Determine the order of the differential equation: $x^{2} y^{\prime \prime}-5 x y^{\prime}+13 y=0$

Step 1 ：The order of a differential equation is determined by the highest power of the derivative present in the equation.

Step 2 ：In the given differential equation, \(x^{2} y^{\prime \prime}-5 x y^{\prime}+13 y=0\), the highest derivative is \(y^{\prime \prime}\), which is the second derivative of \(y\) with respect to \(x\).

Step 3 ：Therefore, the order of the given differential equation is 2.

Step 4 ：\(\boxed{\text{The order of the differential equation } x^{2} y^{\prime \prime}-5 x y^{\prime}+13 y=0 \text{ is 2}}\)