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Suppose that P1(t), p2(t), and p3(t) are continuous on R, and that y1, Y2, and y3 are solutions to the equation y" + P1(t)y" + p2(t)y' + P3(t)y = 0 with Y1 (0) = 1, 4(0) = 2, y(0) = 4, Y2(0) = 1, 2(0) = 0, (0) = 2, Y3(0) = 1, y(0) = 1, y(0) = 3. Are 1 lo and 2lo linearly indenendent on R? Justify vour answer

Suppose that P1(t), p2(t), and p3(t) are continuous on R, and that y1, Y2, and y3 are solutions to the equation y" + P1(t)y" + p2(t)y' + P3(t)y = 0 with Y1 (0) = 1, 4(0) = 2, y(0) = 4, Y2(0) = 1, 2(0) = 0, (0) = 2, Y3(0) = 1, y(0) = 1, y(0) = 3. Are 1 lo and 2lo linearly indenendent on R? Justify vour answer

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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Suppose that p1(t), p2(t), and p3(t) are continuous on R, and that y1,

y2, and y3 are solutions to the equation

y 000 + p1(t)y 00 + p2(t)y0 + p3(t)y = 0

with

y1(0) = 1, y10 (0) = 2, y00

1 (0) = 4,

y2(0) = 1, y

0

2

(0) = 0, y2 00 (0) = 2,

y3(0) = 1, y

0

3

(0) = 1, y3 00 (0) = 3.

Are y1, y2, and y3 linearly independent on R? Justify your answer.

Suppose that P1(t), p2(t), and p3(t) are continuous on R, and that y1, Y2, and y3 are solutions to the equation y" + p1(t)y" + p2(t)y' + P3(t)y = 0 with Y1 (0) = 1, y (0) = 2, y"(0) = 4, Y2(0) = 1, y½(0) = 0, y(0) = 2, Y3 (0) = 1, y(0) = 1, y(0) = 3. Are y1, Y2, and y3 linearly independent on R? Justify your answer.
Transcribed Image Text:Suppose that P1(t), p2(t), and p3(t) are continuous on R, and that y1, Y2, and y3 are solutions to the equation y" + p1(t)y" + p2(t)y' + P3(t)y = 0 with Y1 (0) = 1, y (0) = 2, y"(0) = 4, Y2(0) = 1, y½(0) = 0, y(0) = 2, Y3 (0) = 1, y(0) = 1, y(0) = 3. Are y1, Y2, and y3 linearly independent on R? Justify your answer.
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