28. Variation of Parameters. Consider the following method solving the general linear equation of first order: y' + p(!)y = g(t). (48) a. If g(() = 0 for all r, show that the solution is y = Aexp ( - / p(s) ar ). (49) where A is a constant. b. If g(r) is not everywhere zero, assume that the solution of equation (48) is of the form y = A(D) exp (- / pinar ). (50) where A is now a function of r. By substituting for y in the given differential equation, show that A(r) must satisfy the condition A'(t) = g(nexp ( / ponds ) (51) C. Find A() from equation (51). Then substitute for A(t) in equation (50) and determine y. Verify that the solution obtained in this manner agrees with that of equation (33) in the text. This technique is known as the method of variation of parameters; it is discussed in detail in Section 3.6 in connection with second- order linear equations