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ODE |
Mathematica |
Maple |
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\[
{}x \left (1-2 x^{2} y^{3}\right ) y^{\prime }+\left (1-2 y^{2} x^{3}\right ) y = 0
\] |
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\[
{}x \left (1-x y\right ) \left (1-x^{2} y^{2}\right ) y^{\prime }+\left (x y+1\right ) \left (1+x^{2} y^{2}\right ) y = 0
\] |
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\[
{}\left (x^{2}-y^{4}\right ) y^{\prime } = x y
\] |
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\[
{}\left (x^{3}-y^{4}\right ) y^{\prime } = 3 x^{2} y
\] |
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\[
{}\left (a^{2} x^{2}+\left (x^{2}+y^{2}\right )^{2}\right ) y^{\prime } = a^{2} y x
\] |
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\[
{}2 \left (x -y^{4}\right ) y^{\prime } = y
\] |
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\[
{}\left (4 x -x y^{3}-2 y^{4}\right ) y^{\prime } = \left (2+y^{3}\right ) y
\] |
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\[
{}\left (a \,x^{3}+\left (a x +b y\right )^{3}\right ) y y^{\prime }+x \left (\left (a x +b y\right )^{3}+b y^{3}\right ) = 0
\] |
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\[
{}\left (x +2 y+2 x^{2} y^{3}+y^{4} x \right ) y^{\prime }+\left (1+y^{4}\right ) y = 0
\] |
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\[
{}2 x \left (x^{3}+y^{4}\right ) y^{\prime } = \left (x^{3}+2 y^{4}\right ) y
\] |
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\[
{}x \left (1-x^{2} y^{4}\right ) y^{\prime }+y = 0
\] |
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\[
{}\left (x^{2}-y^{5}\right ) y^{\prime } = 2 x y
\] |
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\[
{}x \left (x^{3}+y^{5}\right ) y^{\prime } = \left (x^{3}-y^{5}\right ) y
\] |
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\[
{}x^{3} \left (1+5 x^{3} y^{7}\right ) y^{\prime }+\left (3 x^{5} y^{5}-1\right ) y^{3} = 0
\] |
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\[
{}\left (1+a \left (x +y\right )\right )^{n} y^{\prime }+a \left (x +y\right )^{n} = 0
\] |
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\[
{}x \left (a +x y^{n}\right ) y^{\prime }+b y = 0
\] |
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\[
{}f \left (x \right ) y^{m} y^{\prime }+g \left (x \right ) y^{m +1}+h \left (x \right ) y^{n} = 0
\] |
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\[
{}y^{\prime } \sqrt {b^{2}+y^{2}} = \sqrt {a^{2}+x^{2}}
\] |
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\[
{}y^{\prime } \sqrt {b^{2}-y^{2}} = \sqrt {a^{2}-x^{2}}
\] |
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\[
{}y^{\prime } \sqrt {y} = \sqrt {x}
\] |
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\[
{}\left (1+\sqrt {x +y}\right ) y^{\prime }+1 = 0
\] |
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\[
{}y^{\prime } \sqrt {x y}+x -y = \sqrt {x y}
\] |
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\[
{}\left (x -2 \sqrt {x y}\right ) y^{\prime } = y
\] |
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\[
{}\left (y+\sqrt {1+y^{2}}\right ) \left (x^{2}+1\right )^{{3}/{2}} y^{\prime } = 1+y^{2}
\] |
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\[
{}\left (y+\sqrt {1+y^{2}}\right ) \left (x^{2}+1\right )^{{3}/{2}} y^{\prime } = 1+y^{2}
\] |
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\[
{}\left (x -\sqrt {x^{2}+y^{2}}\right ) y^{\prime } = y
\] |
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\[
{}x \left (1-\sqrt {x^{2}-y^{2}}\right ) y^{\prime } = y
\] |
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\[
{}x \left (\sqrt {x^{2}+y^{2}}+x \right ) y^{\prime }+y \sqrt {x^{2}+y^{2}} = 0
\] |
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\[
{}x y \left (x +\sqrt {x^{2}-y^{2}}\right ) y^{\prime } = x y^{2}-\left (x^{2}-y^{2}\right )^{{3}/{2}}
\] |
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\[
{}\left (x \sqrt {1+x^{2}+y^{2}}-y \left (x^{2}+y^{2}\right )\right ) y^{\prime } = x \left (x^{2}+y^{2}\right )+y \sqrt {1+x^{2}+y^{2}}
\] |
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\[
{}y^{\prime } \cos \left (y\right ) \left (\cos \left (y\right )-\sin \left (A \right ) \sin \left (x \right )\right )+\cos \left (x \right ) \left (\cos \left (x \right )-\sin \left (A \right ) \sin \left (y\right )\right ) = 0
\] |
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\[
