(a) Construct a linear ­first-order differential equation of the form xy' + 3y = g(x) for which y = x³ 1 c/x³ is its general solution. Give an interval I of defi­nition of this solution.

(b) Give an initial condition y(x₀) = y₀ for the DE found in part (a) so that the solution of the IVP is y = x³ – 1/x³. Repeat if the solution is y = x³ + 2/x³. Give an interval I of de­finition of each of these solutions. Graph the solution curves. Is there an initial-value problem whose solution is defined on (-∞, ∞)?

(c) Is each IVP found in part (b) unique? That is, can there be more than one IVP for which, say, y = x‑ - 1/x³, x in some interval I, is the solution?