The given equation is
p2 + 2py cot x = y2 ...(i)
(p + y cot x)2 = y2(1 + cot2x)
(p + y cot x)2 = y2cosec2 x
(p + y cot x) = ± y cosec x
p = y(cosec x – cot x) ...(ii)
and p = – y(cosec x – cot x) ...(iii)
From Eq. (ii), we get,
dy/dx = y(cosec x – cot x)
dy/y = (cosec x – cot x)dx
dy/y = ((1 – cos x)/sin x)dx
dy/y = tan(x/2) dx
Integrating, we get
