1. ## seperation of variables

dx/x=dy/(x+y)

Seperation of variables is not straight forward here. I have solved in maple and get y=(ln(x) + c1)*x. Since this is a fluids class I can use maple for the hw. How do you do this by hand. Is it a substitution type seperation of variables?

2. Originally Posted by MarionButler
dx/x=dy/(x+y)

Seperation of variables is not straight forward here. I have solved in maple and get y=(ln(x) + c1)*x. Since this is a fluids class I can use maple for the hw. How do you do this by hand. Is it a substitution type seperation of variables?

$
\frac{dy}{dx} = \frac{x+y}{x} = \frac{y}{x} + 1
$

We can do this two ways

1) Homogeneous: If you let $y = xu$ the DE will separate

2) if we write the DE as $
\frac{dy}{dx} - \frac{y}{x}= 1
$
this is linear with a integrating factor of $\frac{1}{x}.$