[コンプリート!] if u(x y)=x^2+y^2+2x-3xy then 968078
Euler S Theorem On Homogeneous Function To ask Unlimited Maths doubts download Doubtnut from https//googl/9WZjCW If `x^3y^33axy=0` then prove that `(d^2y)/(dx^2)=(2a^2x y)/((a xy^2)^3)` Reformulate as a quadratic in a single variable, use the quadratic formula, then reformulate back to find 2x^23xy2y^2 = (2xy)(x2y) If you divide the quadratic through by y^2, then you get (2x^2)/y^2(3xy)/y^2(2y^2)/y^2 = 2(x/y)^23(x/y)2 Let t = x/y and f(t) = 2t^23t2 To factor f(t), find roots of f(t) = 0 using the quadratic formula f(t) = 2t^23t2 is of the form If u(x y)=x^2+y^2+2x-3xy then