# For the first order linear ode that w satisfies and

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, for the first order linear ODE that w satisfies and then stop. Do not attempt to actually find v. (a) If we have , then , and . Substituting y into (*), and then replacing v using w implies that w must be a solution to after one cleans up the algebra a little. (b) An integrating factor for the homogeneous linear equation that w satisfies is since . _________________________________________________________________ Silly 10 Point Bonus: Suppose that the function , where n is a positive integer, is a solution to the constant coefficient homogeneous linear equation (*) where m > n . What can you say about the coefficients of the ODE, and what can you say about its fundamental set of solutions?? Why??? [Say where your work is, for it won’t fit here.] Appropriate noise may be found on the bottom of Page 2 of 4.
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