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## Homework Statement

Verify Differential Equation Solution

dX/dt=(2-x)(1-x)

## Homework Equations

The solution is ln ((2-x)/(1-x))=t

## The Attempt at a Solution

The derivative of the solution is -1/(2-x) dX/dt - (-1)/(1-x) dX/dt=1

But I plug this derivative in and I get stuck. How am I supposed to plug the solution and the derivative of the solution into the original differential equation? Can you help me set this up? I'm going to need a little help along the way...