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