\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 25 t -100 \delta \left (t -\pi \right ) \]

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

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

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

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 50 \,{\mathrm e}^{2 x} \]

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 50 \,{\mathrm e}^{2 x} \]

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }-7 y^{\prime }+6 y = \sin \left (x \right ) \]

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }+9 y = x^{2} {\mathrm e}^{3 x} \]

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

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

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

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

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

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

\[ {}y^{\prime \prime }+10 y^{\prime }+25 y = 14 \,{\mathrm e}^{-5 x} \]

\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 25 x^{2}+12 \]

\[ {}y^{\prime \prime }-y^{\prime }-6 y = 20 \,{\mathrm e}^{-2 x} \]

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 14 \sin \left (2 x \right )-18 \cos \left (2 x \right ) \]

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

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

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

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

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

\[ {}y^{\prime \prime }+4 y = 4 \cos \left (2 x \right )+6 \cos \left (x \right )+8 x^{2}-4 x \]

\[ {}y^{\prime \prime }+9 y = 2 \sin \left (3 x \right )+4 \sin \left (x \right )-26 \,{\mathrm e}^{-2 x}+27 x^{3} \]

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

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

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

\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 64 x \,{\mathrm e}^{-x} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = {\mathrm e}^{x} \]

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }+9 y = \sec \left (2 x \right ) \]

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

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

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

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

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

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

\[ {}y^{\prime \prime }+9 y = -3 \cos \left (2 x \right ) \]

\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 5 \,{\mathrm e}^{3 t} \]

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

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

\[ {}y^{\prime \prime }+3 y^{\prime }-5 y = 1 \]

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

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

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

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

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

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

\[ {}i^{\prime \prime }+2 i^{\prime }+3 i = \left \{\begin {array}{cc} 30 & 0<t <2 \pi \\ 0 & 2 \pi \le t \le 5 \pi \\ 10 & 5 \pi <t <\infty \end {array}\right . \]

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

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

\[ {}y^{\prime \prime }+9 y = {\mathrm e}^{t} \]

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

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = t \]