Differential Equations Question 101
Question: The solution of the equation $ \frac{dy}{dx}=\frac{1}{x+y+1} $ is
Options:
A) $ x=ce^{y}-y-2 $
B) $ y=x+ce^{y}-2 $
C) $ x+ce^{y}-y-2=0 $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ \frac{dy}{dx}=\frac{1}{x+y+1} $
Therefore $ \frac{dx}{dy}=x+y+1 $
Therefore $ \frac{dx}{dy}-x=y+1 $
It is linear equation, therefore I.F. $ ={e^{\int _{{}}^{{}}{-1dy}}}={e^{-y}} $
Hence the solution of the equation is
$ x.{e^{-y}}=\int _{{}}^{{}}{(y+1){e^{-y}}}dy+c $
Therefore $ x=ce^{y}-y-2 $ .
BETA
