Maths with David

    IBDP. AI. HL. DEs. Second Order DEs

    The order of a DE tells us the highest order of derivative, i.e. a second order DE includes terms of \frac{d^2 y}{dx^2}

    Can you think of some examples of second order differential equations?

    Any DE of the form a \frac{d^2x}{dx^2} + b \frac{dx}{dt} + cx = 0 an be rewritten as a system of coupled first order linear DEs, allowing us to use second order linear DEs, as shown in the followign example.

    Worked Example 1

    A Van der Pol oscillator is an electrical circuit involving a triode. It evolves in time according to the second order differential equation first identified by Balthasar van der Pol: \frac{d^2I}{dt^2} - \mu (1-I^2) \frac{dI}{dt} + I = 0 where 0 < \mu < 4 is a parameter.

    Rewrite the equation as a coupled system of first order differential equations.

    Exercise 1

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    Answers to Exercise 1

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