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

\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 2 \ln \left (x \right )^{2}+12 x \]

\[ {}\left (1+x \right )^{3} y^{\prime \prime }+3 \left (1+x \right )^{2} y^{\prime }+\left (1+x \right ) y = 6 \ln \left (1+x \right ) \]

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

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

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

\[ {}\left (2 x^{2}+3 x \right ) y^{\prime \prime }-6 \left (1+x \right ) y^{\prime }+6 y = 6 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }+y = \frac {1}{\sqrt {\sin \left (x \right )^{5} \cos \left (x \right )}} \]

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

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

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

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

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

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

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

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

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

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

\[ {}4 x y^{\prime \prime }+2 y^{\prime }+y = 1 \]

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}x^{\prime \prime }-x \,{\mathrm e}^{x^{\prime }} = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}9 x \left (1-x \right ) y^{\prime \prime }-12 y^{\prime }+4 y = 0 \]

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (4 x^{2}-\frac {1}{9}\right ) y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}\left [x_{1}^{\prime }\left (t \right ) = -2 t x_{1} \left (t \right )^{2}, x_{2}^{\prime }\left (t \right ) = \frac {x_{2} \left (t \right )+t}{t}\right ] \]

\[ {}[x_{1}^{\prime }\left (t \right ) = {\mathrm e}^{t -x_{1} \left (t \right )}, x_{2}^{\prime }\left (t \right ) = 2 \,{\mathrm e}^{x_{1} \left (t \right )}] \]