---
title: "H2 Math Differential Equations Guide (9758) Singapore"
description: "Differential equations connect calculus to the real world. This guide covers solving separable equations, using given substitutions, general versus particular solutions, and modelling."
author: "Gabriel"
author_url: "https://ancourage.academy/authors/gabriel"
published_at: 2026-07-13
modified_at: 2026-07-13
category: "teaching"
tags: ["Mathematics", "JC", "A-Level", "H2 Math", "Differential Equations", "Calculus", "Singapore", "Exam Tips"]
canonical: "https://ancourage.academy/articles/h2-math-differential-equations-guide-singapore"
source: "https://ancourage.academy/articles/h2-math-differential-equations-guide-singapore"
language: "en-SG"
word_count: 1443
reading_time: "PT8M"
cover_image: "https://ancourage.academy/academic-pic/IMG_0153.jpg"
reviewed_by: "Min Hui"
---

# H2 Math Differential Equations Guide (9758) Singapore

Differential equations connect calculus to the real world. This guide covers solving separable equations, using given substitutions, general versus particular solutions, and modelling.

**Differential equations are where H2 calculus meets the real world — in H2 Mathematics every examinable equation is the separable first-order type, solved by separating the variables, integrating both sides, then fixing the arbitrary constant from a given condition.** Students who keep those steps in order find the topic far more predictable than it first appears. This guide is from [Ancourage Academy](https://ancourage.academy/academy), whose [JC H2 Mathematics tuition](https://ancourage.academy/courses/academy/jc/jc2/h2-maths) teaches differential equations step by step in small groups of 3–6 at [Bishan](https://ancourage.academy/find-us/bishan) and [Woodlands](https://ancourage.academy/find-us/woodlands).

This is a single-topic deep-dive — a sibling to our [H2 Math calculus](https://ancourage.academy/articles/h2-math-calculus-differentiation-integration-guide-singapore) and [sequences and series](https://ancourage.academy/articles/h2-math-sequences-series-guide-singapore) guides, and part of our wider [H2 Mathematics overview](https://ancourage.academy/articles/h2-mathematics-jc-guide-singapore). Differential equations build directly on integration, so secure that first.

**If differential equations are a gap, Ancourage Academy's [JC2 H2 Mathematics programme](https://ancourage.academy/courses/academy/jc/jc2/h2-maths) drills the separable-equation method directly — [book a trial class (usually $18)](https://ancourage.academy/trial-class) for a diagnostic assessment.**

## What Do Differential Equations Cover in H2 Math?

**In H2 Mathematics (9758), differential equations covers a single examinable form — the first-order separable equation dy/dx = f(x)g(y) — solved by separating the variables and integrating both sides, reducing an equation to that form using a given substitution, and formulating and interpreting differential equations that model rate-of-change situations.** The [SEAB Mathematics syllabus (9758)](https://www.seab.gov.sg/gce-a-level/a-level-syllabuses-examined-for-school-candidates-2026/) defines what is examinable; second-order equations and the integrating-factor method belong to other syllabuses, not 9758, and any substitution needed is always provided in the question.

## What Forms of Differential Equation Are Examinable?

**H2 Mathematics tests one form — the first-order separable equation, written dy/dx = f(x)g(y), where the right-hand side factorises into a function of x times a function of y.**

-   **Separable, dy/dx = f(x)g(y):** separate the variables and integrate both sides (the method below).
-   **The special case dy/dx = f(x):** this is just the separable form with g(y) = 1, solved by integrating once, y = ∫f(x) dx + C.
-   **Reducible by a given substitution:** a question may supply a substitution that turns a non-separable-looking equation into the separable form.

Each integration introduces one arbitrary constant, so a first-order equation needs exactly one given condition to pin it down. Second-order equations such as d²y/dx² = f(x), and the integrating-factor method, are not part of the 9758 syllabus — you never integrate twice or build an integrating factor. Forgetting the arbitrary constant is the most common single error in the whole topic.

