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

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

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

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

\[ {}x^{4} y^{\prime \prime }+x^{3} y^{\prime }-4 x^{2} y = 1 \]

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

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

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

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

\[ {}4 x^{2} y^{\prime \prime }+y = 8 \sqrt {x}\, \left (\ln \left (x \right )+1\right ) \]

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

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

\[ {}y^{\prime \prime }+20 y^{\prime }+500 y = 100000 \cos \left (100 x \right ) \]

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

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

\[ {}y^{\prime \prime }+2 y^{\prime }-24 y = 16-\left (2+x \right ) {\mathrm e}^{4 x} \]

\[ {}y^{\prime \prime }+3 y^{\prime }-4 y = 6 \,{\mathrm e}^{2 t -2} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }+y^{\prime }+y = x^{3}+x^{2}+x +1 \]

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

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

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

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

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

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

\[ {}y^{\prime \prime }+y^{\prime } = x^{3}+x^{2}+x +1 \]

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

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

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

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

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

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

\[ {}y^{\prime \prime }+y = x^{3}+x^{2}+x +1 \]

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

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

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

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

\[ {}x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+a^{2} y = \frac {1}{x^{2}} \]

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

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

\[ {}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 8 x^{3} \sin \left (x \right )^{2} \]

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }+5 y = {\mathrm e}^{x^{2}} \sec \left (x \right ) \]

\[ {}y^{\prime }+a \phi ^{\prime }\left (x \right ) y^{3}+6 a \phi \left (x \right ) y^{2}+\frac {\left (2 a +1\right ) y \phi ^{\prime \prime }\left (x \right )}{\phi ^{\prime }\left (x \right )}+2+2 a = 0 \]

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }+y^{\prime } \sqrt {x}+\left (\frac {1}{4 \sqrt {x}}+\frac {x}{4}-9\right ) y-x \,{\mathrm e}^{-\frac {x^{\frac {3}{2}}}{3}} = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }-4 y-x \sin \left (x \right )-\left (x^{2} a +12 a +4\right ) \cos \left (x \right ) = 0 \]

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

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

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

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y-5 x = 0 \]

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

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

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y-\sin \left (x \right ) x^{3} = 0 \]

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

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-n \left (n +1\right ) y+\frac {\partial }{\partial x}\operatorname {LegendreP}\left (n , x\right ) = 0 \]

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

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

\[ {}x \left (-1+x \right ) y^{\prime \prime }+\left (\left (\operatorname {a1} +\operatorname {b1} +1\right ) x -\operatorname {d1} \right ) y^{\prime }+\operatorname {a1} \operatorname {b1} \operatorname {d1} = 0 \]

\[ {}x \left (x +3\right ) y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y-\left (20 x +30\right ) \left (x^{2}+3 x \right )^{\frac {7}{3}} = 0 \]

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

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