Question

p²+2ypcotx-y²=0 solve ​

Answer 1

Answer:

Step-by-step explanation: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