Differential Equations

Let \(y = y(x)\) be the solution of the differential equation \((1 - {x^2})dy = \left( {xy + ({x^3} + 2)\sqrt {1 - {x^2}} } \right)dx, - 1 < x < 1\), and \(y(0) = 0\). If \(\int_{{{ - 1} \over 2}}^{{1 \over 2}} {\sqrt {1 - {x^2}} y(x)dx = k}\), then k^\(-\)1 is equal to _____________.