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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 ... 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 determine where the solution crosses the y-axis, we need to analyze the direction field around the point (-2, 1).
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Understanding the Direction Field: The direction field provides visual cues about the behavior of solutions to the differential equation. At each point, the arrows indicate the slope of the solution curves.
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Behavior Near the Point (-2,1): From point (-2, 1), we need to trace the curve as it moves towards the y-axis, where x = 0.
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Finding the Intersection: As we observe the direction of the arrows leading from (-2, 1), we estimate where this curve will next intersect the y-axis (x=0). It appears that it will cross at approximately y = 1.56 based on visual approximation of the nearby arrows.
Thus, the solution that passes through (-2, 1) crosses the y-axis at: C. y = 1.56.