Differential Equations Question 32
Question: The solution of $ \frac{dy}{dx}+\frac{y}{3}=1 $ is
[EAMCET 2002]
Options:
A) $ y=3+c{e^{x/3}} $
B) $ y=3+c{e^{-x/3}} $
C) $ 3y=c+{e^{x/3}} $
D) $ 3y=c+{e^{-x/3}} $
Show Answer
Answer:
Correct Answer: B
Solution:
Given, $ \frac{dy}{dx}+\frac{y}{3}=1 $ ; I.F. = $ {e^{\int{\frac{1}{3}dx}}}={e^{x/3}} $
Hence, solution is $ y.{e^{x/3}}=\int{1.{e^{x/3}}dx+c} $
$ y.{e^{x/3}}=3{e^{x/3}}+c $ ; $ y=3+c{e^{-x/3}} $ .
BETA
