Further MathematicsCode 9231
Differential equations
What this topic asks you to be able to do
- work out an integrating factor for a linear differential equation of first order, then apply that factor to obtain the general solution
- state what is meant by the terms ‘complementary function’ and ‘particular integral’ as they apply to linear differential equations, and state that the general solution equals the complementary function plus a particular integral
- work out the complementary function of a linear differential equation of first or second order whose coefficients are constant
- recall the form a particular integral takes, and find one, for a linear differential equation of first or second order when the right form to try is acos px + b sin px, a polynomial, or a e^bx; and, for other simple cases in which a suitable form for the particular integral is given, find the coefficient(s) that are needed
- apply a substitution provided to transform a differential equation into either a linear equation of first or second order with constant coefficients, or a first order equation whose variables are separable
- use initial conditions to pin down a particular solution of a differential equation, and say what a solution means in the setting of the problem that the equation models