- #1

fluidistic

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## Homework Statement

Calculate the general solution of the following DE reducible to a homogeneous one: x+y-2+(x-y+4)y'=0.

## Homework Equations

Not sure.

## The Attempt at a Solution

My idea is first to write the DE into the homogeneous form and then solve it via any method that work.

I've read on the Internet that a homogeneous DE is of the form y'(x)=ay(x) where a is a constant.

What I've done is [itex]\frac{dy}{dx}=\frac{2-x-y}{x-y+4}[/itex] for x-y different from 4. So it seems I could write [itex]\frac{2-x-y}{x-y+4} =\alpha y(x)[/itex] but I do not see how it's possible.

I don't really know how to go further.