Find the function y1 of t which is the solution of 36y" + 12y' – 3y = 0 with initial conditions Y1 (0) = 1, y (0) = 0. Y1 = Find the function y2 of t which is the solution of 36y" + 12y' - 3y = 0 with initial conditions Y2 (0) = 0, y, (0) = 1. Find the Wronskian W (t) = W(y1, Y2).
Find the function y1 of t which is the solution of 36y" + 12y' – 3y = 0 with initial conditions Y1 (0) = 1, y (0) = 0. Y1 = Find the function y2 of t which is the solution of 36y" + 12y' - 3y = 0 with initial conditions Y2 (0) = 0, y, (0) = 1. Find the Wronskian W (t) = W(y1, Y2).
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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This is in a set of practice problems and I cannot seem to correctly solve it. Could I get some help with it?
![Find the function y1 of t which is the solution of
36y" + 12y' - 3y = 0
with initial conditions y1(0) = 1, y(0) = 0.
Y1 =
Find the function y, of t which is the solution of
36y" + 12y' – 3y = 0
with initial conditions
Y2 (0) = 0, y, (0) = 1.
Y2
Find the Wronskian
W (t)
W (y1, Y2).
W (t) =
Remark: You can find W by direct computation and use Abel's theorem as a check. You should find that W is not zero and so y1 and y2 form a fundamental set of
solutions of
36y" + 12y' – 3y = 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F20ef5b89-bdf5-4ebf-bc1c-34f412b810c9%2F5a40c1ed-6b39-4d5e-b45d-58c8408d0f15%2F21i1dr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Find the function y1 of t which is the solution of
36y" + 12y' - 3y = 0
with initial conditions y1(0) = 1, y(0) = 0.
Y1 =
Find the function y, of t which is the solution of
36y" + 12y' – 3y = 0
with initial conditions
Y2 (0) = 0, y, (0) = 1.
Y2
Find the Wronskian
W (t)
W (y1, Y2).
W (t) =
Remark: You can find W by direct computation and use Abel's theorem as a check. You should find that W is not zero and so y1 and y2 form a fundamental set of
solutions of
36y" + 12y' – 3y = 0.
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