Consider the (linear inhomogeneous) ordinary differential equation df +2f(x) = x². dx (i.) Find a particular solution of this equation by guessing a solution of the form fo(x) = co + €₁x + €₂x². (ii.) Find the general solution of this equation by solving the associated (linear homogeneous) ordinary differential equation +2f(x) = 0. (iii.) Establish that the solutions are closed under affine combinations (i.e. the solutions form an affine subset of functions).

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