Question

Solution of dy/dx = y/x + tan(y/x) is

(A) sin(y/x) = kx

(B) cos(y/x) = kx

(C) tan(y/x) = kx

(D) none of these 

Answer 1

Answer is (A) sin(y/x) = kx

dy/dx = y/x + tan(y/x)

Put y = vx. Then

v + x(dv/dx) = v + tanv

⇒ cotvdv = dx/x

On integrating, we get

ln sin v = ln x + ln k ⇒ sin(y/x) = kx