How Do You Solve Linear Differential Equations with an Integrating Factor?

[franky2727]

methord to use?

find the solution of the initial value problem y'+(3/x)y=e^2x/x³ y(1)=1

 

[cellotim]

What type of question do you think it is?

 

[HallsofIvy]

This is a linear differential equation. Probably the simplest way to do it is to find an integrating factor. Can you find a function, $\mu(x)$ such that
$$\frac{d\mu y}{dx}= \mu\frac{dy}{dx}+\frac{d\mu}{dx}y= \mu\frac{dy}{dx}+(3\mu /x^3)y$$?