What is the degree of the differential equation ((d^2y)/(dx^2))^...

The given differential equation is $\left(\dfrac{d^2y}{dx^2}\right)^{\dfrac{3}{2}} = \left(\dfrac{dy}{dx}\right)^{\dfrac{5}{2}}$.

To find the degree of the differential equation, the powers of the derivatives must be made integers. Squaring both sides, we get:

$\left(\dfrac{d^2y}{dx^2}\right)^3 = \left(\dfrac{dy}{dx}\right)^5$

The highest order derivative is $\dfrac{d^2y}{dx^2}$, which has an order of $2$.

The power of the highest order derivative is $3$.

Therefore, the degree of the differential equation is $3$.