Thread: tricky little first order linear DE

1. 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!

2. 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 $\displaystyle y'-y=0$ 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

3. Yes, there it is, in integral form. I don't think this one can be solved without integral form.

4. 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

5. Thanks for the help, Fernando~