Question

What is integrating factor of $\frac{dy}{dx}$ + y sec x = tan x?
(a) sec x + tan x
(b) log (sec x + tan x)
(c) e^{sec x}
(d) sec x

Answer 1

(a) sec x + tan x

We have,

$$\begin{gathered} \frac{dy}{dx}+y\sec x=\tan x \\ \mathrm{Comparing}\mathrm{with}\frac{dy}{dx}+Py=Q,\mathrm{we}\mathrm{get} \\ P=\sec x \\ Q=\tan x \\ \mathrm{Now}, \\ \mathrm{I}.\mathrm{F}.=e^{\int \sec xdx} \\ =e^{\log \left(\sec x+\tan x\right)} \\ =\sec x+\tan x \end{gathered}$$