Unit 5: Calculus
Topic 5.14: Differential equations (HL only) Questions
Practice 16 exam-style questions for IB Math AI SL Topic 5.14. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
21 mark
2026
The differential equation dy/dx = ky (k constant) has general solution:
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2026
A first-order differential equation is 'separable' when dy/dx can be written as:
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2026
When you integrate both sides of a separated equation, how many constants of integration do you write?
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2026
Solve the differential equation dy/dx = 3x²y given that y = 2 when x = 0.
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2026
A radioactive sample decays so that dm/dt = −0.04m (m in grams, t in years). Initially there are 50 g. Find m(t) and the mass after 25 years.
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2026
Salt dissolves out of a tank so that the mass of salt S (kg) satisfies dS/dt = −S/20, with S = 12 kg at t = 0 (t in minutes). Find S after 30 minutes.
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2026
Given dy/dx = x/y with y = 4 at x = 0, the solution is:
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2026
Write down a differential equation for the population at time , and its general solution.
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2026
After solving dθ/dt = −k(θ − 20) for a cooling object, the long-term temperature (t → ∞) is:
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2026
An online video's number of views N (thousands) grows by dN/dt = kN, t in days. There are 5 thousand views at t = 0 and 20 thousand at t = 3. Find k, then predict the views after 7 days, and comment.
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2026
A hot metal bar cools by Newton's law: dθ/dt = −0.08(θ − 18), θ in °C, t in minutes, room at 18°C. The bar starts at 98°C. Find θ(t) and the temperature after 15 minutes.
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2026
A model gives velocity by dv/dt = x/v in the form dy/dx = x/y, with y = 3 when x = 0. Solve for y.
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