Unit 5: Calculus

Topic 5.18: Differential equations (HL only) Questions

Practice 20 exam-style questions for IB Math AA SL Topic 5.18. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.

11 mark
2026
Which equation is homogeneous (dy/dx depends only on y/x)?
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2Show that1 mark
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Show that the first approximation is .
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31 mark
2026
∫(1/y) dy equals:
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4Find1 mark
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Find in terms of .
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51 mark
2026
After multiplying dy/dx + Py = Q by I = e∫P dx, the left-hand side equals:
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61 mark
2026
Separating dy/dx = y/x gives:
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71 mark
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Euler's method is described as a 'numerical' method because it:
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81 mark
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The general solution of dy/dx = y is:
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91 mark
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A particular solution (as opposed to a general one) is found by:
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101 mark
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For dy/dx = y with y(0) = 1 and h = 1, one Euler step gives y(1) ≈
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111 mark
2026
In Euler's method, h represents:
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12Write down1 mark
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Write down the general solution.
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13Write down1 mark
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Write down the formula used in Euler's method.
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141 mark
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The integrating factor for dy/dx + (1/x)y = x is:
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15Show that1 mark
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Show that the integrating factor is .
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16Find1 mark
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Find the integrating factor.
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17Find3 marks
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For dy/dx = x − y with y(0) = 2, use Euler's method with h = 0.5 to estimate y(1).
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18Show that2 marks
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Show that satisfies .
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19Find3 marks
2026
Find the general solution of dy/dx = 2xy.
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201 mark
2026
Multiplying x dy/dx + y = x² recognises the left side as:
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