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13 Nov 2019
I'm struggling mostly with parts c and d. Please explain your work! Thank you!
Taylor series are good for solving differential equations. Consider the differential equation where k > 0 is a constant. (a) Assume that y 9(2) is of the form 0O n-0 Substitute this expression into the differential equation, and in so doing exhibit a system of equations for all the an terms. (b) Assuming that y(0) = 1 and y'(0-0, what does that say about the an terms? (c) Using your answers to both parts (a) and (b), solve for all of the an terms. (d) We also know that solutions to the above differential equation are sines and cosines Using the Taylor series for sine and/or cosine, reconcile your answer to (c) with a solution in terms of these functions.
I'm struggling mostly with parts c and d. Please explain your work! Thank you!
Taylor series are good for solving differential equations. Consider the differential equation where k > 0 is a constant. (a) Assume that y 9(2) is of the form 0O n-0 Substitute this expression into the differential equation, and in so doing exhibit a system of equations for all the an terms. (b) Assuming that y(0) = 1 and y'(0-0, what does that say about the an terms? (c) Using your answers to both parts (a) and (b), solve for all of the an terms. (d) We also know that solutions to the above differential equation are sines and cosines Using the Taylor series for sine and/or cosine, reconcile your answer to (c) with a solution in terms of these functions.
Elin HesselLv2
20 Apr 2019