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

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

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

\[ {}y^{\prime \prime }+9 y = 6 \,{\mathrm e}^{3 x} \]

\[ {}y^{\prime \prime }-3 y^{\prime } = 2-6 x \]

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

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

\[ {}y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y = 2 x +3 \]

\[ {}y^{\prime \prime \prime \prime }-a^{4} y = 5 a^{4} {\mathrm e}^{a x} \sin \left (a x \right ) \]

\[ {}y^{\prime \prime \prime \prime }+2 a^{2} y^{\prime \prime }+a^{4} y = 8 \cos \left (a x \right ) \]

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

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

\[ {}y^{\prime \prime }-7 y^{\prime }+6 y = \sin \left (x \right ) \]

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

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

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

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

\[ {}[4 x^{\prime }\left (t \right )-y^{\prime }\left (t \right )+3 x \left (t \right ) = \sin \left (t \right ), x^{\prime }\left (t \right )+y \left (t \right ) = \cos \left (t \right )] \]

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

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

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

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

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

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

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

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

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

\[ {}3 \,{\mathrm e}^{x} \tan \left (y\right )+\left (1-{\mathrm e}^{x}\right ) \sec \left (y\right )^{2} y^{\prime } = 0 \]

\[ {}[x^{\prime }\left (t \right ) = 2 x \left (t \right )-3 y \left (t \right ), y^{\prime }\left (t \right ) = 5 x \left (t \right )+6 y \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = -4 x \left (t \right )-10 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = 12 x \left (t \right )+18 y \left (t \right ), y^{\prime }\left (t \right ) = -8 x \left (t \right )-12 y \left (t \right )] \]

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

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

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

\[ {}[x^{\prime }\left (t \right ) = x \left (t \right )-5 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )] \]

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

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

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

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

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

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

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

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

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

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

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

\[ {}[x^{\prime }\left (t \right ) = 0, y^{\prime }\left (t \right ) = x \left (t \right )] \]

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

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

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

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

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

\[ {}[x^{\prime }\left (t \right ) = x \left (t \right )-5 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )] \]

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = 0 \]

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

\[ {}y^{\prime \prime \prime }-7 y^{\prime \prime }+12 y^{\prime } = 0 \]

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

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

\[ {}x^{2} y^{\prime \prime }+6 x y^{\prime }+4 y = 0 \]

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 0 \]

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

\[ {}{y^{\prime }}^{2}-9 x y = 0 \]

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

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

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

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

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

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

\[ {}y^{\prime } = 3 y^{\frac {2}{3}} \]

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

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

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

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

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

\[ {}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = 0 \]

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \]

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \]

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \]

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \]

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \]

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \]

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

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

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

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

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

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