# 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.