Differential Equations Question 58
Question: The number of solutions of $ {y}’=\frac{y+1}{x-1},y(1)=2 $ is
[MP PET 2000]
Options:
A) None
B) One
C) Two
D) Infinite
Show Answer
Answer:
Correct Answer: A
Solution:
$ \frac{dy}{dx}=\frac{y+1}{x-1} $
Therefore $ \frac{dy}{y+1}=\frac{dx}{x-1} $
Integrating both sides, $ \int{\frac{dy}{y+1}=\int{\frac{dx}{x-1}}} $
Therefore $ \log (y+1)=\log (x-1)+\log c $
Therefore $ (y+1)=(x-1)c $
At $ x=1 $
Therefore $ y=-1 $ where as $ y(1)=2 $
Hence, the solution is not possible.
BETA
