X^2-y^2=2 183311-X 2 y 2 2yx

Answer (1 of 4) The graph of x^2(y\sqrt3{x^2})^2=1 is very interesting and is show below using desmos

[無料ダウンロード！ √] if u(x y)=x^2 y^2 2x-3xy then 130259

 answered by nchi (4k points) selected by Darshee Best answer u = x3 y3 3xy2 ∴ u is a homogeneous function in x and y of degree 3 ∴ By Euler's theorem, = 3u Hence Euler's theorem is verified1) is a critical point The second derivative test f xx = 2;f yy = 2;f xy = 0 shows this a local minimum withShowthatu(x,y) = 2x−x33xy2 isharmonic on R2 and find a harmonic conjugate v(x,y) for it Solution Define f(z) = 2z − z3 This function is analytic on C f(xiy) = 2(xiy)−(xiy)3 = 2x2iy−(x33x2iy3xi2y2i3y3) = 2x−x33xy2i(2y−3x2yy3) We have that the real part of f(z) is u(x,y), and hence it is harmonic on R2 Also v(x,y

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If u(x y)=x^2 y^2 2x-3xy then