# Math Help - integration coefficient method eproach problem

1. ## integration coefficient method eproach problem

$(x+2e^{3y})\frac{dy}{dx}=1$

$(x+2e^{3y})dy=dx$

$(x+2e^{3y})dy-dx=0$

$X_{y}\neq Y_{x}$

$\frac{-X_{y}+Y_{x}}{X}=\frac{1}{-1}=-1$

$m'-m=0$

$m=ce^{-x}$

$(x+2e^{3y})e^{-x}dy-e^{-x}dx=0$

it gets much more complicated from here
is there any easier approach
?

2. $
(x+2e^{3y})dy -dx=0
$

Multiplying both sides by e^(-y)

$
(xe^{-y}+2e^{2y})dy -e^{-y}dx=0
$

$
X_{y} \; and \; Y_{x}
$