SECOND ORDER LINEAR DIFFERENTIAL EQUATION-A STUDY

MATHEMATICS

Given real-valued functions ao, a1 and b such that ao(t), a1(t) and b(t) ∈ R ∀ t ∈ R, the differential equation of the form y” + a1(t) y’ + ao(t) y = b(t) is known as a second-order linear differential equation with variable coefficients. The variable coefficients are ao(t) and a1(t). If b(t) = 0 then the above equation is called a homogeneous second-order differential equation. In this section give an in depth discussion on the process used to solve homogeneous, linear, second order differential equations, ay′′+by′+cy=0″+=0. We derive the characteristic polynomial and discuss how the Principle of Superposition is used to get the general solution. In this section we will a look at some of the theory behind the solution to second order differential equations. We define fundamental sets of solutions and discuss how they can be used to get a general solution to a homogeneous second order differential equation. We will also define the Wronskian and show how it can be used to determine if a pair of solutions are a fundamental set of solutions

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