If `u=x^2tan^(-1)(y/x)-y^2tan^(-1)(x/y)`,prove that `(del^2u)/(delxdely)=(x^2-y^2)/(x^2+y^2)`

If u = x ^ (2) tan ^ (- 1) ((y) / (x)) - y ^ (2) tan ^ (- 1) ((x) / (y)), prove that (del ^ (2) u) / (del x del y) = (x ^ (2) -y ^ (2)) / (x ^ (2) + y ^ (2))

If u =tan^(-1)((x)/(y)) show that (del^(2)u)/(delxdely) = (del^(2)u)/(delydelx) .

If cos^(-1)((x^(2)-y^(2))/(x^(2)+y^(2)))=tan^(-1)a, prove that (dy)/(dx)=(y)/(x)

If cos^(-1)((x^(2)-y^(2))/(x^(2)+y^(2)))=tan^(-1)a, prove that (dy)/(dx)=(y)/(x)

If u= tan^(-1) ((x^(3) + y^(3))/(x-y)) , Prove that x(del u)/(del x) + y(del u)/(del y) = sin 2u .

If u =x ^(3) +2xy^(2) -x ^(2)y show that (del^(2)u)/(delxdely) =(del^(2)u)/(delydelx).

If u = (x^2+y^2+z^2)^(-1/2) then prove that (del^2u)/(delx^2)+(del^2u)/(dely^2)+(del^2u)/(delz^2) =0

If u = cos ^(-1) ((x)/(y)) prove that x (del u)/(delx) + y (del u)/(dely)=0.

If cos^(-1)((x^(2)-y^(2))/(x^(2)+y^(2)))=tan^(-1)a , prove than (dy)/(dx)=(y)/(x).

If y=e^(tan^-1x), prove that (1+x^2)y_2+(2x-1)y_1=0