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The diagram shows the direction field of a differential equation - HSC - SSCE Mathematics Extension 1 - Question 3 - 2023 - Paper 1
Question 3
The diagram shows the direction field of a differential equation. A particular solution to the differential equation passes through (−2,1). Where does the solution t... show full transcript
Worked Solution & Example Answer:The diagram shows the direction field of a differential equation - HSC - SSCE Mathematics Extension 1 - Question 3 - 2023 - Paper 1
Step 1
Where does the solution that passes through (−2,1) cross the y-axis?
Answer
To find where the solution crosses the y-axis, we need to identify where the x-coordinate is 0. Starting from the point (−2,1), we can trace the direction field in the diagram to determine the path of the solution.
Observing the direction field, we can see that the solution will move upward as it progresses from (−2,1) towards the y-axis. Based on the trajectory indicated by the arrows in the field, we can interpolate the value of y when x = 0.
From the diagram, it appears that the solution crosses the y-axis roughly at y = 1.56. Therefore, the answer is:
C. y = 1.56