Further Maths - Coupled Differential Equations
Pearson Edexcel Further Mathematics 2022
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Flashcards
Solving coupled first-order systems
What is the general process for solving a coupled first-order differential equation?
Eliminating one of the variables to form a single second-order differential equation.
\[\frac{\text{d}x}{\text{d}t} = x + y \\\\ \frac{\text{d}y}{\text{d}t} = x - y\]
What are the 3 first steps?
Rewriting it as $y = ...$, differentiating and then substituting.
\[\frac{\text{d}x}{\text{d}t} = x + y \\\\ \frac{\text{d}y}{\text{d}t} = x - y\]
You’ve discovered
\[x = Ae^{\sqrt{2}t} + Be^{-\sqrt{2}t}\]
What do you now do to find $y$ in terms of $t$?
Differentiate $x$ and then substitute both back into the original differential equation for $\frac{\text{d}x}{\text{d}t}$.
Homogeneous systems
When is a coupled first-order differential equation “homogenous”?
If there are no extra $f(t)$ or $g(t)$ in either of the definitions.