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5. Consider the nth-order homogeneous linear differential equation: y(m) +an-1y(n-1) '+….+a2y" +a1y'+ ao¥= 0 where an-1,..., a1, a0 are real constants. For each problem below, several functions belonging to the fundamental set are given. What is the smallest value of n for which the given functions can belong to such a fundamental set? What is the fundamental set? (a) yı(t) = t, y2(t) = e", y3(t) = cos(t) (b) y1 (t) = t² sin(t), y2(t) = e' sin(t)

5. Consider the nth-order homogeneous linear differential equation: y(m) +an-1y(n-1) '+….+a2y" +a1y'+ ao¥= 0 where an-1,..., a1, a0 are real constants. For each problem below, several functions belonging to the fundamental set are given. What is the smallest value of n for which the given functions can belong to such a fundamental set? What is the fundamental set? (a) yı(t) = t, y2(t) = e", y3(t) = cos(t) (b) y1 (t) = t² sin(t), y2(t) = e' sin(t)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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5. Consider the nth-order homogeneous linear differential equation: y(m) +an-1y(n-1) '+….+a2y" +a1y'+ ao¥= 0 where an-1,..., a1, a0 are real constants. For each problem below, several functions belonging to the fundamental set are given. What is the smallest value of n for which the given functions can belong to such a fundamental set? What is the fundamental set? (a) yı(t) = t, y2(t) = e", y3(t) = cos(t) (b) y1(t) = t² sin(t), y2(t) = e' sin(t)
Transcribed Image Text:5. Consider the nth-order homogeneous linear differential equation: y(m) +an-1y(n-1) '+….+a2y" +a1y'+ ao¥= 0 where an-1,..., a1, a0 are real constants. For each problem below, several functions belonging to the fundamental set are given. What is the smallest value of n for which the given functions can belong to such a fundamental set? What is the fundamental set? (a) yı(t) = t, y2(t) = e", y3(t) = cos(t) (b) y1(t) = t² sin(t), y2(t) = e' sin(t)
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