A) \[{{e}^{x}}+{{e}^{y}}=c\]
B) \[{{e}^{x}}+{{e}^{-y}}=c\]
C) \[{{e}^{-x}}+{{e}^{y}}=c\]
D) \[{{e}^{-x}}+{{e}^{-y}}=c\]
Correct Answer: B
Solution :
\[\log \left( \frac{dy}{dx} \right)=x+y\] Þ \[{{e}^{x+y}}=\frac{dy}{dx}\]Þ\[{{e}^{x}}{{e}^{y}}=\frac{dy}{dx}\] Þ \[\int_{{}}^{{}}{{{e}^{x}}dx}=\int_{{}}^{{}}{\frac{dy}{{{e}^{y}}}}\] Þ \[{{e}^{x}}=-{{e}^{-y}}+c\]Þ \[{{e}^{x}}+{{e}^{-y}}=c\].
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