A mass$-$spring system is driven by the external force $g(t)=2sin3t+10cos3tN,$ where $t$ is time. The mass equals $1$ kg $,$ the spring constant equals $5\frac{N}{m},$ and the damping coefficient equals $2k\frac{g}{s}.$ If the mass is initially located at $y(0)=-1m,$ with initial velocity $y^{\text{'}}(0)=5\frac{m}{s},$ find its equation of motion:

Analytically $($hand calculations$)$

Using MATLAB Symbolic Toolbox