# Differential Equations – Further Maths Paper 1

Candidates should be able to:

• recall the meaning of the terms ‘complementary function’ and ‘particular integral’ in the context of linear differential equations, and recall that the general solution is the sum of the complementary function and a particular integral;
• find the complementary function for a second order linear differential equation with constant coefficients;
• recall the form of, and find, a particular integral for a second order linear differential equation in the cases where a polynomial or $$e^{bx}$$ or $$a \cos px + b \sin px$$ is a suitable form, and in other simple cases find the appropriate coefficient(s) given a suitable form of particular integral;
• use a substitution to reduce a given differential equation to a second order linear equation with constant coefficients;
• use initial conditions to find a particular solution to a differential equation, and interpret a solution in terms of a problem modelled by a differential equation.

An introduction to the solution of second order differential equation