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Question

Mathematics Question on Derivatives

The rate of activity of a person y with age t is given by (1+t) dydx=ey1\frac{dy}{dx}=e^{-y}-1. For the initial condition y = 1 at r = 0, the dy dt solution is given by,

A

y=in(1t+1)y=in(\frac{1}{t+1})

B

y=in(et+1)y=in(\frac{e}{t+1})

C

y=in(e+tt+1)y=in(\frac{e+t}{t+1})

D

y=in(ett+1)y=in(\frac{e-t}{t+1})

Answer

y=in(e+tt+1)y=in(\frac{e+t}{t+1})

Explanation

Solution

The correct option is(C): y=in(e+tt+1)y=in(\frac{e+t}{t+1})