# tricky little first order linear DE

• November 27th 2010, 07:04 AM
RF7
tricky little first order linear DE
see if you can get this one.

y'=y-t^-2+t^-3-t^-1

t>0

No integration tables, please. And no computers. Thanks for looking and do tell if you can solve this one!
• November 27th 2010, 07:57 AM
FernandoRevilla
Quote:

Originally Posted by RF7
No integration tables, please. And no computers. Thanks for looking and do tell if you can solve this one!

Using the standard method:

(a) The general solution for $y'-y=0$ is $y=Ce^t$ .

(b) Tryng solutions of the form $y=C(t)e^t$ for the complete we obtain:

$y=e^t\left(\displaystyle\int \dfrac{e^{-t}(1-t-t^2)dt}{t^3}+C\right)$

So, no integration tables and no computer. :)

Regards.

Fernando Revilla
• November 27th 2010, 08:01 AM
RF7
Yes, there it is, in integral form. I don't think this one can be solved without integral form.
• November 27th 2010, 08:27 AM
FernandoRevilla
Quote:

Originally Posted by RF7
I don't think this one can be solved without integral form.

Right, it can't be solved in terms of elementary functions.

Regards.

Fernando Revilla
• November 27th 2010, 08:29 AM
RF7
Thanks for the help, Fernando~