{}\left (a \cos \left (b x +a y\right )-b \sin \left (a x +b y\right )\right ) y^{\prime }+b \cos \left (b x +a y\right )-a \sin \left (a x +b y\right ) = 0
\] |
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\[
{}\left (x +\cos \left (x \right ) \sec \left (y\right )\right ) y^{\prime }+\tan \left (y\right )-y \sin \left (x \right ) \sec \left (y\right ) = 0
\] |
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\[
{}\left (1+\left (x +y\right ) \tan \left (y\right )\right ) y^{\prime }+1 = 0
\] |
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\[
{}x \left (x -y \tan \left (\frac {y}{x}\right )\right ) y^{\prime }+\left (x +y \tan \left (\frac {y}{x}\right )\right ) y = 0
\] |
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\[
{}\left ({\mathrm e}^{x}+x \,{\mathrm e}^{y}\right ) y^{\prime }+y \,{\mathrm e}^{x}+{\mathrm e}^{y} = 0
\] |
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\[
{}\left (1-2 x -\ln \left (y\right )\right ) y^{\prime }+2 y = 0
\] |
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\[
{}\left (\sinh \left (x \right )+x \cosh \left (y\right )\right ) y^{\prime }+y \cosh \left (x \right )+\sinh \left (y\right ) = 0
\] |
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\[
{}y^{\prime } \left (1+\sinh \left (x \right )\right ) \sinh \left (y\right )+\cosh \left (x \right ) \left (\cosh \left (y\right )-1\right ) = 0
\] |
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\[
{}2 \left (1+y\right )^{{3}/{2}}+3 x y^{\prime }-3 y = 0
\] |
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\[
{}y^{\prime } = \frac {x y}{x^{2}-y^{2}}
\] |
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\[
{}y^{\prime } = \frac {x +y-3}{-y+x -1}
\] |
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\[
{}y^{\prime } = \frac {2 x +y-1}{4 x +2 y+5}
\] |
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\[
{}y^{\prime }-\frac {2 y}{1+x} = \left (1+x \right )^{2}
\] |
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\[
{}y^{\prime }+x y = x^{3} y^{3}
\] |
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\[
{}\frac {2 x}{y^{3}}+\frac {\left (y^{2}-3 x^{2}\right ) y^{\prime }}{y^{4}} = 0
\] |
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\[
{}y+x y^{2}-x y^{\prime } = 0
\] |
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\[
{}x \left (1-y\right ) y^{\prime }+\left (1+x \right ) y = 0
\] |
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\[
{}y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime } = 0
\] |
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\[
{}x y \left (x^{2}+1\right ) y^{\prime }-1-y^{2} = 0
\] |
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\[
{}1+y^{2}-\left (y+\sqrt {1+y^{2}}\right ) \left (x^{2}+1\right )^{{3}/{2}} y^{\prime } = 0
\] |
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\[
{}\sin \left (x \right ) \cos \left (y\right )-\cos \left (x \right ) \sin \left (y\right ) y^{\prime } = 0
\] |
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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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\[
{}\left (y-x \right ) y^{\prime }+y = 0
\] |
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\[
{}\left (2 \sqrt {x y}-x \right ) y^{\prime }+y = 0
\] |
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\[
{}x y^{\prime }-y-\sqrt {x^{2}+y^{2}} = 0
\] |
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\[
{}x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0
\] |
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\[
{}\left (7 x +5 y\right ) y^{\prime }+10 x +8 y = 0
\] |
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\[
{}2 x -y+1+\left (2 y-1\right ) y^{\prime } = 0
\] |
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\[
{}\left (3-3 x +7 y\right ) y^{\prime }+7-7 x +3 y = 0
\] |
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\[
{}y^{\prime }+\frac {x y}{x^{2}+1} = \frac {1}{2 x \left (x^{2}+1\right )}
\] |
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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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\[
{}y^{\prime }+\frac {y}{\left (-x^{2}+1\right )^{{3}/{2}}} = \frac {x +\sqrt {-x^{2}+1}}{\left (-x^{2}+1\right )^{2}}
\] |
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\[
{}y^{\prime }+y \cos \left (x \right ) = \frac {\sin \left (2 x \right )}{2}
\] |
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\[
{}\left (x^{2}+1\right ) y^{\prime }+y = \arctan \left (x \right )
\] |
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\[
