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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