Final answer:
The equation provided does not appear to be in an exact differential form. A potential solution approach involves a trigonometric substitution, but without more context, a full solution cannot be provided.
Step-by-step explanation:
To determine if the equation x (dy/dx) - y = √x² - y² is exact, we should look for a function F(x,y) such that F_x = x and F_y = -y, where F_x and F_y are the partial derivatives of F with respect to x and y respectively. However, in this case, the equation does not appear to be in an exact differential form directly because the term containing the square root of x² - y² complicates the scenario.
To solve this equation, we could try separating variables or using a substitution if it simplifies the equation. One possible substitution that might be useful in this context is to let y = x · sin(θ), which can help transform the square root into a more manageable form, making use of the trigonometric identity sin²(θ) + cos²(θ) = 1.
Unfortunately, without further context or instructions on the methods to be used for solving, we cannot provide a complete step-by-step solution to this equation.