can someone explain 'change of variables' to me? when do you use it, and why? (not to mention HOW you use it!) I'm taking an intro to DE course, and the textbook only mentions the idea in an exercise, not in the text itself. my prof never covered it in class, either. for example, i was trying to solve this problem: x^2y'' + 5xy' + (4 + pi^2)y = ln x y(1) = y(e) = 0 a solution's manual told me to change variables: let t = ln x after a few lines, they simplified the original equation into: y'' + 4y' + (4 + pi^2)y = t can someone explain this to me?