Consider a generic linear homogeneous ODE L [y] = 0, where L is a linear differential...

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Consider a generic linear homogeneous ODE L [y] = 0, where L is a linear differential operator. That is, for any constant c and suitably differentiable functions v and w we have: i L [cv] = c.L[v] ii L[v+w] = L [v] + L [w]. (a) (2 pts) Suppose that functions y₁ and y2 both solve the homogeneous ODE L [y] = 0, where L [y] is ANY linear differential operator (e.g., L [y] =y" + 5y). Show that Yh = C1y1 + C2Y2 also solves the same ODE. Note: skipping steps that one might normally do in one's head makes this calculation look trivial so include ALL steps. Consider a generic linear homogeneous ODE L [y] = 0, where L is a linear differential operator. That is, for any constant c and suitably differentiable functions v and w we have: i L [cv] = c.L[v] ii L[v+w] = L [v] + L [w]. (a) (2 pts) Suppose that functions y₁ and y2 both solve the homogeneous ODE L [y] = 0, where L [y] is ANY linear differential operator (e.g., L [y] =y" + 5y). Show that Yh = C1y1 + C2Y2 also solves the same ODE. Note: skipping steps that one might normally do in one's head makes this calculation look trivial so include ALL steps.

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Given that Ly 0 is a generic linear homogeneous ODE Where L is a linear differential ... View the full answer