Differential-Equations Question 371
Question: Solution of the differential equation $ \sin \frac{dy}{dx}=a $ with $ y(0)=1 $ is
[Kurukshetra CEE 1998]
Options:
A) $ {{\sin }^{-1}}\frac{(y-1)}{x}=a $
B) $ \sin \frac{(y-1)}{x}=a $
C) $ \sin \frac{(1-y)}{(1+x)}=a $
D) $ \sin \frac{y}{(x+1)}=a $
Show Answer
Answer:
Correct Answer: B
Solution:
Given $ \sin \frac{dy}{dx}=a $ ; $ dy={{\sin }^{-1}}a,dx $ Integrating both sides, $ \int_{{}}^{{}}{dy}=\int_{{}}^{{}}{{{\sin }^{-1}}a,dx} $ $ y=x{{\sin }^{-1}}a+c $ and $ y(0)=0+c=1 $ ,
$ \therefore c=1 $
$ \therefore y=x{{\sin }^{-1}}a+1 $
Þ $ a=\sin \frac{y-1}{x} $ .
BETA
