Personally, I don’t like DEs because they are boring, a bit too much of calculation for my liking. Maybe this is my first and last post on DEs here.

Anyway, this is for a friend’s request…

So how do we solve non-separable ODE of this type?

The answer is multiplying both sides by the integrating factor.

The idea comes from the product rule and this, since

and if we replace the exponent of with , then

by chain rule

Therefore

becomes

then

**For example**

then the integrating factor is

hence, we have

since the initial value , we have

Therefore

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