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Methods of Mathematical Physics, Third Edition by Bertha Jeffreys, Harold Jeffreys

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Chapter 16SOLUTION OF LINEAR DIFFERENTIAL EQUATIONS OF THE SECOND ORDER

A merry road, a mazy road, and such as we did treadThe night we went to Birmingham by way of Beachy Head.

G. K. CHESTERTON, The Flying Inn

16·01.

When the coefficients in a differential equation are variable the chief methods of solution are as follows:

    (1) Direct numerical solution (Chapter 9). This is often laborious, but in many cases it is the only method.

    (2) Solution by power series.

    (3) Solution by substitution of definite or contour integrals.

    (4) Asymptotic solutions (Chapter 17). These can be obtained by several methods. Direct transformation of the differential equation will often yield solutions in the form of asymptotic series; also a solution ...

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