The integrating factor of the differential equation cos x d y-d x-sin x - y-x - x-cos x -0 iA- XB- tan xC- cos xD- sin x

The correct option is A xcos x dy/dx + sin x · y = x· x Dividing the D.E by cos x nbsp; dy/dx + tan x · y = x·^2 x Integrating factor nbsp; = e^∫ nbsp; ta ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Order of a Differential Equation

The integrati...

Question

The integrating factor of the differential equation $cos x \frac{d y}{d x} + sin x \cdot y = x \cdot sec x, (cos x \neq 0)$ is

cos x

No worries! We‘ve got your back. Try BYJU‘S free classes today!

sec x

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

tan x

No worries! We‘ve got your back. Try BYJU‘S free classes today!

sin x

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $sec x$
$cos x \frac{d y}{d x} + sin x \cdot y = x \cdot sec x$
Dividing the D.E by $cos x$
$\frac{d y}{d x} + tan x \cdot y = x \cdot {sec}^{2} x$
Integrating factor
$= e^{\int tan x d x} = e^{ln sec x} = sec x$

Suggest Corrections

The integrating factor of the differential equation cosxdydx+sinx⋅y=x⋅secx, (cosx≠0) is

The correct option is B secxcosxdydx+sinx⋅y=x⋅secx Dividing the D.E by cosx dydx+tanx⋅y=x⋅sec2x Integrating factor =e∫tanx dx=elnsecx=secx

The integrating factor of the differential equation $cos x \frac{d y}{d x} + sin x \cdot y = x \cdot sec x, (cos x \neq 0)$ is

The correct option is B $sec x$
$cos x \frac{d y}{d x} + sin x \cdot y = x \cdot sec x$
Dividing the D.E by $cos x$
$\frac{d y}{d x} + tan x \cdot y = x \cdot {sec}^{2} x$
Integrating factor
$= e^{\int tan x d x} = e^{ln sec x} = sec x$