How to find particular integrals

Complete solution = complementary function + particular integral. 

We must now review the processes for finding particular integrals. Let B be written in place of f(x), so that (1) may be written f(D y = B. Consequently, we may write, 

The right-hand side of either of equations (2), will furnish a particular integral of (1). The operation indicated in (2) depends on the form of /(D). Let us study some particular cases. 

On page 396 we have defined /(D) lB to be that function of x which gives B when operated upon by /(D). Consequently, 

Examples.—(1) In the preceding illustration, put R = eix and show that the general solution is, CxtPx + C P + e%x. 

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