Linear differential equationsHard

Solving a First-Order Differential Equation

Let y = f(x) be the solution of the differential equation $\frac{{dy}}{{dx}} + \frac{{xy}}{{{x^2}-1}} = \frac{{{x^6} + 4x}}{{\sqrt {1 - {x^2}} }}$ , –1 < x < 1 such that f(0) = 0. If 6 $\int\limits_{{\raise0.5ex\hbox{$\scriptstyle { - 1}$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}}^{{\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}} {f\left( x \right)dx = 2\pi -\alpha }$ then α² is equal to __________.

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