Concept:Order of a differential equation: The order of a differential equation is the order of the highest order derivative appearing in the equation.Degree of a differential equation: The degree of a differential equation is the degree of the highest order derivative when differential coefficients are made free from radicals and fractions.Formula used:(a + b)3 = a3 + b3 + 3a2b + 3ab2(am)n = amnCalculation:We have, \(1+\left(\frac{dy}{dx}\right)^2 =\left(\frac{d^2y}{dx^2}\right)^{\frac{4}{3}}\)Since power 4/3 is a fraction, hence we need to remove it first.Doing cube of both sides\([1+\left(\frac{dy}{dx}\right)^2]^3 =[\left(\frac{d^2y}{dx^2}\right)^{\frac{4}{3}}]^3\)? \(1+[\left(\frac{dy}{dx}\right)^2]^3 + 3.1^2.\left(\frac{dy}{dx}\right)^2+3.1.[\left(\frac{dy}{dx}\right)^2]^2 =\left(\frac{d^2y}{dx^2}\right)^{\frac{4\times 3}{3}}\)? \(1+\left(\frac{dy}{dx}\right)^6 + 3\left(\frac{dy}{dx}\right)^2+3\left(\frac{dy}{dx}\right)^4=\left(\frac{d^2y}{dx^2}\right)^{4}\)Clearly, the highest order differential coefficient in this equation is \(\frac{d^2y}{dx^2}\) and its power is 4.? The degree is 4.