The degree of the differential equation obtained from the equation (y - a)^2 = 4(x - b) [where a and b are arbitrary constants] is

Step-by-step solution

Given equation: (y - a)^2 = 4(x - b) Since there are two arbitrary constants a and b , we differentiate the equation twice with respect to x . Differentiating with respect to x : 2(y - a) dy dx = 4 (y - a) dy dx = 2 Differentiating again with respect to x : ( dy dx )^2 + (y - a) d^2y dx^2 = 0 From the first derivative, we have y - a = 2 dy dx . Substituting this into the second derivative equation: ( dy dx )^2 + 2 dy dx d^2y dx^2 = 0 Multiplying the entire equation by dy dx to make it a polynomial in derivatives: (