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Find the function y₁ of t which is the solution of with initial conditions Y1 = 4y" + 36y' + 32y = 0 y₁ (0) = 1, y₁ (0) = 0. Find the function y2 of t which is the solution of Find the Wronskian 4y" + 36y' + 32y = 0 with initial conditions y2 (0) = 0, y⁄₂ (0) = 1. Y2 = 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 4y" + 36y' + 32y = 0.

Find the function y₁ of t which is the solution of with initial conditions Y1 = 4y" + 36y' + 32y = 0 y₁ (0) = 1, y₁ (0) = 0. Find the function y2 of t which is the solution of Find the Wronskian 4y" + 36y' + 32y = 0 with initial conditions y2 (0) = 0, y⁄₂ (0) = 1. Y2 = 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 4y" + 36y' + 32y = 0.

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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Find the function y₁ of t which is the solution of with initial conditions y₁ (0) = 1, y₁ (0) = 0. Y1 = Find the function y2 of t which is the solution of = 4y" + 36y' + 32y = 0 with initial conditions y2 (0) = 0, y₂ (0) = 1. Y2 Find the Wronskian W(t) = 4y" + 36y' + 32y = 0 W(t) = W (y1, 32). 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 4y" + 36y' + 32y = 0.
Transcribed Image Text:Find the function y₁ of t which is the solution of with initial conditions y₁ (0) = 1, y₁ (0) = 0. Y1 = Find the function y2 of t which is the solution of = 4y" + 36y' + 32y = 0 with initial conditions y2 (0) = 0, y₂ (0) = 1. Y2 Find the Wronskian W(t) = 4y" + 36y' + 32y = 0 W(t) = W (y1, 32). 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 4y" + 36y' + 32y = 0.
Expert Solution
Step 1

Given differential equations is

 4y"+36y'+32=0

It can be written as

y"+9y'+8=0

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