What type of initial value problem is this?

Question

So I'm trying to solve this initial value problem:

$x^2 dy/dx + xy = 1$, $y(-1)=1$

Now I think that it's some sort of Linear Equation and I know how to solve linear equations like $dA/dt+1/100A=6$, $A(0)=50$ but for this equation, there's multiple variables and an $x^2$ in front of the dy/dx. So is this even a linear equation and if it is a linear equation then how could I solve it compared to equations like the one above?

Answer 1

Find an integrating factor. Start by diving by $x^2$, so that $\frac{dy}{dx}+\frac{1}{x}y=\frac{1}{x^2}$

Answer 2

Hint

Start changing variable $x y=z$, $y=\frac z x$, $y'=\frac{x z'-z}{x^2}$ and replace in the initial equation. You will arrive to something simple and easy.

I am sure that you can take from here.