Differential Equations Question 322
Question: The solution of the differential equation $ (1+x^{2})\frac{dy}{dx}=x $ is
Options:
A) $ y={{\tan }^{-1}}x+c $
B) $ y=-{{\tan }^{-1}}x+c $
C) $ y=\frac{1}{2}{\log _{e}}(1+x^{2})+c $
D) $ y=-\frac{1}{2}{\log _{e}}(1+x^{2})+c $
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Answer:
Correct Answer: C
Solution:
$ (1+x^{2})\frac{dy}{dx}=x $
Therefore $ dy=\frac{x}{1+x^{2}}dx $
Therefore $ \int{dy}=\int{\frac{x}{1+x^{2}}dx}+c $
Therefore $ y=\frac{1}{2}{\log _{e}}(1+x^{2})+c $ .
BETA
