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!

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- Nov 27th 2010, 07:04 AMRF7tricky 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! - Nov 27th 2010, 07:57 AMFernandoRevilla
Using the standard method:

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

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

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

So, no integration tables and no computer. :)

Regards.

Fernando Revilla - Nov 27th 2010, 08:01 AMRF7
Yes, there it is, in integral form. I don't think this one can be solved without integral form.

- Nov 27th 2010, 08:27 AMFernandoRevilla
Right, it can't be solved in terms of elementary functions.

Regards.

Fernando Revilla - Nov 27th 2010, 08:29 AMRF7
Thanks for the help, Fernando~