1. The problem statement, all variables and given/known data This is a problem from an old exam I am reviewing for practice. Find a good approximation, for x large and positive to the solution of the following equation: y''-(3/x)y'+(15/(4x^2)+x^(1/2))y=0 Hint: remove first derivative term 2. Relevant equations 3. The attempt at a solution I'm not sure first of all that I understand the logic behind the hint. After taking this suggestion, my first inclination is to throw away the 15/4x^2 term, leaving y''+sqrt(x)y=0. This is an equation that while it seems simple, I'm ashamed to say I can't figure out how to solve. Also, according to the problem's solution, you actually throw away just the x^(1/2)y term. This leaves an easily solvable homogeneous Cauchy-Euler DE. But the logic doesn't seem to make sense to me. The solution says that x^(1/2)y and (3/x)y' are negligible at large x. However, isn't the 15/4x^2 term much smaller than these terms?