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

Answer 1

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.