(a) Determine whether the set of functions f₁(x) = x, f₂(x)=x-1, f3(x)=x+3 is linearly independent on the interval (-∞, ∞). (b) Consider the 2nd order linear differential equation xy" + y = 0. (i) Given that y₁ = Inz solves the equation, use reduction of order to obtain the other solution y/2. (ii) Show that the set of solutions {31, 32} is a fundamental set of solutions. (iii) Hence, or otherwise, write down the general solution of the equation.,

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