Consider the differential equation $${{dx} \over {dt}} = 10 – 0.2x$$ with initial conduction x(0) = 1. The response x(t) for t > 0 is

The correct answer is A. 2 – e-0.2t.

The differential equation is separable, so we can write it as $dx = (10 – 0.2x) dt$. Integrating both sides gives $x = 10t – 0.1x^2 + C$, where $C$ is an arbitrary constant. Using the initial condition $x(0) = 1$, we can solve for $C$ to get $C = 2$. Therefore, the solution is $x(t) = 10t – 0.1x^2 + 2$.

Option B is incorrect because it does not include the term $10t$. Option C is incorrect because it does not include the term $-0.1x^2$. Option D is incorrect because it has the wrong sign in front of the exponential term.