Coupled First Order Linear Equations (Edexcel A-Level Further Mathematics): Flashcards

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Coupled First Order Linear Equations
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Coupled 1st order linear equations involve

Two or more dependent variables

Example application of coupled differential equations

Predator-prey dynamics

General form: dfdt=?\frac{df}{dt} = ?, drdt=?\frac{dr}{dt} = ?

af+braf + br, cf+drcf + dr

Step 1 to solve coupled equations

Rewrite as 2nd-order equation for one variable

Step 2 to solve coupled equations

Solve the 2nd-order equation

Step 3 to solve coupled equations

Back-substitute to find other variable

General solution for 2nd-order linear DE

y=Aem1t+Bem2ty = Ae^{m_1t} + Be^{m_2t}

Initial conditions used to find

Constants A and B

emte^{mt} determines the long-term behavior

Exponential growth, decay, or oscillation

Always analyze this in coupled equation solutions

Physical or long-term meaning

Explore Edexcel A-Level Further Mathematics Revision Notes by Topics

First Order Differential Equations

Second Order Differential Equations

Simple Harmonic Motion

Explore Edexcel A-Level Further Mathematics Model Answers by Topics

First Order Differential Equations

Second Order Differential Equations

Simple Harmonic Motion

Explore Edexcel A-Level Further Mathematics Quizzes by Topics

First Order Differential Equations

Second Order Differential Equations

Simple Harmonic Motion

Explore Edexcel A-Level Further Mathematics Exam Questions by Topics

First Order Differential Equations

Second Order Differential Equations

Simple Harmonic Motion

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