Video Transcript
Consider the given slope field
graph representing a differential equation. If the solution of the differential
equation contains point 𝑆, which point can also belong to the solution?
Let’s trace solution curves through
each of the points in the direction of the pattern of slopes mapped out through the
line segments. Starting at the point in question,
𝑆, we can see that the solution curve could go through the point 𝐶. Although 𝐶 doesn’t lie exactly on
the line segment, it is within the pattern of the slope field marked out by a
solution through the point 𝑆. So point 𝐶 is a contender for the
solution through 𝑆. Let’s also check the points 𝐴, 𝐵,
𝐷, and 𝐸. Following the pattern of the slope
field through the point 𝐴, the solution does not coincide with the point 𝑆. So the point 𝐴 cannot belong to
the same solution as 𝑆. Following the pattern through the
point 𝐵, again this solution does not coincide with the point 𝑆. The same applies for point 𝐷 and
also for point 𝐸, so that only point 𝐶 could belong to a solution containing the
point 𝑆.
