$3\mathrm{.}22$ Solve this ODE using a Symbolic software program:

$\frac{d^{4}y}{d{t}^4}+16\frac{d^{3}y}{d{t}^3}+86\frac{d^{2}y}{d{t}^2}+176\frac{dy}{dt}+105y=1$

All initial conditions for $y$ and its derivatives are zero.