Home page for accesible maths 6 Chapter 6 contents 6.28 Some PIs and CFs 6.30 Second order linear, constant coefficients

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6.29 Higher order linear differential equations

Extending the definition given on slide 6.18 to higher degrees, we have:

Definition.

A linear differential equation of order $n$ is an equation of the form:

\frac{d^{n}y}{dx^{n}}+p_{n-1}(x)\frac{d^{n-1}y}{dx^{n-1}}+\ldots+p_{0}(x)y=q(x)

where $p_{n-1}(x),\ldots,p_{0}(x),q(x)$ are functions of $x$ .

The corresponding homogeneous equation is obtained by replacing $q(x)$ by the zero. You already saw how to solve some quadratic (i.e. order 2) linear equations, in slides 4.45-49 in MATH101. We will only (as in MATH101) be interested in second order linear equations with constant coefficients. However, we will now consider the inhomogeneous case. (Only homogeneous equations were considered in MATH101.)