Concept:Order: The order of a differential equation is the order of the highest derivative (also known as differential coefficient) present in the equation.The degree: The degree of the differential equation is represented by the power of the highest order derivative in the given differential equation.If the given differential equation is not a polynomial equation in derivatives, then the degree of this equation is not defined.?Calculation:Given differential equation is\(XY{\left( {\frac{{{d^2}y}}{{d{x^2}}}} \right)^2} - X{\left( {\frac{{dy}}{{dx}}} \right)^3} + Y{\left( {\frac{{dy}}{{dx}}} \right)^2} = 0\)Here \(\frac{d^2y}{dx^2}\) term represents the order of the equation which is 2.Since the power of term \(\frac{d^2y}{dx^2}\) is 2, therefore the degree of the equation is 2.Hence, the differential equation has second order and second degree.