1) it's not exact, I know that
2) I tried turning it into an exact equation using Euler's multiplicating factor (not sure this is the right word in English), but couldn't find the factor
3) tried the y/x=v substitution and ended up with:
xv + 1 + xv^3 - v^3 + x^2v^2v' - xv^2v' = 0
and I've no idea how to separate the x and v here
4) tried separating the variables and ended up with this:
what do I do?
1. no initial conditions
3. no intervals of validity in the text of the problem
2. didn't differentiate the solution, will do
I thought I was supposed to get a solution like "y = ....", not "ln|y+1| + etc = -ln|x-1| + etc +C"
It wouldn't be in the text of the problem. What you want to do is write the original DE in the form dy/dx = f(x,y), and examine the continuity of f(x,y) and compare to the standard existence theorem. In addition, you need to look at the domains of the functions in your solution, and see if that further restricts your intervals of validity. Sometimes the interval of validity is further restricted after you find a solution.3. no intervals of validity in the text of the problem
Hint: implicit differentiation is handy when faced with a solution like you have here. Another hint: differentiate in such a manner that the constant disappears. That's a trick I learned from Danny here on the forum.2. didn't differentiate the solution, will do
Looks like pickslides has answered this one perfectly adequately, as usual.I thought I was supposed to get a solution like "y = ....", not "ln|y+1| + etc = -ln|x-1| + etc +C"