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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }-6 y^{\prime }+13 y = 3 \,{\mathrm e}^{-2 t} \]

\[ {}y^{\prime \prime }+9 y^{\prime }+20 y = -2 t \,{\mathrm e}^{t} \]

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }-8 y^{\prime }+16 y = \frac {{\mathrm e}^{4 t}}{t^{3}} \]

\[ {}y^{\prime \prime }-8 y^{\prime }+16 y = \frac {{\mathrm e}^{4 t}}{t^{3}} \]

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

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

\[ {}x^{\prime \prime }+x = \left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \]

\[ {}x^{\prime \prime }+x = \left \{\begin {array}{cc} \cos \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \]

\[ {}x^{\prime \prime }+x = \left \{\begin {array}{cc} t & 0\le t <1 \\ 2-t & 1\le t <2 \\ 0 & 2\le t \end {array}\right . \]

\[ {}x^{\prime \prime }+4 x^{\prime }+13 x = \left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 1-t & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \]

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

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

\[ {}x^{\prime \prime }+x = \cos \left (\frac {9 t}{10}\right ) \]

\[ {}x^{\prime \prime }+x = \cos \left (\frac {7 t}{10}\right ) \]

\[ {}x^{\prime \prime }+\frac {x^{\prime }}{10}+x = 3 \cos \left (2 t \right ) \]

\[ {}x^{\prime \prime }+16 x = t \sin \left (t \right ) \]

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }-7 y^{\prime } = \left (-1+x \right )^{2} \]

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

\[ {}y^{\prime \prime }+7 y^{\prime } = {\mathrm e}^{-7 x} \]

\[ {}y^{\prime \prime }-8 y^{\prime }+16 y = \left (1-x \right ) {\mathrm e}^{4 x} \]

\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = {\mathrm e}^{5 x} \]

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

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

\[ {}y^{\prime \prime }+25 y = \cos \left (5 x \right ) \]

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

\[ {}y^{\prime \prime }+16 y = \sin \left (4 x +\alpha \right ) \]

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

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

\[ {}y^{\prime \prime }+6 y^{\prime }+13 y = {\mathrm e}^{-3 x} \cos \left (2 x \right ) \]

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

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