Solve the differential equation

$$\frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}-5 \frac{\mathrm{d} y}{\mathrm{~d} x}+6 y=\mathrm{e}^{3 x}$$

subject to the conditions $y=\mathrm{d} y / \mathrm{d} x=0$ when $x=0$.