Having problems with a linear 1st order ODE

I've got a linear 1st order ODE, which I'm trying to solve via integrating factors:

Book Answer:

So, from here, this is what I start out with:

But working from here would seem to require integrating , which I didn't think was trivially doable.

Where am I going wrong?

Re: Having problems with a linear 1st order ODE

Quote:

Originally Posted by

**Lancet** I've got a linear 1st order ODE, which I'm trying to solve via integrating factors:

Book Answer:

So, from here, this is what I start out with:

But working from here would seem to require integrating

, which I didn't think was trivially doable.

Where am I going wrong?

Put x=x'+2, dx=dx' in the ODE.

Edit: will not work!

Re: Having problems with a linear 1st order ODE

Quote:

Originally Posted by

**Also sprach Zarathustra** Put x=x'+2, dx=dx' in the ODE.

I don't understand. I also don't get why this can be done...

Can you clarify, please?

Re: Having problems with a linear 1st order ODE

Quote:

Originally Posted by

**Lancet** I've got a linear 1st order ODE, which I'm trying to solve via integrating factors:

Book Answer:

So, from here, this is what I start out with:

But working from here would seem to require integrating

, which I didn't think was trivially doable.

Where am I going wrong?

If you split up your integral you will have problems. Consider your integral (I have factored out a 3)

and try the substitution .

BTW, your initial ODE is separable

Re: Having problems with a linear 1st order ODE

Quote:

Originally Posted by

**Danny** If you split up your integral you will have problems. Consider your integral (I have factored out a 3)

and try the substitution

.

BTW, your initial ODE is separable

How I didn't see that?! (Headbang)

Re: Having problems with a linear 1st order ODE

Quote:

Originally Posted by

**Danny**

If you split up your integral you will have problems. Consider your integral (I have factored out a 3)

Wow, that's a nasty integration example, simple though it is. Thank you for showing that to me!

Quote:

Originally Posted by

**Danny**

BTW, your initial ODE is separable

<head smack>

Well, that would have made things considerably easier, had I seen that. Of course, I would have lost out on the integration lesson, so I'm happy with how things turned out.

Incidentally, is there a trick to spotting what something like this separates out into? Or is it just trial and error?

Re: Having problems with a linear 1st order ODE

Quote:

Originally Posted by

**Also sprach Zarathustra** How I didn't see that?! (Headbang)

I had the same reaction. :)