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Question

If y=sin(sinx), prove that d2ydx2+tan xdydx+y cos2x=0

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Solution

y=sin(sinx) ... (i)

dydx=cos(sin x).cos x ... (ii)

d2ydx2=sin(sin x)cos x.cos xcos(sin x)sin x

= [sin(sin x).cos2x+cos(sin x)sin x]

= [y.cos2x+dydx.1cos x.sin.x] [using (i) and (ii)]

d2ydx2+y cos2x+tan xdydx=0

or, d2ydx2+tan xdydx+y cos2x=0.

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