If $y = \frac{(\sin^{-1} x)^2}{2}$, then $(1-x^2) y_2 - x y_1 = $

If $f(x) = 10 \cos x + (13 + 2x) \sin x$, then $f''(x) + f(x)$ is equal to

Find the second order derivative of the function $f(x) = x^{20}$.

If $x = \int\limits_0^y {\frac{{dt}}{{\sqrt {1 + {t^2}} }}} $,then $\frac{{{d^2}y}}{{d{x^2}}}$ is equal to

If $x=a$ is a root of multiplicity two of a polynomial equation $f(x)=0$,then

If $y = \sin^2 \alpha + \cos^2(\alpha + \beta) + 2 \sin \alpha \sin \beta \cos(\alpha + \beta)$,then find $\frac{d^3y}{d\alpha^3}$ (keeping $\beta$ as a constant).