Differential Equations Question 38
Question: If $ \frac{dy}{dx}={e^{-2y}} $ and $ y=0 $ when $ x=5, $ the value of x for $ y=3 $ is
[MP PET 2001]
Options:
A) $ e^{5} $
B) $ e^{6}+1 $
C) $ \frac{e^{6}+9}{2} $
D) $ {\log _{e}}6 $
Show Answer
Answer:
Correct Answer: C
Solution:
$ \int _{{}}^{{}}{\frac{dy}{{e^{-2y}}}}=\int _{{}}^{{}}{dx} $
Therefore $ \frac{e^{2y}}{2}=x+c $
At $ x=5,\ y=0 $
Therefore $ c=-\frac{9}{2} $ ;
$ \therefore $ $For $ y=3,\ x=\frac{e^{6}+9}{2} $ .
BETA
