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Solved Solve The Given Differential Equation A X 2 Chegg Com  the "under the bracket" term can be rewrtten as {(1 x 2)(1 y 2)} 1/2 xydy/dx = 0 => (xy)(dy/dx) = (1 x 2) 1/2 (1 y2) 1/2 => y/(1 y 2) 1/2 dy = x(1 x 2) 1/2 dx Now differentiate both sides (do it separately by subs and all whatever required it will be easy for you) then put it back in the equation y^2 = x^2(2lnx c) We can rewrite this Ordinary Differential Equation in differential form (x^2 y^2) \ dx xy \ dy = 0 A as follows \ \ \ \ dy/dx = (x^2 y^2)/(xy) dy/dx = x/y y/x B Leading to a suggestion of a substitution of the form u = y/x iff y = ux And differentiating wrt x whilst applying the product rule dy/dx = u x(du)/dx Substituting into the Solve (x^2 y^2 x)dx xydy=0