2024 HSC Mathematics Extension 1
Question 11(d):
Differential equation
Solve the differential equation , given . Express your answer in the form .
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: (valid since ).
- Integrate: .
- Exponentiate: .
- Write , so . Equivalently is already in the form .
- NESA 11(d): 2 marks for the correct solution; 1 mark for separating the variables (or equivalent merit). Answers may include with .
Common mistake: choosing a familiar formula before checking that its conditions, signs, interval and units match this question.
The paper records 2 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 for , expressing the answer as or with .
Question 2
Solve for . Express in exponential form.
Question 3
Solve with and .