A-Level Further Pure Maths 2-Differential Equations Lesson Booklet + Answers

The resource covers:

• Find an integrating factor for a first order linear differential equation, and use an integrating factor to find the general solution

• 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 first or second order linear differential equation with constant coefficients

• Recall the form of, and find, a particular integral for a first or second order linear differential equation in the cases where a polynomial or ae^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 given substitution to reduce a differential equation to a first or second order linear equation with constant coefficients or to a first order equation with separable variables.

• 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