Are there instances in an unseparable differential equation where after using substitution, the variables are still not separable? ?
If yes, is it ok to integrate?
I'm new to this so I have a lot of questions, pls pardon me if my question is kinda dumb.
- Ian HLv 72 months ago
Yes, there are many DEs that are non-separable
This type of first order linear differential equation is usually non-separable
dy/dx + P(x)y = Q(x)
but fortunately it has a solution given by
I(x)*y = ∫ [I(x)Q(x)] dx
where I = e^ ∫P(x) dx is called the INTEGRATING FACTOR
Justification of this method with several worked examples at this link.