Undetermined Coefficients. Here is an alternative way to solve the equation dy/dt = ay

Chapter 1, Problem 5

(choose chapter or problem)

Undetermined Coefficients. Here is an alternative way to solve the equation dy/dt = ay b. (i) (a) Solve the simpler equation dy/dt = ay. (ii) Call the solution y1(t). (b) Observe that the only difference between Eqs. (i) and (ii) is the constant b in Eq. (i). Therefore it may seem reasonable to assume that the solutions of these two equations also differ only by a constant. Test this assumption by trying to find a constant k such that y = y1(t) + k is a solution of Eq. (i). (c) Compare your solution from part (b) with the solution given in the text in Eq. (17). Note: This method can also be used in some cases in which the constant b is replaced by a function g(t). It depends on whether you can guess the general form that the solution is likely to take. This method is described in detail in Section 3.5 in connection with second order equations.