MATH215 Lecture 11: note11
13 Mar 2017
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Let us consider the nonhomogeneous second order linear di erential equation ay + by + cy = g(x), (1) where a, b, and c are constants with a 6= 0, and g is a continuous function on some open interval. Suppose that y1 and y2 are two linearly independent solutions to the associated complementary equation ay + by + cy = 0. (2) Then the general solution to the homogeneous equation (2) is given by yc = c1y1 + c2y2, where c1 and c2 are arbitrary constants. If we can nd a particular solution yp to the nonhomogeneous equation (2), then the general solution of the nonhomogeneous equation (2) is given by y = yp + yc. In order to nd a particular solution to the nonhomogeneous equation (2), we use the method of variation of parameters. The method consists of seeking a solution to (2) in the form y(x) = v1(x)y1(x) + v2(x)y2(x).
