QPaperGen

The given differential equation is:

$\displaystyle \frac{d}{dx}\left(\frac{dy}{dx}\right)^3 = 0$

Step 1: Expand the derivative

$\displaystyle \frac{d}{dx}\left(\frac{dy}{dx}\right)^3 = 3\left(\frac{dy}{dx}\right)^2 \frac{d^2y}{dx^2} = 0$

Step 2: Identify order and degree

• The highest order derivative is $\dfrac{d^2y}{dx^2}$, so the order is $p = 2$.


• The equation is a polynomial in derivatives, and the degree of the highest derivative is $1$, so $q = 1$.

Step 3: Compute $(p - q)$

$(p - q) = 2 - 1 = 1$

∴ Final Answer: $(p - q) = 1$