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Let y=f(x) is a solution of differential...

Let y=f(x) is a solution of differential equation `e^(y)((dy)/(dx)-1)=e^(x)` and f(0)=0 then f(1) is equal to

A

`1/3`

B

`2/3`

C

`-1/3`

D

`-2/3`

Text Solution

Verified by Experts

The correct Answer is:
D
`kx ^(k-1) + ky^(k-1) (dy)/(dx) =0`
`(dy)/(dx) =-(k (x ^(k-1)))/(k (y ^(k-1)))+ " implies(dy)/(dx) =- ((y)/(x)) ^(1-k)`
now by comparing `1 -k =5/3`
`k =1 - 5/3 implies k =-2/3`
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