The integrating factor of differential equation x dx + y x = 1 is

Given that, x dx + y x = 1 dx + y x = x Here, P = x and Q = x IF = e P dx = e xdx = e x = x

Differential Equations — Class 12 Maths Solution

exemplar objective MCQ NCERT EXEMP.Q.40,Page.196

Question

The integrating factor of differential equation $\cos x\frac{{dy}}{{dx}} + y\sin x = 1$ is

Step-by-step Solution

Given that, $\cos x\frac{{dy}}{{dx}} + y\sin x = 1$

$\Rightarrow$ $\frac{{dy}}{{dx}} + y\tan x = \sec x$

Here, $P = \tan x$ and $Q = \sec x$

$IF = {e^{\int P dx}} = {e^{\int {\tan } xdx}} = {e^{\log \sec x}}$

$\therefore$ $= \sec x$

NCERT & Exemplar solution for CBSE Class 12 Mathematics, Differential Equations. Curated by Sachin Sharma. Free for all students.