question_answer

Find the integrating factor of differential equation \[\frac{dy}{dx}+y\tan x-\sec x=0.\]

Answer:

Given differential equation is \[\frac{dy}{dx}+y\tan x-\sec x=0\] \[\frac{dy}{dx}+\tan xy=\sec x\] Which is of the form of \[\frac{dy}{dx}+Py=Q\] Here, \[P=\tan x\]and \[Q=\sec x\] Now, Integrating Factor \[(lF)={{e}^{\int{pdx}}}={{e}^{\int{\tan xdx}}}\] \[={{e}^{\log \,\,\,|\,\,\sec x|}}\,\,=\sec x\]