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Question: recall that the general homogeneous linear ode of order n...

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Recall that the general homogeneous linear ODE of order n takes the form dy for functions ao()an() with an() 0. Suppose f(x) and g(x) are uppose J(T) and g(T) are solutions to this ODE. Show that: (a) For any constant λ, the function λ/is also a solution to this ODE. (b) The function f +g is also a solution to this ODE. If youve taken a linear algebra course, then you know that this says that the set Sof solutions to the above ODE is a subspace of the vector space of all differentiable functions (defined on an open interval, say, with the usual notions of addition and scalar multiplication)

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