Question

P
solve the differential equation
dy /dx =y(x^2-1)/x(y^2-1)​

Answer 1

Given differential equation is dy/dx = (1 + y2)/(1 + x2) or, (1/(1 + y2)) dy = (1/(1 + x2)) dx on, integrating, ∫(1/(1 + y2)) dx = ∫(1/(1 + x2)) dy or, tan-1 y = tan-1 x + c or tan-1 y - tan-1 x = c or, tan-1 ((y - x)/(1 + yx)) = c or, (y - x)/(1 + yx) = tan c ∴ (y - x)/(1 + yx) = c(constant) is, the require