Differential Equations Question 339
Question: The solution of differential equation $ x\frac{dy}{dx}+y=y^{2} $ is
Options:
A) $ y=1+cxy $
B) $ y=\log {cxy} $
C) $ y+1=cxy $
D) $ y=c+xy $
Show Answer
Answer:
Correct Answer: A
Solution:
$ x\frac{dy}{dx}+y=y^{2} $
Therefore $ x\frac{dy}{dx}=y^{2}-y $
Therefore $ \frac{dy}{y^{2}-y}=\frac{dx}{x} $
Therefore $ [ \frac{1}{y-1}-\frac{1}{y} ]dy=\frac{dx}{x} $
On integrating, we get $ \log (y-1)-\log y=\log x+\log c $
Therefore $ \frac{y-1}{y}=xc $
Therefore $ y=1+cxy $ .
BETA
