Find the general solution of this ODE:

$\frac{d^{2}y}{d{t}^2}+8\frac{dy}{dt}+15y=5t^2+5t+2$

The solution will be of the form:

$y(t)=C{y}_1(t)+D{y}_2(t)+y_p(t)$

so use $C$ and $D$ as the arbitrary constants.

$y(t)=$

$$