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Let y = y(x) be the solution of the dif...

Let `y = y(x) ` be the solution of the differential equation `(1 - x^2)dy = (xy + (x^3 + 2) sqrt(1- x^2))dx, -1 lt x lt 1, and y (0) =0`. If `int_((-1)/2)^(1/2)sqrt(1 - x^2)y(x) dx = k`, then `k^(-1)` is equal to _________.

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