Consider the homogenous ordinary differential equation
$$x^{2}\frac{d^{2}y}{dx^{2}}-3x\frac{dy}{dx}+3y=0, \quad x>0$$
with $y(x)$ as a general solution. Given that
$$y(1)=1 \quad \text{and} \quad y(2)=14$$
the value of $y(1.5),$ rounded off to two decimal places, is________.