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Differential Equations — High School Calculus practice questions

12 multiple-choice questions and 8 flashcards on Differential Equations, about 8% of the High School Calculus bank. Every one carries a written rationale.

Written and maintained by the CoStudy team · last updated 2026-10-02 · how we write and review questions

What this chapter covers

Differential Equations is one of 8 chapters in CoStudy's High School Calculus bank, and it holds 12 of the bank's 150 multiple-choice questions — roughly 8% of the total. That proportion is not arbitrary: chapters follow the certifying body's published exam outline, and the number of questions in each is set by that domain's published weight, so the share of your practice time this chapter takes matches the share of the real exam it accounts for.

Studying by chapter is worth doing once you have a diagnostic score. A single overall percentage tells you whether you are close; it does not tell you which domain is dragging. Working a weak chapter in isolation, and re-testing it in isolation, is the fastest way to move a score that has stalled — and it is why the mock exams in CoStudy report by domain rather than as one number.

Free Differential Equations practice questions

3 questions drawn from this chapter, with the full rationale shown — the controlling principle behind the right answer, and why each wrong option tempts and fails.

What is the general solution of dy/dx = 3y?

  1. y = 3eˣ + C
  2. y = Ceˣ + 3
  3. y = Ce^(3x)
  4. y = 3x + C

Answer: C — y = Ce^(3x)

C) Correct — dy/y = 3 dx, so ln|y| = 3x + c. A) Moves the 3 outside and adds the constant. B) Adds 3 instead of using it as the growth rate. D) Treats y as a constant on the right side.

Which function solves dy/dx = 2x with y(0) = 1?

  1. y = x² + 1
  2. y = x²
  3. y = 2x + 1
  4. y = e^(2x)

Answer: A — y = x² + 1

A) Correct — Integrate to y = x² + C, then y(0) = 1 gives C = 1. B) Ignores the initial condition. C) Forgets to integrate 2x. D) Solves dy/dx = 2y instead.

In the slope field for dy/dx = y − x, what is the slope at (2, 3)?

  1. −1
  2. 5
  3. 1
  4. 3/2

Answer: C — 1

C) Correct — 3 − 2 = 1. A) Computes x − y. B) Adds instead of subtracting. D) Divides y by x.

Differential Equations flashcards

1 cards from the 8 in this chapter.

What is a differential equation?

An equation involving a function and its derivatives.

Practise the full chapter

These are a sample. The full Differential Equations chapter runs 20 items with per-chapter progress tracking, on the web and in the iOS app.

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