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We consider the initial value problem z?y" + 6zy' + 6y = 0, y(1) = 1, y'(1) = -1 By looking for solutions in the form y = z' in an Euler-Cauchy problem Az'y" + Bry' + Cy = 0, we obtain a auxiliary equation Ar2 + (B - A)r +C = 0 which is the analog of the auxiliary equation in the constant coefficient case. (1) For this problem find the auxiliary equation: = 0 (2) Find the roots of the auxiliary equation: (enter your results as a comma separated list) (3) Find a fundamental set of solutions y1, (enter your results as a comma separated list) (4) Recall that the complementary solution (i.e., the general solution) is ye = Cy1 + czyn. Find the unique solution satisfying y(1) = 1, y'(1) = -1

We consider the initial value problem z?y" + 6zy' + 6y = 0, y(1) = 1, y'(1) = -1 By looking for solutions in the form y = z' in an Euler-Cauchy problem Az'y" + Bry' + Cy = 0, we obtain a auxiliary equation Ar2 + (B - A)r +C = 0 which is the analog of the auxiliary equation in the constant coefficient case. (1) For this problem find the auxiliary equation: = 0 (2) Find the roots of the auxiliary equation: (enter your results as a comma separated list) (3) Find a fundamental set of solutions y1, (enter your results as a comma separated list) (4) Recall that the complementary solution (i.e., the general solution) is ye = Cy1 + czyn. Find the unique solution satisfying y(1) = 1, y'(1) = -1

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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We consider the initial value problem z?y" + 6zy' + 6y = 0, y(1) =1, y'(1) = -1 By looking for solutions in the form y = r" in an Euler-Cauchy problem Ar?y" + Bry' + Cy = 0, we obtain a auxiliary equation Ar? + (B – A)r +C= 0 which is the analog of the auxiliary equation in the constant coefficient case. (1) For this problem find the auxiliary equation: = 0 (2) Find the roots of the auxiliary equation: (enter your results as a comma separated list) (3) Find a fundamental set of solutions y1, y2 (enter your results as a comma separated list ) (4) Recall that the complementary solution (i.e., the general solution) is ye = C1y1 + c2y2. Find the unique solution satisfying y(1) = 1, y'(1) = -1 y =
Transcribed Image Text:We consider the initial value problem z?y" + 6zy' + 6y = 0, y(1) =1, y'(1) = -1 By looking for solutions in the form y = r" in an Euler-Cauchy problem Ar?y" + Bry' + Cy = 0, we obtain a auxiliary equation Ar? + (B – A)r +C= 0 which is the analog of the auxiliary equation in the constant coefficient case. (1) For this problem find the auxiliary equation: = 0 (2) Find the roots of the auxiliary equation: (enter your results as a comma separated list) (3) Find a fundamental set of solutions y1, y2 (enter your results as a comma separated list ) (4) Recall that the complementary solution (i.e., the general solution) is ye = C1y1 + c2y2. Find the unique solution satisfying y(1) = 1, y'(1) = -1 y =
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