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Physical Mathematics by Kevin Cahill

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6

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Differential equations

6.1 Ordinary linear differential equations

There are many kinds of differential equation – linear and nonlinear, ordinary and partial, homogeneous and inhomogeneous. Any way of correctly solving any of them is fine. We start our overview with some definitions.

An operator of the form

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(6.1)

is an nth-order, ordinary, linear differential operator. It is nth order because the highest derivative is dn/dxn. It is ordinary because all the derivatives are with respect to the same independent variable x. It is linear ...

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