Consider the equation y" - y' - 2y = 0. Assume that y₁ (t) = e-¹ and y₂(t) = e²¹ form a fundamental set of solutions. (b) Let Y3 (1) = - 6e²t Y4 (t) = y₁ (t) + 6y₂ (t) ys(t) = 6y₁ (t) - 6y3(t). Are y3 (t), y4 (t), and ys (t) also solutions of the given differential equation? O No O Impossible to tell O Yes
Consider the equation y" - y' - 2y = 0. Assume that y₁ (t) = e-¹ and y₂(t) = e²¹ form a fundamental set of solutions. (b) Let Y3 (1) = - 6e²t Y4 (t) = y₁ (t) + 6y₂ (t) ys(t) = 6y₁ (t) - 6y3(t). Are y3 (t), y4 (t), and ys (t) also solutions of the given differential equation? O No O Impossible to tell O Yes
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 equation
y" y' - 2y = 0.
Assume that y₁ (t) = e-¹ and y₂(t) = e²t form a fundamental set of solutions.
(b) Let
Y3 (1)
Y4 (t)
= y₁ (t) + 6y₂ (t)
ys(t) = 6y₁ (t) — 6y3(t).
=
- 6e²t
Are y3 (t), y4 (t), and ys (t) also solutions of the given differential equation?
O No
O Impossible to tell
O Yes
![(c) Determine which of the following pairs forms a fundamental set of solutions:
[y₁ (1), 3(1)]; [Y2(1), y3(t)]; [y₁(t), y4(t)]; [y4(t), y5(t)].
○ [y₁ (t), y3 (t)], [y2(t), y3(t)], and [y4 (t), y5 (t)]
O [yi(t), y3(1)] and [y₁ (t), y4 (1)]
O [y4(1), y5 (1)] and [y₂(1), 3(1)]
O [y2(1), y3(1)] and [y₁ (t), y4 (t)], and [y4 (t), Y5(t)]
○ [y₁ (t), y3(t)], [y₁ (t), y4(t)], and [y4 (t), Y5 (1)]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb2ab1611-88a3-4937-813a-fc6050c69325%2F1966692c-02f5-4e7a-8c42-4c4fd85d3fb6%2F7wbrd2n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(c) Determine which of the following pairs forms a fundamental set of solutions:
[y₁ (1), 3(1)]; [Y2(1), y3(t)]; [y₁(t), y4(t)]; [y4(t), y5(t)].
○ [y₁ (t), y3 (t)], [y2(t), y3(t)], and [y4 (t), y5 (t)]
O [yi(t), y3(1)] and [y₁ (t), y4 (1)]
O [y4(1), y5 (1)] and [y₂(1), 3(1)]
O [y2(1), y3(1)] and [y₁ (t), y4 (t)], and [y4 (t), Y5(t)]
○ [y₁ (t), y3(t)], [y₁ (t), y4(t)], and [y4 (t), Y5 (1)]
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