Differential Equations Question 235
Question: The solutions of $ (x+y+1)dy=dx $ are
Options:
A) $ x+y+2=Ce^{y} $
B) $ x+y+4=Clogy $
C) $ \log (x+y+2)=Cy $
D) $ \log (x+y+2)=C-y $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] Putting $ x+y+1=u, $ we have $ du=dx+dy $ and the given equation reduces to $ u(du-dx)=dx $
$ \Rightarrow \frac{udu}{u+1}=dx\Rightarrow u-\log (u+1)=x $
$ \Rightarrow \log (x+y+2)=y+constant\Rightarrow x+y+2=Ce^{v} $
BETA
