Find the particular solution of the differential equation x2

Find the particular solution of the differential equation ((x^2)/(y^2-4))(dy/dx)=(1/2y), satisfying the initial condition y(1)=sqrt(5).

y=???

(2y/y^2-4)dy=dx/x^2 put y^2=t ln(t-4)=-1/x+lnc (y^2-4)/c=e^-1/x y^2=ce^-1/x+4 using initial condition 5=c/e+4 c=e y=(e^(-1/x+1)+4)^1/2 y=(e^((x-1)/x)+4)^1/2