Differential Equations Question 26
Question: The solution of the equation $ \frac{dy}{dx}={{(x+y)}^{2}} $ is
Options:
A) $ x+y+\tan (x+c)=0 $
B) $ x-y+\tan (x+c)=0 $
C) $ x+y-\tan (x+c)=0 $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
Put $ x+y=v $ and $ 1+\frac{dy}{dx}=\frac{dv}{dx} $
Therefore $ \frac{dv}{dx}=v^{2}+1 $
Therefore $ \frac{dv}{v^{2}+1}=dx $
On integrating, we get $ {{\tan }^{-1}}v=x+c $ or $ v=\tan (x+c) $
Therefore $ x+y=\tan (x+c) $ .
BETA
