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

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Coupled First Order Linear Equations
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What do coupled first-order linear equations involve?

Two or more dependent variables

What real-world situation do coupled equations often model?

Predator-prey dynamics

What is the first step in solving coupled differential equations?

Rewrite as second-order equation

In the worked example, what is the characteristic equation?

m2−6m−48=0m^2 - 6m - 48 = 0

What are the roots of the characteristic equation in the example?

m=10.5m = 10.5 and m=−4.5m = -4.5

What is the general solution form for f(t)f(t) in the worked example?

f(t)=Ae10.5t+Be−4.5tf(t) = Ae^{10.5t} + Be^{-4.5t}

What are the values of constants AA and BB in the worked example?

A=0.5A = 0.5, B=1.5B = 1.5

What is the long-term behaviour as t→∞t \to \infty in the example?

Unbounded growth

Which is a common mistake when solving coupled equations?

Errors in substitution

Explore Edexcel A-Level Further Mathematics Revision Notes by Topics

First Order Differential Equations

Second Order Differential Equations

Simple Harmonic Motion

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First Order Differential Equations

Second Order Differential Equations

Simple Harmonic Motion

Explore Edexcel A-Level Further Mathematics Flashcards 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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