\[ {}i^{\prime }-6 i = 10 \sin \left (2 t \right ) \]

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

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

\[ {}\left (2 s-{\mathrm e}^{2 t}\right ) s^{\prime } = 2 s \,{\mathrm e}^{2 t}-2 \cos \left (2 t \right ) \]

\[ {}x y^{\prime }+y-x^{3} y^{6} = 0 \]

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

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

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

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

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

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

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

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

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

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

\[ {}x y^{\prime } = 2 y+x^{3} {\mathrm e}^{x} \]

\[ {}L i^{\prime }+R i = E \sin \left (2 t \right ) \]

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

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

\[ {}x y^{3}-y^{3}-{\mathrm e}^{x} x^{2}+3 x y^{2} y^{\prime } = 0 \]

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

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

\[ {}x^{2} {y^{\prime }}^{2}+x y y^{\prime }-6 y^{2} = 0 \]

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

\[ {}x {y^{\prime }}^{2}-2 y^{\prime } y+4 x = 0 \]

\[ {}3 x^{4} {y^{\prime }}^{2}-x y^{\prime }-y = 0 \]

\[ {}8 y {y^{\prime }}^{2}-2 x y^{\prime }+y = 0 \]

\[ {}y^{2} {y^{\prime }}^{2}+3 x y^{\prime }-y = 0 \]

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

\[ {}16 y^{3} {y^{\prime }}^{2}-4 x y^{\prime }+y = 0 \]

\[ {}x {y^{\prime }}^{5}-y {y^{\prime }}^{4}+\left (x^{2}+1\right ) {y^{\prime }}^{3}-2 x y {y^{\prime }}^{2}+\left (x +y^{2}\right ) y^{\prime }-y = 0 \]

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

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

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

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

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

\[ {}y {y^{\prime }}^{2}-x y^{\prime }+3 y = 0 \]

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

\[ {}y^{2} {y^{\prime }}^{2}+3 x y^{\prime }-y = 0 \]

\[ {}x {y^{\prime }}^{2}-2 y^{\prime } y+4 x = 0 \]

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

\[ {}\left (3 y-1\right )^{2} {y^{\prime }}^{2} = 4 y \]

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

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

\[ {}y \left (3-4 y\right )^{2} {y^{\prime }}^{2} = 4-4 y \]

\[ {}{y^{\prime }}^{3}-4 x^{4} y^{\prime }+8 y x^{3} = 0 \]

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

\[ {}y^{\prime \prime }+y^{\prime }-6 y = 0 \]

\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = 0 \]

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{5 x} \]

\[ {}y^{\prime \prime }+9 y = x \cos \left (x \right ) \]

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0 \]

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

\[ {}x y^{\prime \prime }-y^{\prime }+4 y x^{3} = 0 \]

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

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

\[ {}y y^{\prime \prime }+{y^{\prime }}^{3} = 0 \]

\[ {}y^{\prime \prime }+2 y^{\prime }-15 y = 0 \]

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

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 0 \]

\[ {}y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+12 y^{\prime \prime }-8 y^{\prime } = 0 \]

\[ {}y^{\prime \prime }-4 y^{\prime }+13 y = 0 \]

\[ {}y^{\prime \prime }+25 y = 0 \]

\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+9 y^{\prime }-9 y = 0 \]

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

\[ {}y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+13 y^{\prime \prime }-12 y^{\prime }+4 y = 0 \]

\[ {}y^{\left (6\right )}+9 y^{\prime \prime \prime \prime }+24 y^{\prime \prime }+16 y = 0 \]

\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = 1 \]

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

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

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

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

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{2 x} \]

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = \frac {1}{1+{\mathrm e}^{-x}} \]

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

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

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

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

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

\[ {}y^{\prime \prime }-9 y = x +{\mathrm e}^{2 x}-\sin \left (2 x \right ) \]

\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime } = x^{2}+4 x +8 \]

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

\[ {}y^{\prime \prime \prime }-y^{\prime \prime }-4 y^{\prime }+4 y = 2 x^{2}-4 x -1+2 x^{2} {\mathrm e}^{2 x}+5 x \,{\mathrm e}^{2 x}+{\mathrm e}^{2 x} \]

\[ {}y^{\prime \prime }+y^{\prime }+y = {\mathrm e}^{3 x}+6 \,{\mathrm e}^{x}-3 \,{\mathrm e}^{-2 x}+5 \]

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

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{x}+x \,{\mathrm e}^{2 x} \]

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

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

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

\[ {}y^{\prime \prime }+5 y = \cos \left (\sqrt {5}\, x \right ) \]

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

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