1. The problem statement, all variables and given/known data Hi,I am learning to solve 2nd-order differential eq. Suppose I have a equation dy/dx - 3x = 0...........(1) Then dy/dx = 3x -----> x = 3(x^2)/2 Now if I have a 2nd order ODE such that: d^2y/dx^2 = 3.............(2) Then it could be solved by integrating both sides wrt x twice,which yields y = 3(x^2)/2 + Ax + B Now,consider the case: d^2y/dx^2 -6dy/dx + 9 = 0.........(3) I know it could be solved by using the idea of auxiliary equation(Putting y = Ae^(sx) into the initial eq) But,why it's not possible to solve (3) by using direct integration on both sides as in (1) and (2)? I can illustrate it here: d^2y/dx^2 = 6dy/dx - 9,then I integrate both sides wrt x dy/dx = 6 -9x + A y = 6x -9(x^2)/2 + Ax + B It's obviously incorrect,the (6+A)x term vanishes in the 2nd order derivative.Can someone tell me what's wrong?(I mean on the idea) Thx 2. Relevant equations 3. The attempt at a solution I have illustrated it in the problem statement.