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The number of solution of dy / dx = (y ...

The number of solution of `dy / dx = (y +1) / (x-1)` when `y(1) = 2` is

A

none

B

one

C

two

D

inifinite

Text Solution

Verified by Experts

Given `(dy)/(dx)=(y+1)/(x-1)`
`Rightarrow (dy)/(y+1)=(dx)/(x-1)`
On integrating both sides, we get
`log(y+1)=log(x-1)-logC`
`Rightarrow C=(x-1)/(y+1)`
When x=1 and y=2, then C=0
So, the required solution is x-1=0.
Hence, only one solution exist.
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