Question

What is integrating factor of \[\frac{dy}{dx}\] + y sec x = tan x?

पर्याय

• sec x + tan x

• log (sec x + tan x)

• e^sec x

• sec x

Answer 1

sec x + tan x

 

We have,

\[\frac{dy}{dx} + y \sec x = \tan x\]

\[\text{ Comparing with }\frac{dy}{dx} + Py = Q, \text{ we get }\]

\[P = \sec x \]

\[Q = \tan x\]

Now,

\[I . F . = e^{\int\sec xdx} \]

\[ = e^{log\left( \sec x + \tan x \right)} \]

\[ = \sec x + \tan x\]