Differential Equations Question 87
Question: The solution of $ y{e^{-x/y}}dx-(x{e^{-x/y}}+y^{3})dy=0 $ is
Options:
A) $ \frac{y^{2}}{2}+{e^{-x/y}}=k $
B) $ \frac{x^{2}}{2}+{e^{-x/y}}=k $
C) $ \frac{x^{2}}{2}+{e^{x/y}}=k $
D) $ \frac{y^{2}}{2}+{e^{x/y}}=k $
Show Answer
Answer:
Correct Answer: A
Solution:
$ y{e^{-x/y}}dx-(x{e^{-x/y}}+y^{3})dy=0 $
$ {e^{-x/y}}(ydx-xdy)=y^{3}dy $
Therefore $ {e^{-x/y}}\frac{(ydx-xdy)}{y^{2}}=ydy $
$ {e^{-x/y}}d( \frac{x}{y} )=ydy $ . Integrating both sides, we get $ k-{e^{-x/y}}=\frac{y^{2}}{2} $
Therefore $ \frac{y^{2}}{2}+{e^{-x/y}}=k $
BETA
