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

`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)}`