Learning outcomes

After studying this course, you should be able to:

• understand the key role of the principle of superposition in the solution of linear constant-coefficient second-order differential equations

• obtain the general solution of a homogeneous linear constant-coefficient second-order differential equation using the solutions of its auxiliary equation

• use the method of undetermined coefficients to find a particular integral for an inhomogeneous linear constant-coefficient second-order differential equation with certain simple forms of right-hand-side function

• obtain the general solution of an inhomogeneous linear constant-coefficient second-order differential equation by combining its complementary function with a particular integral

• use the general solution together with a pair of initial or boundary conditions to obtain, when possible, a particular solution of a linear constant-coefficient second-order differential equation.