Differential Equations Question 135
Question: The solution of $ \frac{dy}{dx}=| x | $ is:
Options:
A) $ y=\frac{x| x |}{2}+c $
B) $ y=\frac{| x |}{2}+c $
C) $ y=\frac{x^{2}}{2}+c $
D) $ y=\frac{x^{3}}{2}+c $ Where c is an arbitrary constant
Show Answer
Answer:
Correct Answer: A
Solution:
[a] $ \frac{dy}{dx}=| x | $
$ \frac{dy}{dx}=x $ for $ x\ge 0; $
$ \frac{dy}{dx}=-x $ for $ x<0; $
$ \int{dy=\int{xdx}} $
$ y=\frac{x^{2}}{2}+C_1 $ ……. (i) $ \int{dy=-1xdx} $
$ y=-\frac{x^{2}}{2}+C_1 $ ……. (ii)
From (i) and (ii) $ y=\frac{x| x |}{2}+C $
BETA
