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ODE |
Mathematica |
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\[ {}y^{\prime } = 3 \cos \left (y\right )^{2} \] |
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\[ {}x y^{\prime } = y \] |
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\[ {}\left (1-x \right ) y^{\prime } = y \] |
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\[ {}y^{\prime } = \frac {4 x y}{x^{2}+1} \] |
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\[ {}y^{\prime } = \frac {2 y}{x^{2}-1} \] |
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\[ {}x^{2} y^{\prime }-y^{2} = 0 \] |
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\[ {}y^{\prime }+2 x y = 0 \] |
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\[ {}\cot \left (x \right ) y^{\prime } = y \] |
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\[ {}y^{\prime } = x \,{\mathrm e}^{-2 y} \] |
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\[ {}y^{\prime }-2 x y = 2 x \] |
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\[ {}x y^{\prime } = x y+y \] |
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\[ {}\left (x^{3}+1\right ) y^{\prime } = 3 x^{2} \tan \left (x \right ) \] |
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\[ {}x \cos \left (y\right ) y^{\prime } = 1+\sin \left (y\right ) \] |
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\[ {}x y^{\prime } = 2 y \left (y-1\right ) \] |
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\[ {}2 x y^{\prime } = 1-y^{2} \] |
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\[ {}\left (1-x \right ) y^{\prime } = x y \] |
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\[ {}\left (x^{2}-1\right ) y^{\prime } = \left (x^{2}+1\right ) y \] |
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\[ {}y^{\prime } = {\mathrm e}^{x} \left (1+y^{2}\right ) \] |
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\[ {}{\mathrm e}^{y} y^{\prime }+2 x = 2 x \,{\mathrm e}^{y} \] |
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\[ {}y \,{\mathrm e}^{2 x} y^{\prime }+2 x = 0 \] |
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\[ {}x y y^{\prime } = \sqrt {y^{2}-9} \] |
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\[ {}\left (x +y-1\right ) y^{\prime } = x -y+1 \] |
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\[ {}x y y^{\prime } = 2 x^{2}-y^{2} \] |
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\[ {}x^{2}-y^{2}+x y y^{\prime } = 0 \] |
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\[ {}x^{2} y^{\prime }-2 x y-2 y^{2} = 0 \] |
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\[ {}x^{2} y^{\prime } = 3 \left (x^{2}+y^{2}\right ) \arctan \left (\frac {y}{x}\right )+x y \] |
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\[ {}x \sin \left (\frac {y}{x}\right ) y^{\prime } = y \sin \left (\frac {y}{x}\right )+x \] |
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\[ {}x y^{\prime } = y+2 \,{\mathrm e}^{-\frac {y}{x}} \] |
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\[ {}y^{\prime } = \left (x +y\right )^{2} \] |
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\[ {}y^{\prime } = \sin \left (x -y+1\right )^{2} \] |
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\[ {}y^{\prime } = \frac {x +y+4}{x -y-6} \] |
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\[ {}y^{\prime } = \frac {x +y+4}{x +y-6} \] |
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\[ {}\left (x +\frac {2}{y}\right ) y^{\prime }+y = 0 \] |
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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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\[ {}y-x^{3}+\left (y^{3}+x \right ) y^{\prime } = 0 \] |
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\[ {}2 y^{2}-4 x +5 = \left (4-2 y+4 x y\right ) y^{\prime } \] |
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\[ {}y+y \cos \left (x y\right )+\left (x +x \cos \left (x y\right )\right ) y^{\prime } = 0 \] |
