The equation dy/dx = x - y has the solution y = x - 1 + Ke⁻ˣ…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
The equation has the solution . The curve passes through . Find and then the heights and to four decimal places. The curve approaches the line . Find how far above the line the curve is at , to four decimal places.
Need a reminder? The key ideaShow
The equation gives the slope at every point. A solution curve follows these slopes, and two curves never cross. A step along the field is
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Given. and the point .
Plan. Find from the point, then evaluate.
Step 1. The constant. , so and .
Step 2. The heights. . Next, .
Step 3. The gap. At the gap is .
Answer: , and a gap of .
Check. The gap shrinks as grows: at , then at and at . The curve hugs the line.
Discussion (0)
Log in to join the discussion.
Loading…