Differential Equations Question 180
Question: The solution to the differential equation $ y\log y+xy’=0 $ , where $ y(1)=e $ , is
Options:
A) $ x(logy)=1 $
B) $ xy(logy)=1 $
C) $ {{(logy)}^{2}}=2 $
D) $ \log y+( \frac{x^{2}}{2} )y=1 $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] $ x\frac{dy}{dx}+y(logy)=0 $ Or $ \int{\frac{dx}{x}+\int{\frac{dy}{y(logy)}=c}} $ Or $ \log x+\log (logy)=logc $ Or $ x\log y=c $
$ y(1)=e $
$ \Rightarrow c=1 $ Hence, the equation of the curve is x log y=1
BETA
