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 are positive $A,B$ such that $|f(t)|\sim A+Bt $ for all large enough $t$?
Asymptotics of solutions to the ode $f''(t)-e^{2t} f(t)=0$
Lucia
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