Solution: Consider the differential equation ay by cy ekx, where a, b, c, and k are
Chapter 4, Problem 43(choose chapter or problem)
Consider the differential equation ay by cy ekx, where a, b, c, and k are constants. The auxiliary equation of the associated homogeneous equation is am2 bm c 0. (a) If k is not a root of the auxiliary equation, show that we can find a particular solution of the form yp Aekx, where A 1(ak2 bk c). (b) If k is a root of the auxiliary equation of multiplicity one, show that we can find a particular solution of the form yp Axekx, where A 1(2ak b). Explain how we know that k b(2a). (c) If k is a root of the auxiliary equation of multiplicity two, show that we can find a particular solution of the form y Ax2ekx, where A 1(2a). 44. Di
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