See Also
Flashcards
2021-09-10
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 $\frac{\text{d}x}{\text{d}t}$.
When is a coupled first-order differential equation “homogenous”??
If there are no extra $f(t)$ or $g(t)$ in either of the definitions.
Backlinks
Metadata
date: 2021-09-10 17:22
tags:
- '@?further-maths'
- '@?school'
- '@?public'
- '@?differential-equations'
title: Further Maths - Coupled Differential Equations