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Question
Choose the correct option from the given alternatives :
If y = `a cos (logx) and "A"(d^2y)/(dx^2) + "B""dy"/"dx" + "C"` = 0, then the values of A, B, C are
Options
x2, – x, – y
x2, x, y
x2, x, – y
x2, –x, y
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Solution
x2, x, y
[Hint : y = a cos (log x) ...(1)
∴ `"dy"/"dx" = a[-sin(logx)] xx (1)/x`
∴ `x"dy"/"dx" = -asin(logx)`
∴ `x(d^2y)/(dx^2) + "dy"/"dx" = -acos(logx) xx (1)/x`
∴ `x(d^2y)/(dx^2) + "dy"/"dx"` = – y ...[By (1)]
∴ `x2(d^2y)/(dx^2) + x"dy"/"dx" + y` = 0
Comparing this with `"A"(d^2y)/(dx^2) + "B""dy"/"dx" + "C"` = 0, we get A = x2, B = x, C = y.
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