\[ {}y^{\prime \prime }+3 y^{\prime }-4 y = -32 t^{2} \]

\[ {}8 y^{\prime \prime }+6 y^{\prime }+y = 5 t^{2} \]

\[ {}y^{\prime \prime }-6 y^{\prime }+8 y = -256 t^{3} \]

\[ {}y^{\prime \prime }-2 y^{\prime } = 52 \sin \left (3 t \right ) \]

\[ {}y^{\prime \prime }-6 y^{\prime }+13 y = 25 \sin \left (2 t \right ) \]

\[ {}y^{\prime \prime }-9 y = 54 t \sin \left (2 t \right ) \]

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = -78 \cos \left (3 t \right ) \]

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = -32 t^{2} \cos \left (2 t \right ) \]

\[ {}y^{\prime \prime }-y^{\prime }-20 y = -2 \,{\mathrm e}^{t} \]

\[ {}y^{\prime \prime }-4 y^{\prime }-5 y = -648 t^{2} {\mathrm e}^{5 t} \]

\[ {}y^{\prime \prime }-7 y^{\prime }+12 y = -2 t^{3} {\mathrm e}^{4 t} \]

\[ {}y^{\prime \prime }+4 y^{\prime } = 8 \,{\mathrm e}^{4 t}-4 \,{\mathrm e}^{-4 t} \]

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

\[ {}y^{\prime \prime }+4 y^{\prime } = -24 t -6-4 t \,{\mathrm e}^{-4 t}+{\mathrm e}^{-4 t} \]

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

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

\[ {}y^{\prime \prime }+3 y^{\prime } = 18 \]

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

\[ {}y^{\prime \prime }-4 y = 32 t \]

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

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

\[ {}y^{\prime \prime }+8 y^{\prime }+16 y = 4 \]

\[ {}y^{\prime \prime }+7 y^{\prime }+10 y = t \,{\mathrm e}^{-t} \]

\[ {}y^{\prime \prime }+6 y^{\prime }+25 y = -1 \]

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

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

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

\[ {}y^{\prime \prime }+4 y^{\prime } = -24 t -6-4 t \,{\mathrm e}^{-4 t}+{\mathrm e}^{-4 t} \]

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

\[ {}y^{\prime \prime }+9 y = \left \{\begin {array}{cc} 2 t & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \]

\[ {}y^{\prime \prime }+9 \pi ^{2} y = \left \{\begin {array}{cc} 2 t & 0\le t <\pi \\ 2 t -2 \pi & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \]

\[ {}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 10 & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \]

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

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

\[ {}4 y^{\prime \prime }+4 y^{\prime }+37 y = \cos \left (3 t \right ) \]

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

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

\[ {}y^{\prime \prime }-7 y^{\prime }+10 y = {\mathrm e}^{3 t} \]

\[ {}y^{\prime \prime }+16 y = 2 \cos \left (4 t \right ) \]

\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = 2 t \,{\mathrm e}^{-2 t} \]

\[ {}y^{\prime \prime }+\frac {y}{4} = \sec \left (\frac {t}{2}\right )+\csc \left (\frac {t}{2}\right ) \]

\[ {}y^{\prime \prime }+16 y = \csc \left (4 t \right ) \]

\[ {}y^{\prime \prime }+16 y = \cot \left (4 t \right ) \]

\[ {}y^{\prime \prime }+2 y^{\prime }+50 y = {\mathrm e}^{-t} \csc \left (7 t \right ) \]

\[ {}y^{\prime \prime }+6 y^{\prime }+25 y = {\mathrm e}^{-3 t} \left (\sec \left (4 t \right )+\csc \left (4 t \right )\right ) \]

\[ {}y^{\prime \prime }-2 y^{\prime }+26 y = {\mathrm e}^{t} \left (\sec \left (5 t \right )+\csc \left (5 t \right )\right ) \]

\[ {}y^{\prime \prime }+12 y^{\prime }+37 y = {\mathrm e}^{-6 t} \csc \left (t \right ) \]

