The integrating factor of dx - y = x 4 - 3x is

Given that, x dx - y = x 4 - 3x dx - x = x 3 - 3 Here, P = - x ,Q = x 3 - 3 IF = e P dx = e - x dx = e - x = x

Differential Equations — Class 12 Maths Solution

exemplar objective MCQ NCERT EXEMP.Q.43,Page.196

Question

The integrating factor of $\frac{{xdy}}{{dx}} - y = {x^4} - 3x$ is

Step-by-step Solution

Given that, $x\frac{{dy}}{{dx}} - y = {x^4} - 3x$

$\Rightarrow$ $\frac{{dy}}{{dx}} - \frac{y}{x} = {x^3} - 3$

Here, $P = - \frac{1}{x},Q = {x^3} - 3$

$\therefore \mid$ $IF = {e^{\int P dx}} = {e^{ - \int {\frac{1}{x}} dx}} = {e^{ - \log x}}$

$= \frac{1}{x}$

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