1. Prove that if a function f(x) solves a linear homogeneous differential equation with constant coefficients Lif(x) = 0, L1 = D" +an-1D"-' + · . .+ a¡D+ ao and function g(x) solves a linear homogeneous differential equation with constant coef- ficients L29(x) = 0, L2 = D™ + bm-1D™-1 +... + bịD+ bo %3D then f(x)+g(x) also solves some linear homogeneous differential equation with constant coefficients. Hint: consider operator L1L2 and use the fact that L,L2 = L2L1.

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