Differential Equations Question 93
Question: The differential equation $ y\frac{dy}{dx}+x=a $ (a is any constant) represents
Options:
A) A set of circles having centre on the y-axis
B) A set of circles centre on the x-axis
C) A set of ellipses
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
We have $ y\frac{dy}{dx}+x=a $ or $ ydy+xdx=adx $
Integrating, we get $ \frac{y^{2}}{2}+\frac{x^{2}}{2}=ax+c $
or $ x^{2}+y^{2}-2ax+k=0 $ , which represents a set of circles having centre on x-axis.
BETA
