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

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

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

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

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

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

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

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

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

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+9 y = 0 \]

\[ {}x^{2} y^{\prime \prime }+7 x y^{\prime }+25 y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 72 x^{5} \]

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

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

\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+3 y = 8 x^{\frac {4}{3}} \]

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+y = \ln \relax (x ) \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}[x^{\prime }\relax (t ) = -3 y \relax (t ), y^{\prime }\relax (t ) = 3 x \relax (t )] \]

\[ {}[x^{\prime }\relax (t ) = 3 x \relax (t )-2 y \relax (t ), y^{\prime }\relax (t ) = 2 x \relax (t )+y \relax (t )] \]

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

\[ {}[x^{\prime }\relax (t ) = y \relax (t )+z \relax (t ), y^{\prime }\relax (t ) = z \relax (t )+x \relax (t ), z^{\prime }\relax (t ) = x \relax (t )+y \relax (t )] \]

\[ {}[x_{1}^{\prime }\relax (t ) = x_{2} \relax (t ), x_{2}^{\prime }\relax (t ) = 2 x_{3} \relax (t ), x_{3}^{\prime }\relax (t ) = 3 x_{4} \relax (t ), x_{4}^{\prime }\relax (t ) = 4 x_{1} \relax (t )] \]

\[ {}[x_{1}^{\prime }\relax (t ) = x_{2} \relax (t )+x_{3} \relax (t )+1, x_{2}^{\prime }\relax (t ) = x_{3} \relax (t )+x_{4} \relax (t )+t, x_{3}^{\prime }\relax (t ) = x_{1} \relax (t )+x_{4} \relax (t )+t^{2}, x_{4}^{\prime }\relax (t ) = x_{1} \relax (t )+x_{2} \relax (t )+t^{3}] \]

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime \prime \prime }-16 y^{\prime \prime }+16 y = 0 \]

\[ {}y^{\prime \prime \prime \prime }+18 y^{\prime \prime }+81 y = 0 \]

\[ {}6 y^{\prime \prime \prime \prime }+11 y^{\prime \prime }+4 y = 0 \]

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

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

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

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

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

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

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

\[ {}2 y^{\prime \prime \prime }-y^{\prime \prime }-5 y^{\prime }-2 y = 0 \]