Question: Let L denote a linear differential operator, and suppose that f is a function of the independent variables. Show that the solutions u of the

Let L denote a linear differential operator, and suppose that f

Let L denote a linear differential operator, and suppose that f is a function of the independent variables. Show that the solutions u of the equation Lu=f are of the form u=u1+u2, where the u1 are the solutions of the equation Lu1=0 and u2 is any particular solution of Lu2=f. (This is a principle of superposition of solutions for nonhomogeneous differential equations.)

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