A) \[y=3+c{{e}^{x/3}}\]
B) \[y=3+c{{e}^{-x/3}}\]
C) \[3y=c+{{e}^{x/3}}\]
D) \[3y=c+{{e}^{-x/3}}\]
Correct Answer: B
Solution :
Given, \[\frac{dy}{dx}+\frac{y}{3}=1\]; I.F. = \[{{e}^{\int{\frac{1}{3}\,d\,x}}}={{e}^{x/3}}\] Hence, solution is \[y\,.\,{{e}^{x/3}}=\int{1\,.\,{{e}^{x/3}}\,dx+c}\] \[y\,.\,{{e}^{x/3}}=3\,{{e}^{x/3}}+c\]; \[y=3+c{{e}^{-x/3}}\].
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