Differential-Equations Question 363
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} $
Þ $ \frac{e^{2y}}{2}=x+c $ At $ x=5,\ y=0 $
Þ $ c=-\frac{9}{2} $ ;
$ \therefore $ For $ y=3,\ x=\frac{e^{6}+9}{2} $ .
BETA
