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We consider the initial value problem z'y" – zy' – 8y = 0, y(1) = -2, y'(1) = 3 By looking for solutions in the form y = z' in an Euler-Cauchy problem Az'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: -2.4 (enter your results as a comma separated list ) (3) Find a fundamental set of solutions y1, 2 e^(-2x),e^(4x) (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) = -2, y'(1) = 3 y =

We consider the initial value problem z'y" – zy' – 8y = 0, y(1) = -2, y'(1) = 3 By looking for solutions in the form y = z' in an Euler-Cauchy problem Az'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: -2.4 (enter your results as a comma separated list ) (3) Find a fundamental set of solutions y1, 2 e^(-2x),e^(4x) (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) = -2, y'(1) = 3 y =

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" – zy' – 8y = 0, y(1) = -2, y'(1) = 3 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: -2,4 (enter your results as a comma separated list ) (3) Find a fundamental set of solutions y1, y2 e^(-2x),e^(4x) (enter your results as a comma separated list) (4) Recall that the complementary solution (i.e., the general solution) is ye = C141 + czy2. Find the unique solution satisfying y(1) = -2, y'(1) = 3 y =
Transcribed Image Text:We consider the initial value problem z'y" – zy' – 8y = 0, y(1) = -2, y'(1) = 3 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: -2,4 (enter your results as a comma separated list ) (3) Find a fundamental set of solutions y1, y2 e^(-2x),e^(4x) (enter your results as a comma separated list) (4) Recall that the complementary solution (i.e., the general solution) is ye = C141 + czy2. Find the unique solution satisfying y(1) = -2, y'(1) = 3 y =
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