1. The problem statement, all variables and given/known data Solve the initial value problem: dx/dt = x(2-x) x(0) = 1 2. Relevant equations Problem statement. 3. The attempt at a solution Based on the format, I attempted to solve the problem as a separable differential equation: ∫dx/(x[2-x]) = ∫dt Evaluating to: (ln|x|)/2 - (ln|2 - x|)/2 + C = t + C Simplifying ln|x| - ln|2 - x| + 2C = 2t + 2C Cancelling the constant ln|x| - ln|2 - x| = 2t Removing the logs x - (2 - x) = e^2t Simplifying further 2x - 2 = e^2t And finally solving for x: (e^2t)/2 + 1 Which gives me a function, but for t = 0, x(0) = 3/2, not 1. Should I be using another technique, or did I make a mistake somewhere in the process above?