- #1

jellicorse

- 40

- 0

I've been going over the derivation for obtaining the integrating factor again in my book and there is one step I don't understand.

There's no point going through the whole thing from scratch, but I've got to the point where we need to multiply the whole DE by a function [tex]\mu(t)[/tex] such that the LHS of the DE is recognizable as the derivative of some function.

Need to choose [tex]\mu(t)[/tex] to satisfy:

[tex]\frac{d\mu(t)}{dt}=2[/tex] for this particular example.

[tex]\frac{d\mu(t)/dt}{\mu(t)}=2[/tex]

But I don't see how the next step follows from the previous one:

[tex]\frac{d}{dt}ln|\mu(t)|=2[/tex]

In particular, I don't see where the [tex]ln|\mu(t)|[/tex] has come from.

Can anyone tell me how this works?