The particular solution of the differential equation xdy + 2ydx = 0 , when x = 2 and y = 1 is

Step-by-step solution

The given differential equation is xdy + 2ydx = 0 Separating the variables, we get: dy y + 2dx x = 0 Integrating both sides: dy y + 2 dx x = 0 y + 2 x = C (y x^2) = C x^2 y = C Substituting x = 2 and y = 1 : (2)^2(1) = C C = 4 The particular solution is x^2 y = 4 Taking the square root on both sides: x y = 2 Since x = 2 and y = 1 satisfies the positive root, we get: x y = 2 Answer: x y = 2