Differential Equations Question 9
Question: The solution of the differential equation $ x(e^{2y}-1)dy+(x^{2}-1)e^{y}dx=0 $ is
[AISSE 1990]
Options:
A) $ e^{y}+{e^{-y}}=\log x-\frac{x^{2}}{2}+c $
B) $ e^{y}-{e^{-y}}=\log x-\frac{x^{2}}{2}+c $
$ $
C) $ e^{y}+{e^{-y}}=\log x+\frac{x^{2}}{2}+c $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ x(e^{2y}-1)dy+(x^{2}-1)e^{y}dx=0 $
Therefore $ \int _{{}}^{{}}{\frac{e^{2y}-1}{e^{y}}}dy=\int _{{}}^{{}}{\frac{1-x^{2}}{x}dx} $
Therefore $ e^{y}+{e^{-y}}=\log x-\frac{x^{2}}{2}+c $ .
BETA
