Differential Equations Question 166
Question: Solution of the differential equation $ \frac{dy}{dx}+\frac{y}{x}=\sin x $ is
[Kerala (Engg.) 2005]
Options:
A) $ x(y+\cos x)=\sin x+c $
B) $ x(y-\cos x)=\sin x+c $
C) $ x(y\cdot \cos x)=\sin x+c $
D) $ x(y-\cos x)=\cos x+c $
E) $ x(y+\cos x)=\cos x+c $
Show Answer
Answer:
Correct Answer: A
Solution:
$ \frac{dy}{dx}+\frac{y}{x}=\sin x $ ; I.F. $ ={e^{\int{\frac{1}{x}dx}}}={e^{\log x}}=x $ \ $ yx=\int{x\sin xdx} $
Therefore $ yx=\int{x\sin xdx} $
Therefore $ xy=-x\cos x+\sin x+c $
Therefore $ x(y+\cos x)=\sin x+c $ .
BETA
