Question: The motion of a particle moving along the x-axis obeys the differential equation:

$ \ddot x - 4 \dot x + 4x =-t^2 $

Find the solution for $ x(t)$, given $ x(0)=0 $ and $ \dot x (0) = 0 $.

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Can this be solved by treating it as a second-order non-homogenous differential equation? If so, re-formatting the questions equation, would it be:

$ \frac{d^2x}{dt^2} - 4 \frac{dx}{dt}+4x=-t^2$ ?

Answer: 
lol. a lot of confusion on this thread. When you are computing the midpoints, what you actually do is find the distance between them and divide by two. This isn't the coordinate of the midpoint; this is just the distance form one end to the midpoint.

What you meant to do is take the average of the x and y *values*, not the average of their difference.

You should get a midpoint of $(-1,-1.5)$.
First you computed midpoint of $X$ wrongly.

Later you evaluated $b$ wrongly.