$(2x+y)\frac{dy}{dx} + x = 0$ Solve:
  $(2x+y)\frac{dy}{dx} + x = 0$ .


Only solving seperable equations and use of an integrating factor have been covered so far, and I can't see how to get it into a form such that it is solvable by these methods.
Try  $y = vx $

$\implies   y' = v'x + v$

The equation becomes
$$(2x+vx)(v'x+v) + x = 0 \\ (2+v)(v'x+v)+1 = 0$$

which is separable
That is :
$(x+y)dy + xdx=0$

Which is
$xdy + ydy + xdx = 0$

Integrate all parts:
$xy + \frac{y^2+x^2}{2}=c$