Differential Equations Question 15
Question: The solution of $ (cosecx\log y)dy+(x^{2}y)dx=0 $ is
[AISSE 1986]
Options:
A) $ \frac{\log y}{2}+(2-x^{2})\cos x+2\sin x=c $
B) $ {{( \frac{\log y}{2} )}^{2}}+(2-x^{2})\cos x+2x\sin x=c $
C) $ {{\frac{(\log y)}{2}}^{2}}+(2-x^{2})\cos x+2x\sin x=c $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ (\text{cosec }x\log y)dy+(x^{2}y)dx=0 $
Therefore $ \frac{1}{y}\log ydy=-x^{2}\sin xdx $
On integrating both sides, we get $ \frac{{{(\log y)}^{2}}}{2}+[x^{2}(-\cos x)+\int _{{}}^{{}}{2x\cos xdx}]=c $
Therefore $ \frac{{{(\log y)}^{2}}}{2}-x^{2}\cos x+2(x\sin x+\cos x)=c $
Therefore $ \frac{{{(\log y)}^{2}}}{2}+(2-x^{2})\cos x+2x\sin x=c $ .
BETA
