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Question

If ey(x+1)=1, then show that d2ydx2=(dydx)2.

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Solution

ey(x+1)=1ey×1+[ey×dydx×(x+1)]=0
Differentiating on both sides
dydx=eyey×(x+1)=1x+1
Differentiating again
d2ydx2=1(x+1)2=1(x+1)2
d2ydx2=1(x+1)2=(1x+1)2=(dydx)2
Hence proved

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