\[ {}x^{\prime \prime }+\frac {x^{\prime }}{t} = a \]

\[ {}t^{2} x^{\prime \prime }-3 t x^{\prime }+3 x = 4 t^{7} \]

\[ {}x^{2} y^{\prime \prime }-6 x y^{\prime }+10 y = 3 x^{4}+6 x^{3} \]

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

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

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

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

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

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

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

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = 2 x^{3} \]

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

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

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

\[ {}x^{2} y^{\prime \prime }-2 y = 4 x -8 \]

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y = -6 x^{3}+4 x^{2} \]

\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 10 x^{2} \]

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = 2 x^{3} \]

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime } \sin \left (x \right )+x y^{\prime }+7 y = 1 \]

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }+\left (2 x +5\right ) y^{\prime }+\left (4 x +8\right ) y = {\mathrm e}^{-2 x} \]

\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = t^{7} \]

\[ {}t^{2} y^{\prime \prime }-6 t y^{\prime }+\sin \left (2 t \right ) y = \ln \left (t \right ) \]

\[ {}y^{\prime \prime }+3 y^{\prime }+\frac {y}{t} = t \]

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

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

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

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

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

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

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

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

\[ {}\sqrt {1-x}\, y^{\prime \prime }-4 y = \sin \left (x \right ) \]

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

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

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

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

\[ {}x y^{\prime \prime }+4 y^{\prime } = 18 x^{2} \]

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

\[ {}x y^{\prime \prime }+4 y^{\prime } = 18 x^{2} \]

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

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

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

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

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

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

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 10 x +12 \]

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 1 \]

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

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 22 x +24 \]

\[ {}x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = x^{2} \]

\[ {}x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = x \]

\[ {}x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = 1 \]

\[ {}x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = 4 x^{2}+2 x +3 \]

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = \frac {5}{x^{3}} \]

\[ {}2 x^{2} y^{\prime \prime }-x y^{\prime }+y = \frac {50}{x^{3}} \]

\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = 85 \cos \left (2 \ln \left (x \right )\right ) \]

\[ {}x^{2} y^{\prime \prime }-2 y = 15 \cos \left (3 \ln \left (x \right )\right )-10 \sin \left (3 \ln \left (x \right )\right ) \]

\[ {}3 x^{2} y^{\prime \prime }-7 x y^{\prime }+3 y = 4 x^{3} \]

\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = \frac {10}{x} \]

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 6 x^{3} \]

\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = 64 x^{2} \ln \left (x \right ) \]

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

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

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 12 x^{3} \]

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

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

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

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

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

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

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }-4 y = \frac {10}{x} \]

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

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 3 \sqrt {x} \]

\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 18 \ln \left (x \right ) \]

\[ {}2 x^{2} y^{\prime \prime }-x y^{\prime }-2 y = 10 x^{2} \]

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

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

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

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

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

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