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

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

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

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

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

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

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

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

\[ {}4 x^{2} y^{\prime \prime }-8 x^{2} y^{\prime }+\left (4 x^{2}+1\right ) y = 0 \]

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

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

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

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

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

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

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

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

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

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

\[ {}\left (x^{2}-x -6\right ) y^{\prime \prime }+\left (3 x +5\right ) y^{\prime }+y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}9 \left (-2+x \right )^{2} \left (x -3\right ) y^{\prime \prime }+6 x \left (-2+x \right ) y^{\prime }+16 y = 0 \]

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

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

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

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

\[ {}L i^{\prime }+R i = E_{0} \theta \relax (t ) \]

\[ {}L i^{\prime }+R i = E_{0} \delta \relax (t ) \]

\[ {}L i^{\prime }+R i = E_{0} \sin \left (\omega t \right ) \]

\[ {}y^{\prime \prime }+3 y^{\prime }-5 y = 1 \]

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

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

\[ {}y^{\prime \prime }-y^{\prime }+y = 3 \,{\mathrm e}^{-t} \]

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

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

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

\[ {}y^{\prime \prime }-7 y^{\prime }+12 y = t \,{\mathrm e}^{2 t} \]

\[ {}i^{\prime \prime }+2 i^{\prime }+3 i = \left \{\begin {array}{cc} 30 & 0<t <2 \pi \\ 0 & 2 \pi \le t \le 5 \pi \\ 10 & 5 \pi <t <\infty \end {array}\right . \]

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

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

\[ {}[x^{\prime }\relax (t ) = x \relax (t )+2 y \relax (t ), y^{\prime }\relax (t ) = 3 x \relax (t )+2 y \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = x \relax (t )+2 y \relax (t )+t -1, y^{\prime }\relax (t ) = 3 x \relax (t )+2 y \relax (t )-5 t -2] \]

\[ {}[x^{\prime }\relax (t ) = x \relax (t )+y \relax (t ), y^{\prime }\relax (t ) = y \relax (t )] \]

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

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

\[ {}[x^{\prime }\relax (t ) = 4 x \relax (t )-2 y \relax (t ), y^{\prime }\relax (t ) = 5 x \relax (t )+2 y \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = 5 x \relax (t )+4 y \relax (t ), y^{\prime }\relax (t ) = -x \relax (t )+y \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = 4 x \relax (t )-3 y \relax (t ), y^{\prime }\relax (t ) = 8 x \relax (t )-6 y \relax (t )] \]

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

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

\[ {}[x^{\prime }\relax (t ) = 7 x \relax (t )+6 y \relax (t ), y^{\prime }\relax (t ) = 2 x \relax (t )+6 y \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = x \relax (t )-2 y \relax (t ), y^{\prime }\relax (t ) = 4 x \relax (t )+5 y \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = x \relax (t )+y \relax (t )-5 t +2, y^{\prime }\relax (t ) = 4 x \relax (t )-2 y \relax (t )-8 t -8] \]

\[ {}[x^{\prime }\relax (t ) = 3 x \relax (t )-4 y \relax (t ), y^{\prime }\relax (t ) = 4 x \relax (t )-7 y \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = x \relax (t )+y \relax (t ), y^{\prime }\relax (t ) = 4 x \relax (t )+y \relax (t )] \]

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

\[ {}[x^{\prime }\relax (t ) = 5 x \relax (t )+3 y \relax (t ), y^{\prime }\relax (t ) = -6 x \relax (t )-4 y \relax (t )] \]

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

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

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

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

\[ {}[x^{\prime }\relax (t ) = 3 x \relax (t )+2 y \relax (t )+z \relax (t ), y^{\prime }\relax (t ) = -2 x \relax (t )-y \relax (t )+3 z \relax (t ), z^{\prime }\relax (t ) = x \relax (t )+y \relax (t )+z \relax (t )] \]

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

\[ {}[x^{\prime }\relax (t ) = x \relax (t )+2 y \relax (t )-4 t +1, y^{\prime }\relax (t ) = -x \relax (t )+2 y \relax (t )+3 t +4] \]

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

\[ {}[x^{\prime }\relax (t ) = -4 x \relax (t )+y \relax (t )-t +3, y^{\prime }\relax (t ) = -x \relax (t )-5 y \relax (t )+t +1] \]

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

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

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

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

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

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

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

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

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

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

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

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