Find the integrating factor of the differential equation $\frac{dy}{dx}+y=e^{-x}$.

Solution

1. The given equation is in the form $\frac{dy}{dx}+Py=Q$ where $P=1$.
2. The integrating factor is defined as $I.F.=e^{\int Pdx}$.
3. Calculate $$\begin{array}{rl}I.F.& =e^{\int 1dx}\\ & =e^x\end{array}$$.
4. Hence the answer is (A).