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ODE |
Mathematica |
Maple |
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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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\[
{}8 y+10 x +\left (5 y+7 x \right ) y^{\prime } = 0
\] |
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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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\[
{}{y^{\prime }}^{2}-5 y^{\prime }+6 = 0
\] |
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\[
{}{y^{\prime }}^{2}-\frac {a^{2}}{x^{2}} = 0
\] |
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\[
{}{y^{\prime }}^{2} = \frac {1-x}{x}
\] |
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\[
{}{y^{\prime }}^{2}+\frac {2 x y^{\prime }}{y}-1 = 0
\] |
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\[
{}y = a y^{\prime }+b {y^{\prime }}^{2}
\] |
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\[
{}x = a y^{\prime }+b {y^{\prime }}^{2}
\] |
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\[
{}y = \sqrt {1+{y^{\prime }}^{2}}+a y^{\prime }
\] |
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\[
{}x = \sqrt {1+{y^{\prime }}^{2}}+a y^{\prime }
\] |
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\[
{}y^{\prime }-\frac {\sqrt {1+{y^{\prime }}^{2}}}{x} = 0
\] |
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\[
{}x^{2} \left (1+{y^{\prime }}^{2}\right )^{3}-a^{2} = 0
\] |
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\[
{}1+{y^{\prime }}^{2} = \frac {\left (x +a \right )^{2}}{2 a x +x^{2}}
\] |
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\[
{}y = x y^{\prime }+y^{\prime }-{y^{\prime }}^{2}
\] |
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\[
{}y = x y^{\prime }+\sqrt {b^{2}-a^{2} {y^{\prime }}^{2}}
\] |
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\[
{}y = x y^{\prime }+x \sqrt {1+{y^{\prime }}^{2}}
\] |
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\[
{}y = x y^{\prime }+a x \sqrt {1+{y^{\prime }}^{2}}
\] |
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\[
{}x -y y^{\prime } = a {y^{\prime }}^{2}
\] |
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\[
{}y y^{\prime }+x = a \sqrt {1+{y^{\prime }}^{2}}
\] |
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\[
{}y y^{\prime } = x +y^{2}-y^{2} {y^{\prime }}^{2}
\] |
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\[
{}y-\frac {1}{\sqrt {1+{y^{\prime }}^{2}}} = x +\frac {y^{\prime }}{\sqrt {1+{y^{\prime }}^{2}}}
\] |
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\[
{}y-2 x y^{\prime } = x {y^{\prime }}^{2}
\] |
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\[
{}\frac {-x y^{\prime }+y}{y^{2}+y^{\prime }} = \frac {-x y^{\prime }+y}{1+x^{2} y^{\prime }}
\] |
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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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\[
{}x +y-\left (x -y\right ) y^{\prime } = 0
\] |
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\[
{}x y^{\prime }-y-\sin \left (\frac {y}{x}\right ) x = 0
\] |
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\[
{}2 x^{2} y+y^{3}+\left (x y^{2}-2 x^{3}\right ) y^{\prime } = 0
\] |
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\[
{}y^{2}+\left (x \sqrt {y^{2}-x^{2}}-x y\right ) y^{\prime } = 0
\] |
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\[
{}\frac {y \cos \left (\frac {y}{x}\right )}{x}-\left (\frac {x \sin \left (\frac {y}{x}\right )}{y}+\cos \left (\frac {y}{x}\right )\right ) y^{\prime } = 0
\] |
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\[
{}y+x \ln \left (\frac {y}{x}\right ) y^{\prime }-2 x y^{\prime } = 0
\] |
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\[
{}2 y \,{\mathrm e}^{\frac {x}{y}}+\left (y-2 x \,{\mathrm e}^{\frac {x}{y}}\right ) y^{\prime } = 0
\] |
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\[
{}x \,{\mathrm e}^{\frac {y}{x}}-y \sin \left (\frac {y}{x}\right )+x \sin \left (\frac {y}{x}\right ) y^{\prime } = 0
\] |
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\[
{}x^{2}+y^{2} = 2 x y y^{\prime }
\] |
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\[
