Differential Equations Question 256
Question: What is the solution of the equation $ \ln ( \frac{dy}{dx} )+x=0 $ -
Options:
A) $ y+e^{x}=c $
B) $ y-{e^{-x}}=c $
C) $ y+{e^{-x}}=c $
D) $ y-e^{x}=c $
Show Answer
Answer:
Correct Answer: C
Solution:
[c] Consider the given differential equation $ \ln ( \frac{dy}{dx} )+x=0\Rightarrow ln( \frac{dy}{dx} )=-x $
$ \Rightarrow \frac{dy}{dx}={e^{-x}} $ On separating the variables, we get $ dy={e^{-x}}dx, $
On integrating both sides, we get $ \int{dy=\int{{e^{-x}}dx}} $
$ \Rightarrow y=\frac{{e^{-x}}}{-1}+C=-{e^{-x}}+C\Rightarrow y+{e^{-x}}=C $
BETA
