Question

A first order linear equation in the form y′+p(x)y=f(x) can be solved by finding an integrating factor μ(x)=exp⁡(∫p(x)dx) (1) given the equation y′+2xy=8x find μ(x)=

Answer 1

Answer-

$The \ integrating \ factor \ \mu (x) = e^{x^{2}}$

Solution-

Given differential equation is,

${y}'+2xy=8x$

Comparing it with the general equation of first order linear equation, we get that,

$p(x)=2x \ and \ f(x)=8x$

Now, calculating the value of the integrating factor,

$I.F. = \mu(x)=e^{\int p(x)dx} = e^{\int 2xdx} = e^{x^{2}}$