Consider the nonhomogeneous nth order linear differential
Chapter 4, Problem 19(choose chapter or problem)
Consider the nonhomogeneous nth order linear differential equationa0y(n) + a1y(n1) ++ any = g(t), (i)where a0, ... , an are constants. Verify that if g(t) is of the formet(b0tm ++ bm),then the substitution y = etu(t) reduces Eq. (i) to the formk0u(n) + k1u(n1) ++ knu = b0tm ++ bm, (ii)where k0, ... , kn are constants. Determine k0 and kn in terms of the as and . Thus theproblem of determining a particular solution of the original equation is reduced to the simplerproblem of determining a particular solution of an equation with constant coefficientsand a polynomial for the nonhomogeneous term.
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