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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime } = 2 y^{\prime }-5 y+30 \,{\mathrm e}^{3 x} \]

\[ {}y^{\prime \prime \prime \prime }+6 y^{\prime \prime }+3 y^{\prime }-83 y-25 = 0 \]

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

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 0 \]

\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = 0 \]

\[ {}x^{2} y^{\prime \prime }-6 x y^{\prime }+12 y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = 9 \,{\mathrm e}^{2 x} \]

\[ {}y^{\prime \prime }-6 y^{\prime }+8 y = {\mathrm e}^{4 x} \]

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

\[ {}x^{2} y^{\prime \prime }-20 y = 27 x^{5} \]

\[ {}x y^{\prime \prime }+\left (2+2 x \right ) y^{\prime }+2 y = 8 \,{\mathrm e}^{2 x} \]

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

\[ {}y^{\prime \prime \prime }-9 y^{\prime \prime }+27 y^{\prime }-27 y = 0 \]

\[ {}y^{\prime \prime \prime }-9 y^{\prime \prime }+27 y^{\prime }-27 y = {\mathrm e}^{3 x} \sin \left (x \right ) \]

\[ {}y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+24 y^{\prime \prime }-32 y^{\prime }+16 y = 0 \]

\[ {}x^{3} y^{\prime \prime \prime }-4 y^{\prime \prime }+10 y^{\prime }-12 y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }-10 y^{\prime }+9 y = 0 \]

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

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

\[ {}y^{\prime \prime \prime \prime }-10 y^{\prime \prime }+9 y = 0 \]

\[ {}y^{\prime \prime }-7 y^{\prime }+10 y = 0 \]

\[ {}y^{\prime \prime }+2 y^{\prime }-24 y = 0 \]

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

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

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

\[ {}3 y^{\prime \prime }+7 y^{\prime }-6 y = 0 \]

\[ {}y^{\prime \prime }-8 y^{\prime }+15 y = 0 \]

\[ {}y^{\prime \prime }-8 y^{\prime }+15 y = 0 \]

\[ {}y^{\prime \prime }-8 y^{\prime }+15 y = 0 \]

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

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

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

\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = 0 \]

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

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

\[ {}25 y^{\prime \prime }-10 y^{\prime }+y = 0 \]

\[ {}16 y^{\prime \prime }-24 y^{\prime }+9 y = 0 \]

\[ {}9 y^{\prime \prime }+12 y^{\prime }+4 y = 0 \]

\[ {}y^{\prime \prime }-8 y^{\prime }+16 y = 0 \]

\[ {}y^{\prime \prime }-8 y^{\prime }+16 y = 0 \]

\[ {}y^{\prime \prime }-8 y^{\prime }+16 y = 0 \]

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

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

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

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

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

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

\[ {}y^{\prime \prime }-4 y^{\prime }+29 y = 0 \]

\[ {}9 y^{\prime \prime }+18 y^{\prime }+10 y = 0 \]

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

\[ {}y^{\prime \prime }+16 y = 0 \]

\[ {}y^{\prime \prime }+16 y = 0 \]

\[ {}y^{\prime \prime }+16 y = 0 \]

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

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

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

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

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

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

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

\[ {}y^{\prime \prime \prime \prime }-34 y^{\prime \prime }+225 y = 0 \]

\[ {}y^{\prime \prime \prime \prime }-81 y = 0 \]