Differential equation — Field discipline

Question

State two properties that any correctly drawn particular solution on a direction field must satisfy.

This practice question was inspired by Question 12(a) in the 2021 NSW HSC Mathematics Extension 1 examination, © NESA. It is an original TestMum variation that practises the same mathematical idea, not an official NESA question.

Set up the solution: separate or integrate the differential equation, include the constant, then use the initial condition.It passes through the prescribed initial point.
State the final answer clearly in the form the question requested.At every point on the curve, the tangent matches the direction-field element (no transverse crossings of slope marks).

Common mistake: changing so many features that the new example no longer tests the same mathematical idea.

Verification: These are the marking criteria in the exam note.

Any mark labels are a TestMum study aid, not an official NESA marking allocation.