Second Order Differential Equations – Edexcel FP2

5. Second Order Differential Equations – Edexcel Further Pure Mathematics 2 (FP2)

What students need to learn:
The linear second order differential equation $a\dfrac{d^2y}{dx^2} + b\dfrac{dy}{dx} + cy = f(x)$ where $a$, $b$ and $c$ are real constants and the particular integral can be found by inspection or trial.
The auxiliary equation may have real distinct, equal or complex roots. $f(x)$ will have one of the forms $ke^{px}, A + Bx, p + qx + cx^2$ or $m \cos \omega x + n \sin \omega x$.

Students should be familiar with the terms ‘complementary function’ and ‘particular integral’.

Students should be able to solve equations of the form
$\dfrac{d^2y}{dx^2} + 4y = \sin 2x$.

Differential equations reducible to the above types by means of a given substitution.

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