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212 5. Some worked examples arising from physical problems

Figure 11. Circuit diagram for the triode oscillator.

The method of multiple scales leads us to introduce

and then equation (5.44), for becomes

We seek a solution in the form

which is periodic in T and uniformly valid as The equations for the first
three terms are

The general solution of equation (5.45a) is

(for arbitrary functions and and then equation (5.45b) can be written