Maths with David

    IBDP. AI. HL. DEs. Coupled Linear DEs

    Let’s consider the following specific form of coupled DEs:

    \frac{dx}{dt} = ax + by

    \frac{dy}{dt} = cx + dy

    We can rewrite these in matrix form as \begin{pmatrix} \frac{dx}{dt} \\ \frac{dy}{dt} \end{pmatrix} = \begin{pmatrix} a & b \\ c & d \end{pmatrix}

    In matrix notation we can write this as \bold { \dot{x} } = \bold{A} \bold{x}