Differential Equations Question 30
Question: The general solution of the differential equation $ \log ( \frac{dy}{dx} )=x+y $ is
[MP PET 1994; 1995; DSSE 1984]
Options:
A) $ e^{x}+e^{y}=c $
B) $ e^{x}+{e^{-y}}=c $
C) $ {e^{-x}}+e^{y}=c $
D) $ {e^{-x}}+{e^{-y}}=c $
Show Answer
Answer:
Correct Answer: B
Solution:
$ \log ( \frac{dy}{dx} )=x+y $
Therefore $ {e^{x+y}}=\frac{dy}{dx} $
Therefore $ e^{x}e^{y}=\frac{dy}{dx} $
Therefore $ \int _{{}}^{{}}{e^{x}dx}=\int _{{}}^{{}}{\frac{dy}{e^{y}}} $
Therefore $ e^{x}=-{e^{-y}}+c $
Therefore $ e^{x}+{e^{-y}}=c $ .
BETA
