Differential Equations Question 292
Question: What is the solution of $ \frac{dy}{dx}+2y=1 $ satisfying $ y(0)=0 $ -
Options:
A) $ y=\frac{1-{e^{-2x}}}{2} $
B) $ y=\frac{1+{e^{-2x}}}{2} $
C) $ y=1+e^{x} $
D) $ y=\frac{1+e^{x}}{2} $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] $ \frac{dy}{dx}+2y=1;\frac{dy}{dx}=1-2y $
$ \int{\frac{dy}{1-2y}=\int{dx}} $
$ -\frac{1}{2}\log | 1-2y |=x+C $ at $ x=0,y=0 $
$ -\frac{1}{2}\log 1=0+C\Rightarrow C=0 $
$ 1-2y={e^{-2x}};y=\frac{1-{e^{-2x}}}{2} $
BETA
