Consider the differential equation ay" + by' + cy = ix, where a, b, c, and k are
Chapter 3, Problem 43(choose chapter or problem)
Consider the differential equation ay" + by' + cy = ix, 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 = l/(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 =Ax, whereA = l/(2ak+ b).Explain how weknow 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= l/(2a).
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