In this question, you will find a Taylor polynomial approximation of the solution to the differential...

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In this question, you will find a Taylor polynomial approximation of the solution to the differential equation: dy dx = -8y Suppose that we are looking for a solution f(x) = a + ax + 2x + +an" that passes through the point (0, 7). dy The differential equation requires the function y and its derivative Use this fact to find a relationship between a1 and ao: Now write a in terms of a. Then write a2 in terms of ao. Write a3 in terms of a2. Then write a3 in terms of ao. ao Also, two polynomials are equal if and only if they have the same coefficients on dx like power terms. a = .ao= a2 = .ao= a3 = -a0= In this question, you will find a Taylor polynomial approximation of the solution to the differential equation: dy dx = -8y Suppose that we are looking for a solution f(x) = a + ax + 2x + +an" that passes through the point (0, 7). dy The differential equation requires the function y and its derivative Use this fact to find a relationship between a1 and ao: Now write a in terms of a. Then write a2 in terms of ao. Write a3 in terms of a2. Then write a3 in terms of ao. ao Also, two polynomials are equal if and only if they have the same coefficients on dx like power terms. a = .ao= a2 = .ao= a3 = -a0=