Consider the following. y" + 36y = 0; Y₁ = cos 6t, y₂ = sin 6t Verify that the functions ₁ and ₂ are solutions of the given differential equation. Y₁"(t) = -36 cos 6t Y₂"(t) = -36 sin 6t X X Do they constitute a fundamental set of solutions? Since W(cos 6t, sin 6t) = , the functions Y₁ and Y2 constitute a fundamental set of solutions.
Consider the following. y" + 36y = 0; Y₁ = cos 6t, y₂ = sin 6t Verify that the functions ₁ and ₂ are solutions of the given differential equation. Y₁"(t) = -36 cos 6t Y₂"(t) = -36 sin 6t X X Do they constitute a fundamental set of solutions? Since W(cos 6t, sin 6t) = , the functions Y₁ and Y2 constitute a fundamental set of solutions.
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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Transcribed Image Text:Consider the following.
y" + 36y = 0; Y₁ = cos 6t, y₂ = sin 6t
Verify that the functions Y₁ and y₂ are solutions of the given differential equation.
Y₁"(t) = -36 cos 6t
X
Y₂"(t) = -36 sin 6t
X
Do they constitute a fundamental set of solutions?
Since W(cos 6t, sin 6t) =
the functions y₁ and Y₂
I
constitute a fundamental set of solutions.
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