solve the differential equation for p ; xy(y-px)= x+yp

Xy²- pyx²-x-yp = 0

xy²-p(yx²+yp) –x= 0

xy²-x= p(yx²+y)

p= xy²-x/ yx²+y

dy/dx= x(y²-1)/ y(x²+1)

y/(y²-1) dy= x/ (x²+1)dx

 

let,

 y²-1= t

2ydy= dt

y dy= dt/2

and x²+1= v

2x dx= dv

x dx= dv/2

then,

dt/2t= dv/2v

1/2logt=1/2logv+logc

logt= logcv

t=  cv

(y²-1)= (x²+1)c

y²= (x²+1)c+1