## How Do You Solve a Separable Equation?

**A first-order equation is separable when you can write it so that all the y terms are on one side and all the x terms on the other — then you integrate both sides.**

1.  **Separate:** rearrange dy/dx = g(x)h(y) into (1/h(y)) dy = g(x) dx.
2.  **Integrate both sides** — remember the single arbitrary constant.
3.  **Make y the subject** if the question asks for the explicit solution.

When a substitution is provided (for example, "use the substitution u = …"), differentiate the substitution, replace the terms in the original equation, solve the resulting separable equation in the new variable, then substitute back. The substitution is always given — you are never expected to invent it.

## What Is the Difference Between General and Particular Solutions?

**The general solution contains the arbitrary constant(s) and represents a whole family of solution curves; the particular solution uses given conditions to fix the constant(s) and pick out one specific curve.**

| Term | Meaning |
| --- | --- |
| General solution | Includes the arbitrary constant(s) — a family of curves |
| Particular solution | Constant(s) found from given conditions — one curve |
| Family of solution curves | Sketch showing the general solution for several constant values |

When asked to sketch a family of solution curves, show how the curves shift as the constant changes and include any equilibrium or asymptotic behaviour — this is a graph-sketching question as much as a calculus one, drawing on [functions and graphs](https://ancourage.academy/articles/h2-math-functions-graphs-guide-singapore) skills.

## How Are Differential Equations Used in Modelling?

**Real-world rate-of-change problems are translated into a differential equation, solved, and then interpreted — the most common being exponential growth and decay, where the rate is proportional to the amount present.**

-   **Exponential model:** "the rate of change is proportional to the quantity" becomes dx/dt = kx, whose solution is exponential.
-   **Limited growth / cooling:** "the rate is proportional to the difference from a fixed value" leads to models such as Newton's law of cooling.

Translating the words into the correct equation is half the question — read carefully for "proportional to," the sign of k (growth vs decay), and the meaning of any constants in context.

## The Most Common Differential Equations Mistakes

**In our H2 Math classes at Ancourage Academy, a handful of recurring errors cause most avoidable mark loss in this topic.**

| Mistake | Why it happens | How to fix it |
| --- | --- | --- |
| Omitting the arbitrary constant | Treating it like a definite integral | Add the constant C when you integrate, before applying the given condition |
| Not separating fully | Leaving an x or y on the wrong side | Confirm only y-terms with dy and only x-terms with dx before integrating |
| Wrong sign of k | Misreading growth as decay | Decay means the quantity falls, so dx/dt is negative — check the context |
| Forgetting to substitute back | Leaving the answer in the substituted variable | After solving in u, replace u with the original expression |
| Mishandling the constant after a logarithm | Leaving ln |y| without exponentiating correctly | From ln |y| = g(x) + C, write y = A e^(g(x)), absorbing the constant into A |

## How Do Differential Equations Connect to the Rest of H2 Math?

**Differential equations are applied calculus, and they pull in graphing and earlier algebra.**

-   **Calculus:** integration is the engine of every solution. See our [calculus deep-dive](https://ancourage.academy/articles/h2-math-calculus-differentiation-integration-guide-singapore).
-   **Functions and graphs:** sketching families of solution curves uses graph-sketching skills. See our [functions and graphs guide](https://ancourage.academy/articles/h2-math-functions-graphs-guide-singapore).
-   **Partial fractions:** some separable equations need a fraction decomposed before integrating. See our A-Maths [partial-fractions guide](https://ancourage.academy/articles/a-maths-polynomials-partial-fractions-singapore).

## A Study Plan for Mastering H2 Differential Equations

**Work this topic in order: integration revision, then separable equations, then given substitutions, then modelling.**

1.  **Week 1 — integration revision:** make sure integration techniques are fluent, since every solution relies on them.
2.  **Week 2 — separable equations:** drill separating the variables and integrating both sides, tracking the arbitrary constant.
3.  **Week 3 — given substitutions:** practise reducing equations to separable form using the substitution provided in the question.
4.  **Week 4 — modelling:** translate worded rate-of-change problems into equations and interpret the solutions.

