this is very simple use separation for solving differential eqn:

dy/(2y)=-dx/(x-1)

integrate both sides

(1/2)ln(y)=-ln(x-1)+c0

cross multiplying 2 u get

ln(y)=(-2)ln(x-1)+2c0

now using log properyies and taking 2c0=ln(m0)

ln(y)=ln((x-1)^-2)+ln(m0)

use log (ab)=log a+ log b

u get

ln(y)=ln((x-1)^(-2)*m0)

comparing u get

y=m0*(1/(x-1)^(-2))