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Separable solution families and maximal intervals topic check

Practise separable solution families and maximal intervals in H2 Mathematics, check independently, and return later to review. This check covers selected skills, not the whole course topic.

Learning goals

Formulate, use and interpret a mathematical model
Produce complete families, excluded solutions and initial-value solutions for polynomial-rate exponential equations
Produce exponential solution families and initial-value solutions in the original variable after a given dependent-variable shift
Produce quadratic-rate separable solution families, retain lost solutions and determine maximal initial-value intervals
Return quadratic-rate solutions from a supplied dependent-variable shift and determine their maximal initial-value intervals

GCE A-Level H2 Mathematics 2027

Start · Practise · Check · Review

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Answer each question and say how sure you are to find what to practise next.

Choose a practice setSolve exponential separable equations · 2 questionsReturn a supplied substitution to y · 2 questionsSolve quadratic-rate equations and select maximal intervals · 5 questionsRestore shifted quadratic-rate solutions and their domains · 5 questionsAll skills in this check

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Differential equations

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Differential equations

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Differential equations

Solve exponential separable equations · Check your progress

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Differential equations

Return a supplied substitution to y · Check your progress

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Differential equations

Solve quadratic-rate equations and select maximal intervals · Check your progress

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Differential equations

Restore shifted quadratic-rate solutions and their domains · Check your progress

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Differential equations

Solve exponential separable equations · Check again

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Differential equations

Return a supplied substitution to y · Check again

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Differential equations

Solve quadratic-rate equations and select maximal intervals · Check again

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Differential equations

Restore shifted quadratic-rate solutions and their domains · Check again

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Differential equations

Retention check

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Differential equations

Solve exponential separable equations · Retention check

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Differential equations

Return a supplied substitution to y · Retention check

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Differential equations

Solve quadratic-rate equations and select maximal intervals · Retention check

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Differential equations

Restore shifted quadratic-rate solutions and their domains · Retention check

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Differential equations

Practise: Solve exponential separable equations

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Differential equations

Practise: Return a supplied substitution to y

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Differential equations

Practise: Solve quadratic-rate equations and select maximal intervals

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Differential equations

Practise: Restore shifted quadratic-rate solutions and their domains

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Differential equations

Revision notes

Revise differential equations

Solve separable equations, retain initial-value domains and excluded solutions, then formulate and interpret changing-quantity models.

Key ideas

Separation, initial values and lost solutions
Retain equilibrium solutions, transform derivatives and initial-value domains, and formulate rate models with physical limits.

What the syllabus asks

From the GCE A-Level H2 Mathematics 2027 syllabus

Include: general and particular solutions of dy/dx = f(x)g(y), including reducing to this form by a given substitution; formulating a differential equation from a problem situation; interpreting an equation and its solution contextually.