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Question

If y=acos(logx)+bsin(logx), show that x2y2+xy1+y=0

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Solution

y=acos(logx)+bsin(logx)

dydx=asin(logx)x+bsin(logx)x

xdydx=asin(logx)+bsin(logx)

xd2ydx2+dydx=acos(logx)xbsin(logx)x

x2d2ydx2+xdydx=acos(logx)bsin(logx)

x2d2ydx2+xdydx=y

x2d2ydx2+xdydx+y=0

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