Consider the ode 
$$
f''(t)-e^{-2t} f(t)=0.
$$
What is the general behaviour of $|f|$ for large $t$s? 

Is it true that there exists an $A\in \mathbb{R}$ and there exists a positive $B$ such that $|f(t)|\sim  A+Bt $ for all large enough $t$?