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!
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
Right, it can't be solved in terms of elementary functions.
Regards.
Fernando Revilla