Let \( y(x) \) be the solution of the differential equation \( x^2 \dfrac{dy}{dx} + xy = x^2 + y^2, \ x > \dfrac{1}{e} \), satisfying \( y(1) = 0 \).Then the value of \( 2\dfrac{\,(y(e))^2}{y(e^2)} \) is _____________.
