Differential Equations Question 197
Question: The general solution of the equation $ \frac{dy}{dx}=1+xy $ is
Options:
A) $ y=c{e^{-x^{2}/2}} $
B) $ y=c{e^{x^{2}/2}} $
C) $ y=(x+c){e^{-x^{2}/2}} $
D) None of these
Show Answer
Answer:
Correct Answer: D
Solution:
[d] $ \frac{dy}{dx}=1+xy $ Or $ \frac{dy}{dx}-xy=1 $ I.F. $ ={e^{\int{-xdx}}}={e^{-x^{2}/2}} $ Hence solutions is $ y.{e^{-x^{2}/2}}=\int{{e^{-x^{2}/2}}dx+c.} $
$ \int{{e^{-{x^{2/2}}}}dx} $ is not further integrable.
BETA
