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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 shown in the diagram around the point (−2,1). The y-axis corresponds to the location where x = 0.
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Visual Analysis: From the diagram, trace the direction field lines starting from (−2,1). Observe how the solution curve behaves as it approaches the y-axis.
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Estimate Intersection: Identify the point on the y-axis where the directional arrows suggest the solution is headed. This requires estimating through the visual representation.
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Select from Options: Given the options (y = 1.12, 1.34, 1.56, 1.78), the correct y-value as per the direction field indicates that the solution crosses the y-axis at approximately y = 1.56.
Therefore, the solution crosses the y-axis at y = 1.56, which corresponds to option C.