Differential Equations Question 318
Question: The solution of the equation $ \frac{dy}{dx}={e^{x-y}}+x^{2}{e^{-y}} $ is
[MP PET 2004]
Options:
A) $ e^{y}=e^{x}+\frac{x^{3}}{3}+c $
B) $ e^{y}=e^{x}+2x+c $
C) $ e^{y}=e^{x}+x^{3}+c $
D) $ y=e^{x}+c $
Show Answer
Answer:
Correct Answer: A
Solution:
$ \frac{dy}{dx}={e^{x-y}}+x^{2}{e^{-y}}={e^{-y}}(e^{x}+x^{2}) $
Therefore $ e^{y}dy=(x^{2}+e^{x})dx $
Now integrating both sides, we get $ e^{y}=\frac{x^{3}}{3}+e^{x}+c $ .
BETA
