Differential Equations Question 255
Question: What is the solution of the differential equation $ \sin ( \frac{dy}{dx} )-a=0 $ -
Options:
A) $ y=x{{\sin }^{-1}}a+c $
B) $ x=y{{\sin }^{-1}}a+c $
C) $ y=x+x{{\sin }^{-1}}a+c $
D) $ y={{\sin }^{-1}}a+c $ where c is an arbitrary constant.
Show Answer
Answer:
Correct Answer: A
Solution:
[a] $ \sin ( \frac{dy}{dx} )-a=0 $
$ \sin ( \frac{dy}{dx} )=a\Rightarrow \frac{dy}{dx}={{\sin }^{-1}}a;dy={{\sin }^{-1}}adx $ Now, integrating both sides, $ \int{dy=\int{{{\sin }^{-1}}adx}} $
$ y=x{{\sin }^{-1}}a+c $
BETA
