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
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Which equation is homogeneous (dy/dx depends only on y/x)?
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Show that the first approximation is .
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After multiplying dy/dx + Py = Q by I = e∫P dx, the left-hand side equals:
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Euler's method is described as a 'numerical' method because it:
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A particular solution (as opposed to a general one) is found by:
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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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Write down the general solution.
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Write down the formula used in Euler's method.
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The integrating factor for dy/dx + (1/x)y = x is:
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Show that the integrating factor is .
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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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Find the general solution of dy/dx = 2xy.
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Multiplying x dy/dx + y = x² recognises the left side as:
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