Ancourage Academy's [JC1](https://ancourage.academy/courses/academy/jc/jc1/h2-maths) and [JC2 H2 Mathematics](https://ancourage.academy/courses/academy/jc/jc2/h2-maths) programmes work through differential equations on exactly this progression in small groups of 3–6. Book a [trial class (usually $18)](https://ancourage.academy/trial-class) for a diagnostic, or [WhatsApp us](https://api.whatsapp.com/send/?phone=6588498106&type=phone_number&app_absent=0) with any questions.

## Common Questions About H2 Math Differential Equations

### What types of differential equation does H2 Math test?

H2 Mathematics tests one form: the first-order separable equation dy/dx = f(x)g(y), solved by separating the variables and integrating both sides. The special case dy/dx = f(x) is simply g(y) = 1, integrated once. A question may provide a substitution that reduces an equation to the separable form. It also tests forming and interpreting differential equations from real-world rate-of-change situations such as exponential growth and decay. Second-order equations and integrating factors are not in the 9758 syllabus.

### What is the difference between a general and a particular solution?

The general solution contains the arbitrary constant(s) from integration and represents an entire family of solution curves. The particular solution uses given conditions — such as a known value of y at a particular x — to find the constant(s) and identify one specific curve. A first-order separable equation has a single arbitrary constant, so one given condition is enough to fix it and pick out one specific solution curve.

### How do you solve a separable differential equation?

Rearrange dy/dx = g(x)h(y) so that all the y terms are with dy on one side and all the x terms are with dx on the other: (1/h(y)) dy = g(x) dx. Integrate both sides, adding a single arbitrary constant, then make y the subject if an explicit solution is required. If the equation is not directly separable, apply the substitution given in the question, solve, and substitute back.

### How do you model exponential growth with a differential equation?

When a quantity changes at a rate proportional to its current amount, the relationship is dx/dt = kx, where k is a constant. Separating and integrating gives an exponential solution. A positive k models growth and a negative k models decay, so read the context carefully to set the sign. Translating the worded statement into the correct equation is where most marks are won or lost.

Related: [H2 Mathematics Overview](https://ancourage.academy/articles/h2-mathematics-jc-guide-singapore) · [H2 Math Calculus](https://ancourage.academy/articles/h2-math-calculus-differentiation-integration-guide-singapore) · [Functions & Graphs](https://ancourage.academy/articles/h2-math-functions-graphs-guide-singapore) · [Sequences & Series](https://ancourage.academy/articles/h2-math-sequences-series-guide-singapore) · [A-Maths Partial Fractions](https://ancourage.academy/articles/a-maths-polynomials-partial-fractions-singapore)

## Related Courses

- [JC2 H2 Mathematics](https://ancourage.academy/courses/academy/jc/jc2/h2-maths) — Differential equations and A-Level exam preparation in small groups of 3–6
- [JC1 H2 Mathematics](https://ancourage.academy/courses/academy/jc/jc1/h2-maths) — Build the integration foundations differential equations rely on
- [JC Mathematics Programme](https://ancourage.academy/courses/academy/jc/mathematics) — All JC Mathematics courses at Bishan and Woodlands
- [Trial Class (Usually $18)](https://ancourage.academy/trial-class) — Diagnostic assessment of your child’s H2 Maths foundations

## Sources

- [Mathematics (Syllabus 9758) — 2026 Examination (seab.gov.sg)](https://www.seab.gov.sg/gce-a-level/a-level-syllabuses-examined-for-school-candidates-2026/) — Singapore Examinations and Assessment Board
- [A-Level Curriculum and Subject Syllabuses (moe.gov.sg)](https://www.moe.gov.sg/post-secondary/a-level-curriculum-and-subject-syllabuses) — Ministry of Education, Singapore
- [List of Formulae and Results for Mathematics and Further Mathematics (MF27) (seab.gov.sg)](https://www.seab.gov.sg/gce-a-level/) — Singapore Examinations and Assessment Board