diff-equation

Question: The solution of the differential equation $xy\frac{dy}{dx}=\frac{(1+{{y}^{2}})(1+x+{{x}^{2}})}{(1+{{x}^{2}})}$ is

1) $\frac{1}{2}\log (1+{{y}^{2}})=\log x-{{\tan }^{-1}}x+c$

2) $\frac{1}{2}\log (1+{{y}^{2}})=\log x+{{\tan }^{-1}}x+c$

3) $\log (1+{{y}^{2}})=\log x-{{\tan }^{-1}}x+c$

4) $\log (1+{{y}^{2}})=\log x+{{\tan }^{-1}}x+c$

Solution:

Explanation: No Explanation

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