Answer-
[tex]The \ integrating \ factor \ \mu (x) = e^{x^{2}}[/tex]
Solution-
Given differential equation is,
[tex]{y}'+2xy=8x[/tex]
Comparing it with the general equation of first order linear equation, we get that,
[tex]p(x)=2x \ and \ f(x)=8x[/tex]
Now, calculating the value of the integrating factor,
[tex]I.F. = \mu(x)=e^{\int p(x)dx} = e^{\int 2xdx} = e^{x^{2}}[/tex]
