Q.

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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a

4

b

6

c

5

d

9

answer is D.

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Detailed Solution

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