integration coefficient method eproach problem

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October 21st 2010, 10:12 AM
transgalactic

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
?
October 21st 2010, 01:57 PM
zzzoak

$<br /> (x+2e^{3y})dy -dx=0<br />$
Multiplying both sides by e^(-y)

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

Now test please

$<br /> X_{y} \; and \; Y_{x}<br />$

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