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

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Answer

$\boxed{\text{The order of the differential equation } x^{2} y^{\prime \prime}-5 x y^{\prime}+13 y=0 \text{ is 2}}$

Steps

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

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

Answer

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