Differential Equations Question 328
Question: The solution of the differential equation $ \frac{dy}{dx}=(1+x)(1+y^{2}) $ is
Options:
A) $ y=\tan (x^{2}+x+c) $
B) $ y=\tan (2x^{2}+x+c) $
C) $ y=\tan (x^{2}-x+c) $
D) $ y=\tan ( \frac{x^{2}}{2}+x+c ) $
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Answer:
Correct Answer: D
Solution:
$ \frac{dy}{dx}=(1+x)(1+y^{2}) $
Therefore $ \frac{dy}{1+y^{2}}=(1+x)dx $
On integrating both sides, we get $ {{\tan }^{-1}}y=\frac{x^{2}}{2}+x+c $
Therefore $ y=\tan ( \frac{x^{2}}{2}+x+c ) $ .
BETA
