A) \[y=\frac{1}{2}(\cos x+\sin x)+c{{e}^{-x}}\]
B) \[y=\frac{1}{2}(\cos x-\sin x)+c{{e}^{-x}}\]
C) \[y=\cos x+\sin x+c{{e}^{-x}}\]
D) None of these
Correct Answer: A
Solution :
It is linear equation of the form \[\frac{dy}{dx}+Py=Q\] So, I.F. \[={{e}^{\int_{{}}^{{}}{1dx}}}={{e}^{x}}\] Hence solution is \[y.{{e}^{x}}=\int_{{}}^{{}}{\cos x.{{e}^{x}}dx+c}\] Þ \[y=\frac{1}{2}(\cos x+\sin x)+c{{e}^{-x}}\].
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