# 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.

### 1 Answer

Relevance

- 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.

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