Differential Equations Question 91
Question: Solution of the differential equation, $ ydx-xdy+xy^{2}dx=0 $ can be
Options:
A) $ 2x+x^{2}y=\lambda y $
B) $ 2y+y^{2}x=\lambda y $
C) $ 2y-y^{2}x=\lambda y $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ \frac{ydx-xdy}{y^{2}}=-xdx $
Therefore $ d( \frac{x}{y} )=-xdx $
Integrating both side, we get $ \frac{x}{y}=-\frac{x^{2}}{2}+c $
Therefore $ 2x+x^{2}y=2cy $
Therefore $ 2x+x^{2}y=\lambda y $ [ $ \lambda =2c $ ]
BETA
