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$If x = \int_{0}^{y} \frac{d t}{\sqrt{1 + 9 t^{2}}} and \frac{d^{2} y}{d x^{2}} = a y, then a =$

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Correct option is A

x=∫0y dt1+9t2 Differentiating w.r.t. y , we get dxdy=11+9y2 or dydx=1+9y2 or ddxdydx=ddy1+9y2dydx or d2ydx2=18y21+9y21+9y2=9y or a=9

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If x=∫0y dt1+9t2 and d2ydx2=ay, then a =

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$If x = \int_{0}^{y} \frac{d t}{\sqrt{1 + 9 t^{2}}} and \frac{d^{2} y}{d x^{2}} = a y, then a =$