1. The problem statement, all variables and given/known data Use separation of variables to solve (x+2y)y'=1 y(0)=2 2. Relevant 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 3. 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?