1. The problem statement, all variables and given/known data Show that the origin (0,0) is a critical point. Write the linear differential equation in operator format and solve. 2. Relevant equations x'' + 10x' + 25x = 0 3. The attempt at a solution I am not sure how to show that the origin is a critical point (without using a graph). As for solving the 2nd-order linear differential equation, here's what I did: x'' + 10x' + 25x = 0 Auxillary equation: m2 + 10m + 25 = 0 Roots: m1 = m2 = -5 General solution: x = c1e-5x + c2xe-5x I believe my general solution is correct, but am not sure if I solved it by "operator method".