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\[ {}\cos \left (x \right ) \cos \left (y\right )^{2}+2 \sin \left (x \right ) \sin \left (y\right ) \cos \left (y\right ) y^{\prime } = 0 \] |
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\[ {}\left (\sin \left (x \right ) \sin \left (y\right )-x \,{\mathrm e}^{y}\right ) y^{\prime } = {\mathrm e}^{y}+\cos \left (x \right ) \cos \left (y\right ) \] |
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\[ {}-\frac {\sin \left (\frac {x}{y}\right )}{y}+\frac {x \sin \left (\frac {x}{y}\right ) y^{\prime }}{y^{2}} = 0 \] |
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\[ {}1+y+\left (1-x \right ) y^{\prime } = 0 \] |
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\[ {}2 x y^{3}+\cos \left (x \right ) y+\left (3 y^{2} x^{2}+\sin \left (x \right )\right ) y^{\prime } = 0 \] |
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\[ {}1 = \frac {y}{1-y^{2} x^{2}}+\frac {x y^{\prime }}{1-y^{2} x^{2}} \] |
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\[ {}\left (3 x^{2}-y^{2}\right ) y^{\prime }-2 x y = 0 \] |
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\[ {}x y-1+\left (x^{2}-x y\right ) y^{\prime } = 0 \] |
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\[ {}\left (x +3 x^{3} y^{4}\right ) y^{\prime }+y = 0 \] |
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\[ {}\left (x -1-y^{2}\right ) y^{\prime }-y = 0 \] |
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\[ {}y-\left (x +x y^{3}\right ) y^{\prime } = 0 \] |
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\[ {}x y^{\prime } = x^{5}+x^{3} y^{2}+y \] |
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\[ {}\left (x +y\right ) y^{\prime } = y-x \] |
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\[ {}x y^{\prime } = y+x^{2}+9 y^{2} \] |
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\[ {}x y^{\prime }-3 y = x^{4} \] |
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\[ {}y^{\prime }+y = \frac {1}{1+{\mathrm e}^{2 x}} \] |
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\[ {}2 x y+\left (x^{2}+1\right ) y^{\prime } = \cot \left (x \right ) \] |
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\[ {}y^{\prime }+y = 2 x \,{\mathrm e}^{-x}+x^{2} \] |
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\[ {}y^{\prime }+\cot \left (x \right ) y = 2 x \csc \left (x \right ) \] |
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\[ {}2 y-x^{3} = x y^{\prime } \] |
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\[ {}\left (1-x y\right ) y^{\prime } = y^{2} \] |
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\[ {}2 x +3 y+1+\left (2 y-3 x +5\right ) y^{\prime } = 0 \] |
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\[ {}x y^{\prime } = \sqrt {x^{2}+y^{2}} \] |
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\[ {}y^{2} = \left (x^{3}-x y\right ) y^{\prime } \] |
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\[ {}x^{2}+y+y^{3} = \left (x^{3} y^{2}-x \right ) y^{\prime } \] |
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\[ {}x y^{\prime }+y = x \cos \left (x \right ) \] |
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\[ {}\left (x y-x^{2}\right ) y^{\prime } = y^{2} \] |
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\[ {}\left ({\mathrm e}^{x}-3 y^{2} x^{2}\right ) y^{\prime }+{\mathrm e}^{x} y = 2 x y^{3} \] |
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\[ {}x^{2}+y = x y^{\prime } \] |
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\[ {}x y^{\prime }+y = \cos \left (x \right ) x^{2} \] |
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\[ {}6 x +4 y+3+\left (3 x +2 y+2\right ) y^{\prime } = 0 \] |
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\[ {}\cos \left (x +y\right )-x \sin \left (x +y\right ) = x \sin \left (x +y\right ) y^{\prime } \] |
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\[ {}y^{2} {\mathrm e}^{x y}+\cos \left (x \right )+\left ({\mathrm e}^{x y}+x y \,{\mathrm e}^{x y}\right ) y^{\prime } = 0 \] |
