- #1

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## Homework Statement

Solve the initial value problem:

dx/dt = x(2-x) x(0) = 1

## Homework Equations

Problem statement.

## 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?