I'm under the impression that any implicit method for numerically solving ODE should be providing high stability in exchange for accuracy. I'm trying to solve the differential equation: dy/dx = -1000y + 3000 - 2000exp(-x) with intial conditions (0,0). I still can't understand how come the numerical solution using the Implicit Midpoint is oscillating if it is supposed to be a stable method. Judging from the values, they oscillate between ~0 and~2. Am I missing something here?