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If the variables $x$ and $y$ are related by the equation
$x = \int_{0}^{y} \frac{d x}{\sqrt{1 + 9 x^{2}}}$ and $\frac{d^{2} y}{d x^{2}}$ is proportional to y then
the constant of proportionality is

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detailed solution

Correct option is D

dxdy=11+9y2→dydx=1+9y2d2ydx2=1218y1+9y2dydx=9y. Thus the constant of proportionality is equal to 9.

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If the variables x and y are related by the equation x=∫0y dx1+9x2and d2ydx2 is proportional to y then the constant of proportionality is

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Ready to Test Your Skills?

free study material

If the variables $x$ and $y$ are related by the equation
$x = \int_{0}^{y} \frac{d x}{\sqrt{1 + 9 x^{2}}}$ and $\frac{d^{2} y}{d x^{2}}$ is proportional to y then
the constant of proportionality is