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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

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 12CR
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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
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)]
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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