Problem

Find the particular solution of the differential equation

$$5\frac{\mathrm{d}^2y}{\mathrm{d}x^2} + 2\frac{\mathrm{d}y}{\mathrm{d}x} + y = x^2 + 5x + 3,$$

given that, when $x = 0$, $y = \frac{\mathrm{d}y}{\mathrm{d}x} = 0$.