Question

how to find integrating factor of dy/dx - y=x​

Answer 1

Answer:

we have dy/dx - y= x

here p= -1

so integrating factors= e^✓ pdx

I.F = e^ ✓-1 dx = e^-x

Answer 2

Answer:

The integrating factor of the given expression will be:

$I.F=e^{-x}$

Step-by-step explanation:

Given function is:

$\dfrac{dy}{dx}-y=x$

If we write:

$\dfrac{dy}{dx}=y'$

Hence the given function will become as:

$y'-y=x$

This is is the form of first order linear differential equation.

The general form is:

$y'+P(x)y=Q(x)$

Hence we can write as:

$P(x)=-1\\Q(x)=x$

Therefore integrating factor (I.F) will be:

$I.F=e^{\int P(x)\ dx}\\I.F=e^{\int -1\ dx}\\I.F=e^{-x}$