Question

Solve y'=(y+x)/x explicitly.

Answer 1

@SithsAndGiggles

Answer 2

What method do I use?

Answer 3

It's a linear equation:
\[\begin{align*}
y'&=\frac{y+x}{x}\\
&=\frac{1}{x}y+1\\
y'-\frac{1}{x}y&=1
\end{align*}\]

Answer 4

So integrating factor method?

Answer 5

Yes

Answer 6

Got it! I was overthinking. :)

Answer 7

You could probably also try a substitution to make it separable... but rewriting as a linear eq is simple enough.

Answer 8

Thanks for the extra info!