\[ {}y^{\prime \prime }-y = 0 \]

\[ {}y^{\prime \prime }-9 y = 0 \]

\[ {}y^{\prime \prime }+4 y = 0 \]

\[ {}y^{\prime \prime }+25 y = 0 \]

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

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

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

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

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

\[ {}y^{\prime \prime }-10 y^{\prime }+25 y = 0 \]

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

\[ {}y^{\prime \prime }+6 y^{\prime }+13 y = 0 \]

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

\[ {}y^{\prime \prime }+2 y^{\prime }-15 y = 0 \]

\[ {}y^{\prime \prime }+5 y^{\prime } = 0 \]

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

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

\[ {}4 y^{\prime \prime }+8 y^{\prime }+3 y = 0 \]

\[ {}4 y^{\prime \prime }+4 y^{\prime }+y = 0 \]

\[ {}9 y^{\prime \prime }-12 y^{\prime }+4 y = 0 \]

\[ {}6 y^{\prime \prime }-7 y^{\prime }-20 y = 0 \]

\[ {}35 y^{\prime \prime }-y^{\prime }-12 y = 0 \]

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

\[ {}y^{\prime \prime }-4 y = 12 \]

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

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

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

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

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

\[ {}y^{\prime \prime }-4 y = 0 \]

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

\[ {}y^{\prime \prime }+3 y^{\prime }-10 y = 0 \]

\[ {}2 y^{\prime \prime }-7 y^{\prime }+3 y = 0 \]

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 0 \]

\[ {}y^{\prime \prime }+5 y^{\prime }+5 y = 0 \]

\[ {}4 y^{\prime \prime }-12 y^{\prime }+9 y = 0 \]

\[ {}y^{\prime \prime }-6 y^{\prime }+13 y = 0 \]

\[ {}y^{\prime \prime }+8 y^{\prime }+25 y = 0 \]

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

\[ {}9 y^{\prime \prime }+6 y^{\prime }+4 y = 0 \]

\[ {}y^{\prime \prime }-6 y^{\prime }+25 y = 0 \]

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

\[ {}y^{\prime \prime }-i y^{\prime }+6 y = 0 \]

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

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

\[ {}3 x^{\prime \prime }+30 x^{\prime }+63 x = 0 \]

\[ {}x^{\prime \prime }+8 x^{\prime }+16 x = 0 \]

\[ {}2 x^{\prime \prime }+12 x^{\prime }+50 x = 0 \]

\[ {}4 x^{\prime \prime }+20 x^{\prime }+169 x = 0 \]

\[ {}2 x^{\prime \prime }+16 x^{\prime }+40 x = 0 \]

\[ {}x^{\prime \prime }+10 x^{\prime }+125 x = 0 \]

\[ {}y^{\prime \prime }+16 y = {\mathrm e}^{3 x} \]

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

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

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

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

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

\[ {}y^{\prime \prime }-4 y = \sinh \left (x \right ) \]

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

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

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

\[ {}y^{\prime \prime }+9 y = 2 x^{2} {\mathrm e}^{3 x}+5 \]

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }+9 y = \sin \left (x \right )^{4} \]

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

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

\[ {}y^{\prime \prime }-2 y^{\prime }-8 y = 3 \,{\mathrm e}^{-2 x} \]

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

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

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

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

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

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

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

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

\[ {}x^{\prime \prime }+9 x = 10 \cos \left (2 t \right ) \]

\[ {}x^{\prime \prime }+4 x = 5 \sin \left (3 t \right ) \]

\[ {}x^{\prime \prime }+100 x = 225 \cos \left (5 t \right )+300 \sin \left (5 t \right ) \]

\[ {}x^{\prime \prime }+25 x = 90 \cos \left (4 t \right ) \]

\[ {}m x^{\prime \prime }+k x = F_{0} \cos \left (\omega t \right ) \]

\[ {}x^{\prime \prime }+4 x^{\prime }+4 x = 10 \cos \left (3 t \right ) \]

\[ {}x^{\prime \prime }+3 x^{\prime }+5 x = -4 \cos \left (5 t \right ) \]

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

\[ {}x^{\prime \prime }+3 x^{\prime }+3 x = 8 \cos \left (10 t \right )+6 \sin \left (10 t \right ) \]

\[ {}x^{\prime \prime }+4 x^{\prime }+5 x = 10 \cos \left (3 t \right ) \]

\[ {}x^{\prime \prime }+6 x^{\prime }+13 x = 10 \sin \left (5 t \right ) \]

\[ {}x^{\prime \prime }+6 x^{\prime }+13 x = 10 \sin \left (5 t \right ) \]

\[ {}x^{\prime \prime }+2 x^{\prime }+26 x = 600 \cos \left (10 t \right ) \]

\[ {}x^{\prime \prime }+8 x^{\prime }+25 x = 200 \cos \left (t \right )+520 \sin \left (t \right ) \]

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

\[ {}5 y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime } = 0 \]