2025 HSC Mathematics Extension 1
Question 12(d):
Differential equation
Find the solution of , given that when .
How to recognise this question
Question type: differential equations
- The command and notation point to differential equations.
- The requested response is a worked solution.
How to handle it: separate or integrate the differential equation, include the constant, then use the initial condition.
Watch out: Do not select a formula until its domain, interval, sign and units match the question.
Step-by-step answer
- Separate variables: .
- Integrating in the form used by the marking guide gives .
- Using gives .
- Therefore , so on the applicable interval.
Common mistake: choosing a familiar formula before checking that its conditions, signs, interval and units match this question.
The paper records 3 total marks for this group. Where the official marking guide provides useful partial-credit criteria, those criteria are stated in the steps above.
Try your hand at it again by answering these questions
Question 1
Solve given .
Question 2
Solve with .
Question 3
Solve with and .