If the order and degree of the differential equation \(\sqrt {\frac{d^2y}{dx^2}}\) =\((1+\frac{dy}{dx})^{\frac{1}{3}}\) are a and b respectively, then the value of a2 + b2 is

2 3 5 13

13

\(\sqrt {\frac{d^2y}{dx^2}}=(1+\frac{dy}{dx})^{\frac{1}{3}}=(\frac{d^2y}{dx^2})^3=(1+\frac{dy}{dx})^2\) = order = 2 = a degree = 3 = b $∴ a^2 + b^2 = 2^2 + 3^2 = 4 + 9 = 13$ Option D is correct.