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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = x^{2} \]

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }+y = {\mathrm e}^{3 x} \left (1+\sin \left (2 x \right )\right ) \]

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime \prime }-4 y^{\prime \prime } = {\mathrm e}^{2 x} \left (x -3\right ) \]

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

\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = x^{2} {\mathrm e}^{2 x} \]

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

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

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

\[ {}y^{\prime \prime \prime }+4 y^{\prime \prime }+5 y^{\prime } = \cos \left (x \right ) {\mathrm e}^{-2 x} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}x^{\prime \prime }-k^{2} x = 0 \]

\[ {}x^{\prime \prime }+\omega _{0}^{2} x = a \cos \left (\omega t \right ) \]

\[ {}f^{\prime \prime }+2 f^{\prime }+5 f = 0 \]

\[ {}f^{\prime \prime }+2 f^{\prime }+5 f = {\mathrm e}^{-t} \cos \left (3 t \right ) \]

\[ {}f^{\prime \prime }+6 f^{\prime }+9 f = {\mathrm e}^{-t} \]

\[ {}f^{\prime \prime }+8 f^{\prime }+12 f = 12 \,{\mathrm e}^{-4 t} \]

\[ {}f^{\prime \prime }+8 f^{\prime }+12 f = 12 \,{\mathrm e}^{-4 t} \]

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

\[ {}y^{\prime \prime \prime }-12 y^{\prime }+16 y = 32 x -8 \]

\[ {}y^{\prime \prime }-y = x^{n} \]

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

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

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

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

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

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

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

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

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

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

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

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