\[ {}[y_{1}^{\prime }\left (x \right ) = y_{1} \left (x \right ), y_{2}^{\prime }\left (x \right ) = y_{1} \left (x \right )+y_{2} \left (x \right )] \]

\[ {}[y_{1}^{\prime }\left (x \right ) = y_{2} \left (x \right ), y_{2}^{\prime }\left (x \right ) = 6 y_{1} \left (x \right )+y_{2} \left (x \right )] \]

\[ {}[y_{1}^{\prime }\left (x \right ) = y_{1} \left (x \right )+y_{2} \left (x \right ), y_{2}^{\prime }\left (x \right ) = y_{1} \left (x \right )+y_{2} \left (x \right )+{\mathrm e}^{3 x}] \]

\[ {}[y_{1}^{\prime }\left (x \right ) = 3 y_{1} \left (x \right )+x y_{3} \left (x \right ), y_{2}^{\prime }\left (x \right ) = y_{2} \left (x \right )+x^{3} y_{3} \left (x \right ), y_{3}^{\prime }\left (x \right ) = 2 x y_{2} \left (x \right )-y_{2} \left (x \right )+{\mathrm e}^{x} y_{3} \left (x \right )] \]

\[ {}y^{\prime } = 2 x \]

\[ {}x y^{\prime } = 2 y \]

\[ {}y^{\prime } y = {\mathrm e}^{2 x} \]

\[ {}y^{\prime } = k y \]

\[ {}y^{\prime \prime }+4 y = 0 \]

\[ {}y^{\prime \prime }-4 y = 0 \]

\[ {}x y^{\prime }+y = y^{\prime } \sqrt {1-x^{2} y} \]

\[ {}x y^{\prime } = y+x^{2}+y^{2} \]

\[ {}y^{\prime } = \frac {x y}{y^{2}+x^{2}} \]

\[ {}2 x y y^{\prime } = y^{2}+x^{2} \]

\[ {}x y^{\prime }+y = x^{4} {y^{\prime }}^{2} \]

\[ {}y^{\prime } = \frac {y^{2}}{x y-x^{2}} \]

\[ {}\left (y \cos \left (y\right )-\sin \left (y\right )+x \right ) y^{\prime } = y \]

\[ {}1+y^{2}+y^{2} y^{\prime } = 0 \]

\[ {}y^{\prime } = {\mathrm e}^{3 x}-x \]

\[ {}y^{\prime } = x \,{\mathrm e}^{x^{2}} \]

\[ {}\left (1+x \right ) y^{\prime } = x \]

\[ {}\left (x^{2}+1\right ) y^{\prime } = x \]

\[ {}\left (x^{2}+1\right ) y^{\prime } = \arctan \left (x \right ) \]

\[ {}x y^{\prime } = 1 \]

\[ {}y^{\prime } = \arcsin \left (x \right ) \]

\[ {}\sin \left (x \right ) y^{\prime } = 1 \]

\[ {}\left (x^{3}+1\right ) y^{\prime } = x \]

\[ {}\left (x^{2}-3 x +2\right ) y^{\prime } = x \]

\[ {}y^{\prime } = x \,{\mathrm e}^{x} \]

\[ {}y^{\prime } = 2 \sin \left (x \right ) \cos \left (x \right ) \]

\[ {}y^{\prime } = \ln \left (x \right ) \]

\[ {}\left (x^{2}-1\right ) y^{\prime } = 1 \]

\[ {}x \left (x^{2}-4\right ) y^{\prime } = 1 \]

\[ {}\left (1+x \right ) \left (x^{2}+1\right ) y^{\prime } = 2 x^{2}+x \]

\[ {}y^{\prime } = 2 x y+1 \]

\[ {}y^{\prime \prime }-5 y^{\prime }+4 y = 0 \]

\[ {}y^{\prime } = \frac {2 x y^{2}}{1-x^{2} y} \]

\[ {}2 y^{\prime \prime \prime }+y^{\prime \prime }-5 y^{\prime }+2 y = 0 \]

\[ {}x^{5} y^{\prime }+y^{5} = 0 \]

\[ {}y^{\prime } = 4 x y \]

\[ {}y^{\prime }+\tan \left (x \right ) y = 0 \]

\[ {}\left (x^{2}+1\right ) y^{\prime }+1+y^{2} = 0 \]

\[ {}y \ln \left (y\right )-x y^{\prime } = 0 \]

\[ {}x y^{\prime } = \left (-4 x^{2}+1\right ) \tan \left (y\right ) \]

\[ {}y^{\prime } \sin \left (y\right ) = x^{2} \]

\[ {}y^{\prime }-\tan \left (x \right ) y = 0 \]

\[ {}x y y^{\prime } = y-1 \]

\[ {}y^{2} x -x^{2} y^{\prime } = 0 \]

\[ {}y^{\prime } y = 1+x \]

\[ {}x^{2} y^{\prime } = y \]

\[ {}\frac {y^{\prime }}{x^{2}+1} = \frac {x}{y} \]

\[ {}y^{2} y^{\prime } = 2+x \]

\[ {}y^{\prime } = x^{2} y^{2} \]

\[ {}y^{\prime } \left (y+1\right ) = -x^{2}+1 \]

\[ {}\frac {y^{\prime \prime }}{y^{\prime }} = x^{2} \]

