A) 0
B) 1
C) 2
D) None of these
Correct Answer: A
Solution :
\[y\sqrt{{{x}^{2}}+1}=\log \left\{ \sqrt{{{x}^{2}}+1}-x \right\}\] Differentiating both sides w.r.t. x, we get \[\frac{dy}{dx}\sqrt{{{x}^{2}}+1}+y.\frac{1}{2\sqrt{{{x}^{2}}+1}}.2x=\frac{1}{\sqrt{{{x}^{2}}+1}-x}\times \left\{ \frac{1}{2}\frac{2x}{\sqrt{{{x}^{2}}+1}}-1 \right\}\] Þ \[({{x}^{2}}+1)\frac{dy}{dx}+xy=\sqrt{{{x}^{2}}+1}.\frac{-1}{\sqrt{{{x}^{2}}+1}}\] Þ \[({{x}^{2}}+1)\frac{dy}{dx}+xy+1=0\].You need to login to perform this action.
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