Integrating factor of the differential equation is:

Question

Philoid · Accepted Answer

The differential equation is

Compare with we get P = tanx and Q = sec x

The IF integrating factor is given by e^∫Pdx

⇒ e^∫Pdx = e^∫tanxdx

Substitute cosx = t hence hence sinxdx = -dt

⇒ e^∫Pdx = e^-logt

Resubstitute value of t

⇒ e^∫Pdx = e^-log(cosx)

⇒ e^∫Pdx = e^log(secx)

⇒ e^∫Pdx = sec x

Hence IF is sec x