FRQ — Differential Equations

Free response·Hard exam skill (4/5)·No calculatorNeeds mentor review

Difficulty guide

The label describes the problem, not your ability.

1/5 - Foundational

Warm-up setup; checks one basic idea.

2/5 - Routine exam skill

Normal syllabus skill; usually one main rule or interpretation.

3/5 - Standard multi-step

Exam-style problem with multiple steps or a common trap.

4/5 - Hard exam skill

High-end exam problem; combines methods carefully.

5/5 - Challenge

Stretch problem beyond normal exam pressure.

Question

Consider the differential equation

\frac{dy}{dx}=\frac{x}{y}

and the function

y=\sqrt{x^2+8}.

Total: 4 points

(a) Verify that $y=\sqrt{x^2+8}$ satisfies the differential equation. (2 points)

(b) Determine the value of $y(1)$ and state whether the function satisfies the initial condition $y(1)=3$ . (1 point)

Your response (optional — you can also work on paper)

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