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\[ {}y^{\prime } \ln \left (x -y\right ) = 1+\ln \left (x -y\right ) \] |
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\[ {}y^{\prime }+2 x y = {\mathrm e}^{-x^{2}} \] |
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\[ {}y^{2}-3 x y-2 x^{2} = \left (x^{2}-x y\right ) y^{\prime } \] |
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\[ {}2 x y+\left (x^{2}+1\right ) y^{\prime } = 4 x^{3} \] |
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\[ {}{\mathrm e}^{x} \sin \left (y\right )-y \sin \left (x y\right )+\left ({\mathrm e}^{x} \cos \left (y\right )-x \sin \left (x y\right )\right ) y^{\prime } = 0 \] |
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\[ {}\left (y-x^{2}+x \,{\mathrm e}^{y}\right ) y^{\prime } = 2 x y-{\mathrm e}^{y}-x \] |
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\[ {}{\mathrm e}^{x} \left (1+x \right ) = \left (x \,{\mathrm e}^{x}-y \,{\mathrm e}^{y}\right ) y^{\prime } \] |
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\[ {}2 x y+x^{2} y^{\prime } = 0 \] |
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\[ {}x +y+\left (x -y\right ) y^{\prime } = 0 \] |
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\[ {}y^{\prime } \ln \left (x \right )+\frac {x +y}{x} = 0 \] |
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\[ {}\cos \left (y\right )-x \sin \left (y\right ) y^{\prime } = \sec \left (x \right )^{2} \] |
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\[ {}y \sin \left (\frac {x}{y}\right )+x \cos \left (\frac {x}{y}\right )-1+\left (x \sin \left (\frac {x}{y}\right )-\frac {x^{2} \cos \left (\frac {x}{y}\right )}{y}\right ) y^{\prime } = 0 \] |
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\[ {}\frac {x}{x^{2}+y^{2}}+\frac {y}{x^{2}}+\left (\frac {y}{x^{2}+y^{2}}-\frac {1}{x}\right ) y^{\prime } = 0 \] |
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\[ {}x^{2} \left (1+y^{2}\right ) y^{\prime }+y^{2} \left (x^{2}+1\right ) = 0 \] |
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\[ {}x \left (-1+x \right ) y^{\prime } = \cot \left (y\right ) \] |
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\[ {}r y^{\prime } = \frac {\left (a^{2}-r^{2}\right ) \tan \left (y\right )}{a^{2}+r^{2}} \] |
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\[ {}\sqrt {x^{2}+1}\, y^{\prime }+\sqrt {1+y^{2}} = 0 \] |
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\[ {}y^{\prime } = \frac {x \left (1+y^{2}\right )}{y \left (x^{2}+1\right )} \] |
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\[ {}y^{2} y^{\prime } = 2+3 y^{6} \] |
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\[ {}\cos \left (y\right )^{2}+\left (1+{\mathrm e}^{-x}\right ) \sin \left (y\right ) y^{\prime } = 0 \] |
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\[ {}y^{\prime } = \frac {x^{3} {\mathrm e}^{x^{2}}}{y \ln \left (y\right )} \] |
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\[ {}x \cos \left (y\right )^{2}+{\mathrm e}^{x} \tan \left (y\right ) y^{\prime } = 0 \] |
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\[ {}x \left (1+y^{2}\right )+\left (2 y+1\right ) {\mathrm e}^{-x} y^{\prime } = 0 \] |
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\[ {}x y^{3}+{\mathrm e}^{x^{2}} y^{\prime } = 0 \] |
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\[ {}x \cos \left (y\right )^{2}+\tan \left (y\right ) y^{\prime } = 0 \] |
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\[ {}x y^{3}+\left (y+1\right ) {\mathrm e}^{-x} y^{\prime } = 0 \] |
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\[ {}y^{\prime }+\frac {x}{y}+2 = 0 \] |
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\[ {}-y+x y^{\prime } = x \cot \left (\frac {y}{x}\right ) \] |
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\[ {}x \cos \left (\frac {y}{x}\right )^{2}-y+x y^{\prime } = 0 \] |
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\[ {}x y^{\prime } = y \left (1+\ln \left (y\right )-\ln \left (x \right )\right ) \] |
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