Question

If the solution curve y = y(x) of the differential equation y²dx + (x² – xy + y²)dy = 0, which passes through the point (1, 1) and intersects the line y = √3 x at the point (α, √3α), then value of log_e (√3 α) is equal to

(A) π/3

(B) π/2

(C) π/12

(D) π/6

Answer 1

Correct option is (C) π/12

y²dx – xy dy = – (x² + y²)dy 

y(y dx – x dy) = – (x² + y²) dy 

– y(x dx – y dx) = – (x² + y²)dy