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If y = sin (log x), then prove that \(x^2\frac{d^2y}{dx^2}+\)\(\frac{dy}{dx}+y=0\).

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Given,

y = sin (log x)

= RHS

+1 vote
by (50 points)

y = sin(logx)

dy/dx = cos(logx) / x

d2y/dx= [-sin(logx) - cos(logx) ] / x2

X. d2y/ dx= -y -cos(logx)

X. d2y/ dx= -y - x dy/dx

Xd2y/dx+ y + x dy/dx = 0

Hence proved.

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