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Question

If y = 3 cos (log x) + 4 sin (log x), show that x2y2+xy1+y=0
where y1 & y2 are the successive derivatives of y.

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Solution

y=3 cos(log x)+4 sin(logx)y1=3sin(log x)x+4cos(log x)xxy1=3sin(log x)+4 cos(log x)y2=dy1dx=x(3cos(log x)x4sin(log x)x)1.(3 sin(log x)x+4 cos(log x)x)x2y2=(3 cos(log x)+4 sin(log x))(3 sin(log x)+4 cos(log x)x)x2x2y2=(y)(y1)x2y2+y1+y=0


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