{}\left (-x^{2}+1\right ) z^{\prime }-x z = a x z^{2}
\] |
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\[
{}3 z^{2} z^{\prime }-a z^{3} = 1+x
\] |
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\[
{}z^{\prime }+2 x z = 2 a \,x^{3} z^{3}
\] |
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\[
{}z^{\prime }+z \cos \left (x \right ) = z^{n} \sin \left (2 x \right )
\] |
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\[
{}x y^{\prime }+y = y^{2} \ln \left (x \right )
\] |
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\[
{}x^{3}+3 x y^{2}+\left (y^{3}+3 x^{2} y\right ) y^{\prime } = 0
\] |
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\[
{}1+\frac {y^{2}}{x^{2}}-\frac {2 y y^{\prime }}{x} = 0
\] |
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\[
{}\frac {3 x}{y^{3}}+\left (\frac {1}{y^{2}}-\frac {3 x^{2}}{y^{4}}\right ) y^{\prime } = 0
\] |
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\[
{}x +y y^{\prime }+\frac {x y^{\prime }}{x^{2}+y^{2}}-\frac {y}{x^{2}+y^{2}} = 0
\] |
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\[
{}1+{\mathrm e}^{\frac {x}{y}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime } = 0
\] |
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\[
{}{\mathrm e}^{x} \left (x^{2}+y^{2}+2 x \right )+2 y \,{\mathrm e}^{x} y^{\prime } = 0
\] |
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\[
{}n \cos \left (n x +m y\right )-m \sin \left (m x +n y\right )+\left (m \cos \left (n x +m y\right )-n \sin \left (m x +n y\right )\right ) y^{\prime } = 0
\] |
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\[
{}\frac {x}{\sqrt {1+x^{2}+y^{2}}}+\frac {y y^{\prime }}{\sqrt {1+x^{2}+y^{2}}}+\frac {y}{x^{2}+y^{2}}-\frac {x y^{\prime }}{x^{2}+y^{2}} = 0
\] |
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\[
{}\frac {x^{n} y^{\prime }}{b y^{2}-c \,x^{2 a}}-\frac {a y x^{a -1}}{b y^{2}-c \,x^{2 a}}+x^{a -1} = 0
\] |
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\[
{}2 x y+\left (y^{2}-2 x^{2}\right ) y^{\prime } = 0
\] |
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\[
{}\frac {1}{x}+\frac {y^{\prime }}{y}+\frac {2}{y}-\frac {2 y^{\prime }}{x} = 0
\] |
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\[
{}x y^{\prime }-y = \sqrt {x^{2}+y^{2}}
\] |
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\[
{}\left (7 x +5 y\right ) y^{\prime }+10 x +8 y = 0
\] |
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\[
{}x^{2}+2 x y-y^{2}+\left (y^{2}+2 x y-x^{2}\right ) y^{\prime } = 0
\] |
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\[
{}y^{2}+\left (x y+x^{2}\right ) y^{\prime } = 0
\] |
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\[
{}\left (x \cos \left (\frac {y}{x}\right )+y \sin \left (\frac {y}{x}\right )\right ) y+\left (x \cos \left (\frac {y}{x}\right )-y \sin \left (\frac {y}{x}\right )\right ) x y^{\prime } = 0
\] |
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\[
{}\left (x^{2} y^{2}+x y\right ) y+\left (x^{2} y^{2}-1\right ) x y^{\prime } = 0
\] |
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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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\[
{}x^{2}+y^{2}+2 x +2 y y^{\prime } = 0
\] |
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\[
{}x^{2}+y^{2}-2 x y y^{\prime } = 0
\] |
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\[
{}2 x y+\left (y^{2}-3 x^{2}\right ) y^{\prime } = 0
\] |
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\[
{}y+\left (-x +2 y\right ) y^{\prime } = 0
\] |
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\[
{}x y^{\prime }-a y+y^{2} = x^{-2 a}
\] |
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\[
{}x y^{\prime }-a y+y^{2} = x^{-\frac {2 a}{3}}
\] |
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\[
{}u^{\prime }+u^{2} = \frac {c}{x^{{4}/{3}}}
\] |
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\[
{}u^{\prime }+b u^{2} = \frac {c}{x^{4}}
\] |
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\[
{}u^{\prime }-u^{2} = \frac {2}{x^{{8}/{3}}}
\] |
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\[
{}\frac {\sqrt {f \,x^{4}+c \,x^{3}+c \,x^{2}+b x +a}\, y^{\prime }}{\sqrt {a +b y+c y^{2}+c y^{3}+f y^{4}}} = -1
\] |
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\[
{}2 x y+\left (x^{2}+y^{2}\right ) y^{\prime } = 0
\] |
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\[
{}\left (x +\sqrt {y^{2}-x y}\right ) y^{\prime }-y = 0
\] |
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