Second Order Homogeneous Linear Equations

A second order differential equation is an equation involving an independent variable t, a dependent variable y, and the first two derivatives y' and y". The general solution of a second order differential equation will usually involve two constants. Two initial values are needed to determine a particular solution. A second order initial value problem is a second order differential equation together with initial values for y and y'. This section gives a solution method for second order equations of the following very simple type.