I am not quite sure if this question is appropriate for this site as it might be not of a research level. I am interested in the following ordinary differential equation on the real line $$f’’(x)+(x-a)f(x)=0$$ where $a>0$.
Is it possible to solve it explicitly? or using say hypergeometric functions? In any case, I would be interested to know asymptotic behavior of solutions when $x\to +\infty$.