Construct a first-order linear ordinary differential equation so that all solutions are asymptotic to the functionf(t)=1+t2

ast

tends to infinity.

Construct a first-order linear ordinary differential equation so that all solutions are asymptotic to the function t) = 1 + t2 as t tends to innity. Hint: Basically this is a "guess and check" and "working backwards" type of problem. Assume that all your solutions are of the form y(t) = 1 + t2 + A(t) where the A(t) is some "nice" function with limtsoo A(t) = 0. Then find some sort of simple relationship involving y(t) and y' (t) that does not contain A(t). That relationship will be your differential equation