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## Homework Statement

Use separation of variables to solve (x+2y)y'=1 y(0)=2

## Homework Equations

u=2y+x >>I did not know how to start this, so i looked at the back of the book and it said to use that substitution

y=(u-x)/2, du=2dy+dx, dy=(du-dx)/2

## The Attempt at a Solution

so i got the following:

dy/dx=1/(x+2y)

(du-dx)/(2dx)=1/(x+2(u+x)/2)

(du-dx)/(2dx)=1/u

I could not separate the variables from here. Also, according to the back of the book, the answer is supposed to be 2y-2ln|2+x+2y|+4+2ln2=0. But the term -2ln|2+x+2y| has both x and y variables, so aren't the variables not separated? That still qualifies as a solution by Separation of Variables?