Find the particular solution of the differential equation x2/y2 - 4 dy/dx = 1/ 2y satisfying the initial condition y ( 1 ) = 5 . Answer: y = Solution using variable separable form 2y/(y^2-4) * dy = dx/x^2 now integrating we get ln(y^2 -4) = -1/x +C given y(1) = 5 => ln(25-4) = -1/1 +c => ln(21) +1 =C => c= ln (21*e) => ln (y^2 -4) = -1/x + ln (21*e).