You can apply the two-step subspace test to prove that the set of all solutions (functions) satisfying the linear, homogeneous, ordinary differential equation with constant coefficients, y" + 5y' + 6y = 0, is a subspace of the larger vector space F(-∞, ∞) under the addition and scalar multiplication defined on F(-∞, ∞). Hence, the solution space of y" + 5y' + 6y = 0 has the mathematical structure of a vector space. Another important set of differential equations are linear, non-homogeneous, ordinary differential equations with constant coefficients. An example would be the differential equation y" + 5y' + 6y = 12 sin(x) Does the solution space of y" + 5y' + 6y = 12 sin(x) form a subspace of F(-∞, ∞)? Why or why not? If it is a subspace, prove it. If it is not a subspace explain why not

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