\[ {}y^{\prime \prime } y^{\prime } = \left (1+x \right ) x \]

\[ {}y^{\prime }-x y = 0 \]

\[ {}y^{\prime }+x y = x \]

\[ {}y^{\prime }+y = \frac {1}{{\mathrm e}^{2 x}+1} \]

\[ {}y^{\prime }+y = 2 x \,{\mathrm e}^{-x}+x^{2} \]

\[ {}2 y-x^{3} = x y^{\prime } \]

\[ {}y^{\prime }+2 x y = 0 \]

\[ {}x y^{\prime }-3 y = x^{4} \]

\[ {}\left (x^{2}+1\right ) y^{\prime }+2 x y = \cot \left (x \right ) \]

\[ {}y^{\prime }+y \cot \left (x \right ) = 2 x \csc \left (x \right ) \]

\[ {}y-x +x y \cot \left (x \right )+x y^{\prime } = 0 \]

\[ {}y^{\prime }-x y = 0 \]

\[ {}y^{\prime }-2 x y = 6 x \,{\mathrm e}^{x^{2}} \]

\[ {}x \ln \left (x \right ) y^{\prime }+y = 3 x^{3} \]

\[ {}y^{\prime }-\frac {y}{x} = x^{2} \]

\[ {}y^{\prime }+4 y = {\mathrm e}^{-x} \]

\[ {}x^{2} y^{\prime }+x y = 2 x \]

\[ {}x y^{\prime }+y = x^{4} y^{3} \]

\[ {}x y^{2} y^{\prime }+y^{3} = x \cos \left (x \right ) \]

\[ {}x y^{\prime }+y = y^{2} x \]

\[ {}y^{\prime }+x y = x y^{4} \]

\[ {}\left ({\mathrm e}^{y}-2 x y\right ) y^{\prime } = y^{2} \]

\[ {}y-x y^{\prime } = y^{\prime } y^{2} {\mathrm e}^{y} \]

\[ {}x y^{\prime }+2 = x^{3} \left (y-1\right ) y^{\prime } \]

\[ {}x y^{\prime } = 2 x^{2} y+y \ln \left (x \right ) \]

\[ {}y^{\prime } \sin \left (2 x \right ) = 2 y+2 \cos \left (x \right ) \]

\[ {}\left (x +\frac {2}{y}\right ) y^{\prime }+y = 0 \]

\[ {}\sin \left (x \right ) \tan \left (y\right )+1+\cos \left (x \right ) \sec \left (x \right )^{2} y y^{\prime } = 0 \]

\[ {}y-x^{3}+\left (x +y^{3}\right ) y^{\prime } = 0 \]

\[ {}2 y^{2}-4 x +5 = \left (4-2 y+4 x y\right ) y^{\prime } \]

\[ {}y+y \cos \left (x y\right )+\left (x +x \cos \left (x y\right )\right ) y^{\prime } = 0 \]

\[ {}\cos \left (x \right ) \cos \left (y\right )^{2}+2 \sin \left (x \right ) \sin \left (y\right ) \cos \left (y\right ) y^{\prime } = 0 \]

\[ {}\left (\sin \left (x \right ) \sin \left (y\right )-x \,{\mathrm e}^{y}\right ) y^{\prime } = {\mathrm e}^{y}+\cos \left (x \right ) \cos \left (y\right ) \]

\[ {}-\frac {\sin \left (\frac {x}{y}\right )}{y}+\frac {x \sin \left (\frac {x}{y}\right ) y^{\prime }}{y^{2}} = 0 \]

\[ {}1+y+\left (1-x \right ) y^{\prime } = 0 \]

\[ {}2 x y^{3}+y \cos \left (x \right )+\left (3 x^{2} y^{2}+\sin \left (x \right )\right ) y^{\prime } = 0 \]

\[ {}\frac {y}{1-x^{2} y^{2}}+\frac {x y^{\prime }}{1-x^{2} y^{2}} = 1 \]

\[ {}2 x y^{4}+\sin \left (y\right )+\left (4 x^{2} y^{3}+x \cos \left (y\right )\right ) y^{\prime } = 0 \]

\[ {}\frac {x y^{\prime }+y}{1-x^{2} y^{2}}+x = 0 \]

\[ {}2 x \left (1+\sqrt {x^{2}-y}\right ) = \sqrt {x^{2}-y}\, y^{\prime } \]

\[ {}x \ln \left (y\right )+x y+\left (y \ln \left (x \right )+x y\right ) y^{\prime } = 0 \]

\[ {}{\mathrm e}^{y^{2}}-\csc \left (y\right ) \csc \left (x \right )^{2}+\left (2 x y \,{\mathrm e}^{y^{2}}-\csc \left (y\right ) \cot \left (y\right ) \cot \left (x \right )\right ) y^{\prime } = 0 \]

\[ {}1+y^{2} \sin \left (2 x \right )-2 y \cos \left (x \right )^{2} y^{\prime } = 0 \]

\[ {}\frac {x}{\left (y^{2}+x^{2}\right )^{\frac {3}{2}}}+\frac {y y^{\prime }}{\left (y^{2}+x^{2}\right )^{\frac {3}{2}}} = 0 \]

\[ {}3 x^{2} \left (1+\ln \left (y\right )\right )+\left (\frac {x^{3}}{y}-2 y\right ) y^{\prime } = 0 \]