Chapter 14.7, Problem 7ES

Solve for x and y in terms of $u\text{and}\upsilon ,$ and then find the Jacobian $\partial \left(x,y\right)/\partial \left(u,\upsilon \right).$

$u=x^2-y^2,\upsilon =x^2+y^2\left(x>0,y>0\right)$