AN EXAMPLE OF A NON-HOMOGENEOUS EQUATION’S SOLUTION USING OPERATOR NOTATION

THE DIFFERENTIAL EQUATION

d2y/dx - dy/dx - 6y = x

CAN BE WRITTEN IN OPERATOR NOTATION

(D2 - D - 6)y = x

SYMBOLIC "FACTORING”, (D - 3)(D + 2)y = x

LET u = (D + 2)y, THEN WE HAVE (D - 3)u = x.

USING AN INTEGRATING FACTOR, exp{-3x}

OR, AFTER INTEGRATING,

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