \left (t \right )^{3}-x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = 2 y \left (t \right )-y \left (t \right )^{5}-y \left (t \right ) x \left (t \right )^{4}]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )^{2}+y \left (t \right )^{2}+1, y^{\prime }\left (t \right ) = x \left (t \right )^{2}-y \left (t \right )^{2}]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 6 x \left (t \right )-6 x \left (t \right )^{2}-2 x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = 4 y \left (t \right )-4 y \left (t \right )^{2}-2 x \left (t \right ) y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = \tan \left (x \left (t \right )+y \left (t \right )\right ), y^{\prime }\left (t \right ) = x \left (t \right )+x \left (t \right )^{3}]
\] |
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\[
{}2 x +3 y+2+\left (y-x \right ) y^{\prime } = 0
\] |
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\[
{}3 x -y+2+\left (x +2 y+1\right ) y^{\prime } = 0
\] |
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\[
{}x y^{2}+2 y+\left (2 y^{3}-x^{2} y+2 x \right ) y^{\prime } = 0
\] |
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\[
{}\left (x^{2}+y^{2}-2 y\right ) y^{\prime } = 2 x
\] |
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\[
{}y-x^{2} \sqrt {x^{2}-y^{2}}-x y^{\prime } = 0
\] |
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\[
{}\sec \left (y\right )^{2} y^{\prime } = \tan \left (y\right )+2 x \,{\mathrm e}^{x}
\] |
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\[
{}y^{\prime \prime } = {y^{\prime }}^{2} \cos \left (x \right )
\] |
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\[
{}\left (1+{y^{\prime }}^{2}\right )^{2} = y^{2} y^{\prime \prime }
\] |
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\[
{}y^{\prime \prime } = {y^{\prime }}^{2} \sin \left (x \right )
\] |
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\[
{}1+\left (2 y-x^{2}\right ) {y^{\prime }}^{2}-2 y {y^{\prime }}^{2} x^{2} = 0
\] |
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\[
{}y {y^{\prime }}^{2} x +\left (x y-1\right ) y^{\prime } = y
\] |
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\[
{}x^{3} \left (x^{2}+3\right ) y^{\prime \prime }+5 x y^{\prime }-\left (1+x \right ) y = 0
\] |
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\[
{}y^{\prime \prime }+\frac {y}{z^{3}} = 0
\] |
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\[
{}y^{\prime }+p \left (x \right ) y+q \left (x \right ) y^{2} = r \left (x \right )
\] |
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\[
{}y \,{\mathrm e}^{x y}+\left (2 y-x \,{\mathrm e}^{x y}\right ) y^{\prime } = 0
\] |
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\[
{}\left [x_{1}^{\prime }\left (t \right ) = t \cot \left (t^{2}\right ) x_{1} \left (t \right )+\frac {t \cos \left (t^{2}\right ) x_{3} \left (t \right )}{2}, x_{2}^{\prime }\left (t \right ) = \frac {x_{2} \left (t \right )}{t}-x_{3} \left (t \right )+2-t \sin \left (t \right ), x_{3}^{\prime }\left (t \right ) = \csc \left (t^{2}\right ) x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right )+1-\cos \left (t \right ) t\right ]
\] |
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\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{x \left (x -3\right )}-\frac {y}{x^{3} \left (x +3\right )} = 0
\] |
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\[
{}y^{2} \left (x^{2}+1\right )+y+\left (2 x y+1\right ) y^{\prime } = 0
\] |
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\[
{}\sin \left (x \right ) \tan \left (y\right )+1+\cos \left (x \right ) \sec \left (y\right )^{2} y^{\prime } = 0
\] |
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\[
{}2 y^{2}-4 x +5 = \left (4-2 y+4 x y\right ) y^{\prime }
\] |
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\[
{}x^{2}+y^{3}+y+\left (x^{3}+y^{2}-x \right ) y^{\prime } = 0
\] |
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\[
{}y^{\prime } = f \left (x \right )+a y+b y^{2}
\] |
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\[
{}y^{\prime } = f \left (x \right )+g \left (x \right ) y+y^{2} a
\] |
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\[
{}y^{\prime } = f \left (x \right )+g \left (x \right ) y+h \left (x \right ) y^{2}
\] |
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\[
{}y^{\prime } = \operatorname {f0} \left (x \right )+\operatorname {f1} \left (x \right ) y+\operatorname {f2} \left (x \right ) y^{2}+\operatorname {f3} \left (x \right ) y^{3}
\] |
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\[
{}y^{\prime } = f \left (x \right )+g \left (x \right ) y+h \left (x \right ) y^{n}
\] |
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\[
{}y^{\prime }+\left (f \left (x \right )-y\right ) g \left (x \right ) \sqrt {\left (y-a \right ) \left (y-b \right )} = 0
\] |
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\[
{}y^{\prime }+f \left (x \right )+g \left (x \right ) \sin \left (a y\right )+h \left (x \right ) \cos \left (a y\right ) = 0
\] |
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\[
{}y^{\prime } = \left (1+\cos \left (x \right ) \sin \left (y\right )\right ) \tan \left (y\right )
\] |
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\[
{}y^{\prime }+f \left (x \right )+g \left (x \right ) \tan \left (y\right ) = 0
\] |
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\[
{}2 y^{\prime } = 2 \sin \left (y\right )^{2} \tan \left (y\right )-x \sin \left (2 y\right )
\] |
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\[
{}x y^{\prime } = \sin \left (x -y\right )
\] |
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\[
{}x^{k} y^{\prime } = a \,x^{m}+b y^{n}
\] |
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\[
{}y y^{\prime }+x^{3}+y = 0
\] |
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\[
{}y y^{\prime }+f \left (x \right ) = g \left (x \right ) y
\] |
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\[
{}\left (\tan \left (x \right ) \sec \left (x \right )-2 y\right ) y^{\prime }+\sec \left (x \right ) \left (1+2 y \sin \left (x \right )\right ) = 0
\] |
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\[
{}x \left (a +y\right ) y^{\prime }+b x +c y = 0
\] |
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\[
{}\left (a +x \left (x +y\right )\right ) y^{\prime } = b \left (x +y\right ) y
\] |
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