{}x \,{\mathrm e}^{\frac {y}{x}}+y = x y^{\prime }
\] |
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\[
{}y^{\prime }-\frac {y}{x}+\csc \left (\frac {y}{x}\right ) = 0
\] |
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\[
{}x y-y^{2}-x^{2} y^{\prime } = 0
\] |
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\[
{}x +2 y-4-\left (2 x -4 y\right ) y^{\prime } = 0
\] |
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\[
{}3 x +2 y+1-\left (3 x +2 y-1\right ) y^{\prime } = 0
\] |
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\[
{}x +y+1+\left (2 x +2 y+2\right ) y^{\prime } = 0
\] |
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\[
{}x +y-1+\left (2 x +2 y-3\right ) y^{\prime } = 0
\] |
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\[
{}x +y-1-\left (-y+x -1\right ) y^{\prime } = 0
\] |
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\[
{}x +y+\left (2 x +2 y-1\right ) y^{\prime } = 0
\] |
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\[
{}7 y-3+\left (2 x +1\right ) y^{\prime } = 0
\] |
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\[
{}x +2 y+\left (3 x +6 y+3\right ) y^{\prime } = 0
\] |
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\[
{}x +2 y+\left (y-1\right ) y^{\prime } = 0
\] |
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\[
{}3 x -2 y+4-\left (2 x +7 y-1\right ) y^{\prime } = 0
\] |
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\[
{}x +y+\left (3 x +3 y-4\right ) y^{\prime } = 0
\] |
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\[
{}3 x +2 y+3-\left (x +2 y-1\right ) y^{\prime } = 0
\] |
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\[
{}y+7+\left (2 x +y+3\right ) y^{\prime } = 0
\] |
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\[
{}x +y+2-\left (x -y-4\right ) y^{\prime } = 0
\] |
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\[
{}3 x^{2} y+8 x y^{2}+\left (x^{3}+8 x^{2} y+12 y^{2}\right ) y^{\prime } = 0
\] |
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\[
{}\frac {2 x y+1}{y}+\frac {\left (y-x \right ) y^{\prime }}{y^{2}} = 0
\] |
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\[
{}2 x y+\left (x^{2}+y^{2}\right ) y^{\prime } = 0
\] |
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\[
{}{\mathrm e}^{x} \sin \left (y\right )+{\mathrm e}^{-y}-\left (x \,{\mathrm e}^{-y}-{\mathrm e}^{x} \cos \left (y\right )\right ) y^{\prime } = 0
\] |
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\[
{}\cos \left (y\right )-\left (x \sin \left (y\right )-y^{2}\right ) y^{\prime } = 0
\] |
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\[
{}x -2 x y+{\mathrm e}^{y}+\left (y-x^{2}+x \,{\mathrm e}^{y}\right ) y^{\prime } = 0
\] |
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\[
{}x^{2}-x +y^{2}-\left ({\mathrm e}^{y}-2 x y\right ) y^{\prime } = 0
\] |
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\[
{}2 x +y \cos \left (x \right )+\left (2 y+\sin \left (x \right )-\sin \left (y\right )\right ) y^{\prime } = 0
\] |
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\[
{}x \sqrt {x^{2}+y^{2}}-\frac {x^{2} y y^{\prime }}{y-\sqrt {x^{2}+y^{2}}} = 0
\] |
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\[
{}4 x^{3}-\sin \left (x \right )+y^{3}-\left (y^{2}+1-3 x y^{2}\right ) y^{\prime } = 0
\] |
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\[
{}{\mathrm e}^{x} \left (y^{3}+x y^{3}+1\right )+3 y^{2} \left (x \,{\mathrm e}^{x}-6\right ) y^{\prime } = 0
\] |
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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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\[
{}y^{2} {\mathrm e}^{x y^{2}}+4 x^{3}+\left (2 x y \,{\mathrm e}^{x y^{2}}-3 y^{2}\right ) y^{\prime } = 0
\] |
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\[
{}y^{2}+y-x y^{\prime } = 0
\] |
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\[
{}y \sec \left (x \right )+\sin \left (x \right ) y^{\prime } = 0
\] |
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\[
{}{\mathrm e}^{x}-\sin \left (y\right )+\cos \left (y\right ) y^{\prime } = 0
\] |
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\[
{}x y+\left (x^{2}+1\right ) y^{\prime } = 0
\] |
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