I've some doubts about initial values problems involving differential equation with absolute values.
For example if I have a differential equation like $y'=|x+1|$ with initial condition $y(3)=-2$, since $3>-1$ I can trascurate the absolute value and solve $y'=x+1$, is it correct?
But if the condition is for instance $y(-1)=2$ then I must consider the two different cases? That is, $y'=x+1$ if $x>-1$ and $y'=-x-1$ if $x<-1$
Is this the right way to solve this kind of problems?