\[ {}y^{\prime \prime }-6 y^{\prime }+34 y = {\mathrm e}^{3 t} \tan \left (5 t \right ) \]

\[ {}y^{\prime \prime }-10 y^{\prime }+34 y = {\mathrm e}^{5 t} \cot \left (3 t \right ) \]

\[ {}y^{\prime \prime }-12 y^{\prime }+37 y = {\mathrm e}^{6 t} \sec \left (t \right ) \]

\[ {}y^{\prime \prime }-8 y^{\prime }+17 y = {\mathrm e}^{4 t} \sec \left (t \right ) \]

\[ {}y^{\prime \prime }-9 y = \frac {1}{1+{\mathrm e}^{3 t}} \]

\[ {}y^{\prime \prime }-25 y = \frac {1}{1-{\mathrm e}^{5 t}} \]

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

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

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

\[ {}y^{\prime \prime }+8 y^{\prime }+16 y = \frac {{\mathrm e}^{-4 t}}{t^{4}} \]

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = \frac {{\mathrm e}^{-3 t}}{t} \]

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = {\mathrm e}^{-3 t} \ln \left (t \right ) \]

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

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = {\mathrm e}^{-2 t} \sqrt {-t^{2}+1} \]

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

\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = {\mathrm e}^{5 t} \ln \left (2 t \right ) \]

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

\[ {}y^{\prime \prime }+8 y^{\prime }+16 y = \frac {{\mathrm e}^{-4 t}}{t^{2}+1} \]

\[ {}y^{\prime \prime }+y = \sec \left (\frac {t}{2}\right )+\csc \left (\frac {t}{2}\right ) \]

\[ {}y^{\prime \prime }+9 y = \tan \left (3 t \right )^{2} \]

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

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

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

\[ {}y^{\prime \prime }+16 y = \tan \left (2 t \right ) \]

\[ {}y^{\prime \prime }+4 y = \tan \left (t \right ) \]

\[ {}y^{\prime \prime }+9 y = \sec \left (3 t \right ) \tan \left (3 t \right ) \]

\[ {}y^{\prime \prime }+4 y = \sec \left (2 t \right ) \tan \left (2 t \right ) \]

\[ {}y^{\prime \prime }+9 y = \frac {\csc \left (3 t \right )}{2} \]

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

\[ {}y^{\prime \prime }-16 y = 16 t \,{\mathrm e}^{-4 t} \]

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

\[ {}y^{\prime \prime }+4 y = \sec \left (2 t \right )+\tan \left (2 t \right ) \]

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

\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = 65 \cos \left (2 t \right ) \]

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

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

\[ {}t^{2} y^{\prime \prime }-4 t y^{\prime }-6 y = 2 \ln \left (t \right ) \]

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

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

\[ {}y^{\prime \prime }+4 y = f \left (t \right ) \]

\[ {}t^{2} y^{\prime \prime }-4 t y^{\prime }+\left (t^{2}+6\right ) y = 0 \]

\[ {}t^{2} y^{\prime \prime }-4 t y^{\prime }+\left (t^{2}+6\right ) y = t^{3}+2 t \]

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

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

\[ {}4 t^{2} y^{\prime \prime }+4 t y^{\prime }+\left (16 t^{2}-1\right ) y = 0 \]

\[ {}4 t^{2} y^{\prime \prime }+4 t y^{\prime }+\left (16 t^{2}-1\right ) y = 16 t^{\frac {3}{2}} \]

\[ {}4 t^{2} y^{\prime \prime }+4 t y^{\prime }+\left (16 t^{2}-1\right ) y = 16 t^{\frac {3}{2}} \]

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

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

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

\[ {}4 x^{2} y^{\prime \prime }-8 x y^{\prime }+5 y = 0 \]

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

\[ {}2 x^{2} y^{\prime \prime }-8 x y^{\prime }+8 y = 0 \]