H2 Mathematics Differential Equations is a canonical JC topic guide for Singapore-Cambridge H2 Mathematics 9758, aligned to the 2027 SEAB syllabus. It is designed to sit between the stable mathematical object in BTT’s Knowledge Warehouse and the actual H2 examination demand.
Differential equations turn a statement about rate into a statement about the evolving quantity itself. In H2, the key move is modelling: translate a physical or real-world relationship into dy/dx, solve the separable equation, use initial conditions and interpret the result.
The 2027 syllabus includes general and particular solutions of separable differential equations, equations reducible to separable form by a given substitution, formulation from problem situations and interpretation of solutions.
Separate before integrating
For dy/dx=f(x)g(y), rearrange all y terms with dy and x terms with dx, then integrate. Division by g(y) can exclude equilibrium solutions when g(y)=0, so check whether a constant solution was lost during separation.
General versus particular solution
Integration introduces an arbitrary constant. An initial condition selects the particular member of the solution family. Students who substitute the condition before integrating often lose the logic of where the constant comes from.
Model formulation
“Rate of change is proportional to the amount present” translates to dQ/dt=kQ, with the sign of k determined by growth or decay. “Rate is proportional to the difference from ambient temperature” creates a Newton-cooling style model. Translate words into rate relationships before solving.
Interpret the solution
A mathematical solution may permit values that make no sense in context—negative population, time before the experiment begins, or quantity beyond a physical capacity. State the meaningful domain and interpret constants in context where possible.
- Failure: forgetting equilibrium solutions.
- Failure: missing +C.
- Failure: applying initial condition incorrectly.
- Failure: using the wrong sign in a growth/decay model.
- Failure: solving correctly but never returning to the model’s meaning.
H2 examination control
- State the mathematical model or condition before calculating.
- Keep exact values until the question requires approximation.
- Show enough working to expose the method; unsupported incorrect answers earn no marks.
- Use the approved graphing calculator as a tool, not as a substitute for interpretation.
- Re-read the answer in the context of the original question.
Return to JC Mathematics. Stable conceptual owner: Mathematics Knowledge Warehouse. Examination execution: Mathematics Examination Craft.
Syllabus check: SEAB H2 Mathematics 9758 for examination in 2027; checked 26 September 2026.
World Mathematics route: return to the World Mathematics Atlas to connect this JC topic with its prerequisites, international equivalents, examination routes and university Mathematics.